0.019/0.019 NO 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 0.019/0.019 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 Confluence Problem: 0.019/0.019 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.019/0.019 (STRATEGY CONTEXTSENSITIVE 0.019/0.019 (U101 1) 0.019/0.019 (U102 1) 0.019/0.019 (U103 1) 0.019/0.019 (U104 1) 0.019/0.019 (U105 1) 0.019/0.019 (U106 1) 0.019/0.019 (U11 1) 0.019/0.019 (U111 1) 0.019/0.019 (U112 1) 0.019/0.019 (U12 1) 0.019/0.019 (U121 1) 0.019/0.019 (U122 1) 0.019/0.019 (U13 1) 0.019/0.019 (U131 1) 0.019/0.019 (U14 1) 0.019/0.019 (U141 1) 0.019/0.019 (U151 1) 0.019/0.019 (U161 1) 0.019/0.019 (U171 1) 0.019/0.019 (U172 1) 0.019/0.019 (U181 1) 0.019/0.019 (U182 1) 0.019/0.019 (U183 1) 0.019/0.019 (U191 1) 0.019/0.019 (U192 1) 0.019/0.019 (U193 1) 0.019/0.019 (U201 1) 0.019/0.019 (U202 1) 0.019/0.019 (U203 1) 0.019/0.019 (U204 1) 0.019/0.019 (U205 1) 0.019/0.019 (U206 1) 0.019/0.019 (U21 1) 0.019/0.019 (U211 1) 0.019/0.019 (U22 1) 0.019/0.019 (U221 1) 0.019/0.019 (U23 1) 0.019/0.019 (U231 1) 0.019/0.019 (U232 1) 0.019/0.019 (U24 1) 0.019/0.019 (U241 1) 0.019/0.019 (U242 1) 0.019/0.019 (U243 1) 0.019/0.019 (U244 1) 0.019/0.019 (U245 1) 0.019/0.019 (U246 1) 0.019/0.019 (U251 1) 0.019/0.019 (U252 1) 0.019/0.019 (U253 1) 0.019/0.019 (U254 1) 0.019/0.019 (U255 1) 0.019/0.019 (U256 1) 0.019/0.019 (U261 1) 0.019/0.019 (U262 1) 0.019/0.019 (U271 1) 0.019/0.019 (U272 1) 0.019/0.019 (U281 1) 0.019/0.019 (U282 1) 0.019/0.019 (U291 1) 0.019/0.019 (U292 1) 0.019/0.019 (U293 1) 0.019/0.019 (U294 1) 0.019/0.019 (U301 1) 0.019/0.019 (U302 1) 0.019/0.019 (U303 1) 0.019/0.019 (U304 1) 0.019/0.019 (U31 1) 0.019/0.019 (U311 1) 0.019/0.019 (U312 1) 0.019/0.019 (U32 1) 0.019/0.019 (U321 1) 0.019/0.019 (U322 1) 0.019/0.019 (U323 1) 0.019/0.019 (U324 1) 0.019/0.019 (U325 1) 0.019/0.019 (U326 1) 0.019/0.019 (U327 1) 0.019/0.019 (U33 1) 0.019/0.019 (U331 1) 0.019/0.019 (U332 1) 0.019/0.019 (U333 1) 0.019/0.019 (U334 1) 0.019/0.019 (U34 1) 0.019/0.019 (U341 1) 0.019/0.019 (U342 1) 0.019/0.019 (U343 1) 0.019/0.019 (U344 1) 0.019/0.019 (U41 1) 0.019/0.019 (U42 1) 0.019/0.019 (U43 1) 0.019/0.019 (U44 1) 0.019/0.019 (U45 1) 0.019/0.019 (U46 1) 0.019/0.019 (U51 1) 0.019/0.019 (U52 1) 0.019/0.019 (U53 1) 0.019/0.019 (U54 1) 0.019/0.019 (U55 1) 0.019/0.019 (U56 1) 0.019/0.019 (U61 1) 0.019/0.019 (U62 1) 0.019/0.019 (U63 1) 0.019/0.019 (U71 1) 0.019/0.019 (U72 1) 0.019/0.019 (U73 1) 0.019/0.019 (U81 1) 0.019/0.019 (U82 1) 0.019/0.019 (U83 1) 0.019/0.019 (U91 1) 0.019/0.019 (U92 1) 0.019/0.019 (U93 1) 0.019/0.019 (afterNth 1 2) 0.019/0.019 (fst 1) 0.019/0.019 (head 1) 0.019/0.019 (isLNat) 0.019/0.019 (isLNatKind) 0.019/0.019 (isNatural) 0.019/0.019 (isNaturalKind) 0.019/0.019 (isPLNat) 0.019/0.019 (isPLNatKind) 0.019/0.019 (natsFrom 1) 0.019/0.019 (sel 1 2) 0.019/0.019 (snd 1) 0.019/0.019 (splitAt 1 2) 0.019/0.019 (tail 1) 0.019/0.019 (take 1 2) 0.019/0.019 (0) 0.019/0.019 (cons 1) 0.019/0.019 (fSNonEmpty) 0.019/0.019 (nil) 0.019/0.019 (pair 1 2) 0.019/0.019 (s 1) 0.019/0.019 (tt) 0.019/0.019 ) 0.019/0.019 (RULES 0.019/0.019 U101(tt,V1:S,V2:S) -> U102(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U102(tt,V1:S,V2:S) -> U103(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U103(tt,V1:S,V2:S) -> U104(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U104(tt,V1:S,V2:S) -> U105(isNatural(V1:S),V2:S) 0.019/0.019 U105(tt,V2:S) -> U106(isLNat(V2:S)) 0.019/0.019 U106(tt) -> tt 0.019/0.019 U11(tt,N:S,XS:S) -> U12(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U111(tt,V2:S) -> U112(isLNatKind(V2:S)) 0.019/0.019 U112(tt) -> tt 0.019/0.019 U12(tt,N:S,XS:S) -> U13(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U121(tt,V2:S) -> U122(isLNatKind(V2:S)) 0.019/0.019 U122(tt) -> tt 0.019/0.019 U13(tt,N:S,XS:S) -> U14(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U131(tt) -> tt 0.019/0.019 U14(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.019/0.019 U141(tt) -> tt 0.019/0.019 U151(tt) -> tt 0.019/0.019 U161(tt) -> tt 0.019/0.019 U171(tt,V2:S) -> U172(isLNatKind(V2:S)) 0.019/0.019 U172(tt) -> tt 0.019/0.019 U181(tt,V1:S) -> U182(isLNatKind(V1:S),V1:S) 0.019/0.019 U182(tt,V1:S) -> U183(isLNat(V1:S)) 0.019/0.019 U183(tt) -> tt 0.019/0.019 U191(tt,V1:S) -> U192(isNaturalKind(V1:S),V1:S) 0.019/0.019 U192(tt,V1:S) -> U193(isNatural(V1:S)) 0.019/0.019 U193(tt) -> tt 0.019/0.019 U201(tt,V1:S,V2:S) -> U202(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U202(tt,V1:S,V2:S) -> U203(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U203(tt,V1:S,V2:S) -> U204(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U204(tt,V1:S,V2:S) -> U205(isNatural(V1:S),V2:S) 0.019/0.019 U205(tt,V2:S) -> U206(isLNat(V2:S)) 0.019/0.019 U206(tt) -> tt 0.019/0.019 U21(tt,X:S,Y:S) -> U22(isLNatKind(X:S),X:S,Y:S) 0.019/0.019 U211(tt) -> tt 0.019/0.019 U22(tt,X:S,Y:S) -> U23(isLNat(Y:S),X:S,Y:S) 0.019/0.019 U221(tt) -> tt 0.019/0.019 U23(tt,X:S,Y:S) -> U24(isLNatKind(Y:S),X:S) 0.019/0.019 U231(tt,V2:S) -> U232(isLNatKind(V2:S)) 0.019/0.019 U232(tt) -> tt 0.019/0.019 U24(tt,X:S) -> X:S 0.019/0.019 U241(tt,V1:S,V2:S) -> U242(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 U242(tt,V1:S,V2:S) -> U243(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U243(tt,V1:S,V2:S) -> U244(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U244(tt,V1:S,V2:S) -> U245(isLNat(V1:S),V2:S) 0.019/0.019 U245(tt,V2:S) -> U246(isLNat(V2:S)) 0.019/0.019 U246(tt) -> tt 0.019/0.019 U251(tt,V1:S,V2:S) -> U252(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U252(tt,V1:S,V2:S) -> U253(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U253(tt,V1:S,V2:S) -> U254(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U254(tt,V1:S,V2:S) -> U255(isNatural(V1:S),V2:S) 0.019/0.019 U255(tt,V2:S) -> U256(isLNat(V2:S)) 0.019/0.019 U256(tt) -> tt 0.019/0.019 U261(tt,V2:S) -> U262(isLNatKind(V2:S)) 0.019/0.019 U262(tt) -> tt 0.019/0.019 U271(tt,V2:S) -> U272(isLNatKind(V2:S)) 0.019/0.019 U272(tt) -> tt 0.019/0.019 U281(tt,N:S) -> U282(isNaturalKind(N:S),N:S) 0.019/0.019 U282(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.019/0.019 U291(tt,N:S,XS:S) -> U292(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U292(tt,N:S,XS:S) -> U293(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U293(tt,N:S,XS:S) -> U294(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U294(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.019/0.019 U301(tt,X:S,Y:S) -> U302(isLNatKind(X:S),Y:S) 0.019/0.019 U302(tt,Y:S) -> U303(isLNat(Y:S),Y:S) 0.019/0.019 U303(tt,Y:S) -> U304(isLNatKind(Y:S),Y:S) 0.019/0.019 U304(tt,Y:S) -> Y:S 0.019/0.019 U31(tt,N:S,XS:S) -> U32(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U311(tt,XS:S) -> U312(isLNatKind(XS:S),XS:S) 0.019/0.019 U312(tt,XS:S) -> pair(nil,XS:S) 0.019/0.019 U32(tt,N:S,XS:S) -> U33(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U321(tt,N:S,X:S,XS:S) -> U322(isNaturalKind(N:S),N:S,X:S,XS:S) 0.019/0.019 U322(tt,N:S,X:S,XS:S) -> U323(isNatural(X:S),N:S,X:S,XS:S) 0.019/0.019 U323(tt,N:S,X:S,XS:S) -> U324(isNaturalKind(X:S),N:S,X:S,XS:S) 0.019/0.019 U324(tt,N:S,X:S,XS:S) -> U325(isLNat(XS:S),N:S,X:S,XS:S) 0.019/0.019 U325(tt,N:S,X:S,XS:S) -> U326(isLNatKind(XS:S),N:S,X:S,XS:S) 0.019/0.019 U326(tt,N:S,X:S,XS:S) -> U327(splitAt(N:S,XS:S),X:S) 0.019/0.019 U327(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.019/0.019 U33(tt,N:S,XS:S) -> U34(isLNatKind(XS:S),N:S) 0.019/0.019 U331(tt,N:S,XS:S) -> U332(isNaturalKind(N:S),XS:S) 0.019/0.019 U332(tt,XS:S) -> U333(isLNat(XS:S),XS:S) 0.019/0.019 U333(tt,XS:S) -> U334(isLNatKind(XS:S),XS:S) 0.019/0.019 U334(tt,XS:S) -> XS:S 0.019/0.019 U34(tt,N:S) -> N:S 0.019/0.019 U341(tt,N:S,XS:S) -> U342(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U342(tt,N:S,XS:S) -> U343(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U343(tt,N:S,XS:S) -> U344(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U344(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.019/0.019 U41(tt,V1:S,V2:S) -> U42(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U42(tt,V1:S,V2:S) -> U43(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U43(tt,V1:S,V2:S) -> U44(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U44(tt,V1:S,V2:S) -> U45(isNatural(V1:S),V2:S) 0.019/0.019 U45(tt,V2:S) -> U46(isLNat(V2:S)) 0.019/0.019 U46(tt) -> tt 0.019/0.019 U51(tt,V1:S,V2:S) -> U52(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U52(tt,V1:S,V2:S) -> U53(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U53(tt,V1:S,V2:S) -> U54(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U54(tt,V1:S,V2:S) -> U55(isNatural(V1:S),V2:S) 0.019/0.019 U55(tt,V2:S) -> U56(isLNat(V2:S)) 0.019/0.019 U56(tt) -> tt 0.019/0.019 U61(tt,V1:S) -> U62(isPLNatKind(V1:S),V1:S) 0.019/0.019 U62(tt,V1:S) -> U63(isPLNat(V1:S)) 0.019/0.019 U63(tt) -> tt 0.019/0.019 U71(tt,V1:S) -> U72(isNaturalKind(V1:S),V1:S) 0.019/0.019 U72(tt,V1:S) -> U73(isNatural(V1:S)) 0.019/0.019 U73(tt) -> tt 0.019/0.019 U81(tt,V1:S) -> U82(isPLNatKind(V1:S),V1:S) 0.019/0.019 U82(tt,V1:S) -> U83(isPLNat(V1:S)) 0.019/0.019 U83(tt) -> tt 0.019/0.019 U91(tt,V1:S) -> U92(isLNatKind(V1:S),V1:S) 0.019/0.019 U92(tt,V1:S) -> U93(isLNat(V1:S)) 0.019/0.019 U93(tt) -> tt 0.019/0.019 afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(nil) -> tt 0.019/0.019 isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(nil) -> tt 0.019/0.019 isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isNatural(0) -> tt 0.019/0.019 isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 isNaturalKind(0) -> tt 0.019/0.019 isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 ) 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 0.019/0.019 CleanTRS Processor: 0.019/0.019 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 Confluence Problem: 0.019/0.019 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.019/0.019 (STRATEGY CONTEXTSENSITIVE 0.019/0.019 (U101 1) 0.019/0.019 (U102 1) 0.019/0.019 (U103 1) 0.019/0.019 (U104 1) 0.019/0.019 (U105 1) 0.019/0.019 (U106 1) 0.019/0.019 (U11 1) 0.019/0.019 (U111 1) 0.019/0.019 (U112 1) 0.019/0.019 (U12 1) 0.019/0.019 (U121 1) 0.019/0.019 (U122 1) 0.019/0.019 (U13 1) 0.019/0.019 (U131 1) 0.019/0.019 (U14 1) 0.019/0.019 (U141 1) 0.019/0.019 (U151 1) 0.019/0.019 (U161 1) 0.019/0.019 (U171 1) 0.019/0.019 (U172 1) 0.019/0.019 (U181 1) 0.019/0.019 (U182 1) 0.019/0.019 (U183 1) 0.019/0.019 (U191 1) 0.019/0.019 (U192 1) 0.019/0.019 (U193 1) 0.019/0.019 (U201 1) 0.019/0.019 (U202 1) 0.019/0.019 (U203 1) 0.019/0.019 (U204 1) 0.019/0.019 (U205 1) 0.019/0.019 (U206 1) 0.019/0.019 (U21 1) 0.019/0.019 (U211 1) 0.019/0.019 (U22 1) 0.019/0.019 (U221 1) 0.019/0.019 (U23 1) 0.019/0.019 (U231 1) 0.019/0.019 (U232 1) 0.019/0.019 (U24 1) 0.019/0.019 (U241 1) 0.019/0.019 (U242 1) 0.019/0.019 (U243 1) 0.019/0.019 (U244 1) 0.019/0.019 (U245 1) 0.019/0.019 (U246 1) 0.019/0.019 (U251 1) 0.019/0.019 (U252 1) 0.019/0.019 (U253 1) 0.019/0.019 (U254 1) 0.019/0.019 (U255 1) 0.019/0.019 (U256 1) 0.019/0.019 (U261 1) 0.019/0.019 (U262 1) 0.019/0.019 (U271 1) 0.019/0.019 (U272 1) 0.019/0.019 (U281 1) 0.019/0.019 (U282 1) 0.019/0.019 (U291 1) 0.019/0.019 (U292 1) 0.019/0.019 (U293 1) 0.019/0.019 (U294 1) 0.019/0.019 (U301 1) 0.019/0.019 (U302 1) 0.019/0.019 (U303 1) 0.019/0.019 (U304 1) 0.019/0.019 (U31 1) 0.019/0.019 (U311 1) 0.019/0.019 (U312 1) 0.019/0.019 (U32 1) 0.019/0.019 (U321 1) 0.019/0.019 (U322 1) 0.019/0.019 (U323 1) 0.019/0.019 (U324 1) 0.019/0.019 (U325 1) 0.019/0.019 (U326 1) 0.019/0.019 (U327 1) 0.019/0.019 (U33 1) 0.019/0.019 (U331 1) 0.019/0.019 (U332 1) 0.019/0.019 (U333 1) 0.019/0.019 (U334 1) 0.019/0.019 (U34 1) 0.019/0.019 (U341 1) 0.019/0.019 (U342 1) 0.019/0.019 (U343 1) 0.019/0.019 (U344 1) 0.019/0.019 (U41 1) 0.019/0.019 (U42 1) 0.019/0.019 (U43 1) 0.019/0.019 (U44 1) 0.019/0.019 (U45 1) 0.019/0.019 (U46 1) 0.019/0.019 (U51 1) 0.019/0.019 (U52 1) 0.019/0.019 (U53 1) 0.019/0.019 (U54 1) 0.019/0.019 (U55 1) 0.019/0.019 (U56 1) 0.019/0.019 (U61 1) 0.019/0.019 (U62 1) 0.019/0.019 (U63 1) 0.019/0.019 (U71 1) 0.019/0.019 (U72 1) 0.019/0.019 (U73 1) 0.019/0.019 (U81 1) 0.019/0.019 (U82 1) 0.019/0.019 (U83 1) 0.019/0.019 (U91 1) 0.019/0.019 (U92 1) 0.019/0.019 (U93 1) 0.019/0.019 (afterNth 1 2) 0.019/0.019 (fst 1) 0.019/0.019 (head 1) 0.019/0.019 (isLNat) 0.019/0.019 (isLNatKind) 0.019/0.019 (isNatural) 0.019/0.019 (isNaturalKind) 0.019/0.019 (isPLNat) 0.019/0.019 (isPLNatKind) 0.019/0.019 (natsFrom 1) 0.019/0.019 (sel 1 2) 0.019/0.019 (snd 1) 0.019/0.019 (splitAt 1 2) 0.019/0.019 (tail 1) 0.019/0.019 (take 1 2) 0.019/0.019 (0) 0.019/0.019 (cons 1) 0.019/0.019 (fSNonEmpty) 0.019/0.019 (nil) 0.019/0.019 (pair 1 2) 0.019/0.019 (s 1) 0.019/0.019 (tt) 0.019/0.019 ) 0.019/0.019 (RULES 0.019/0.019 U101(tt,V1:S,V2:S) -> U102(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U102(tt,V1:S,V2:S) -> U103(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U103(tt,V1:S,V2:S) -> U104(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U104(tt,V1:S,V2:S) -> U105(isNatural(V1:S),V2:S) 0.019/0.019 U105(tt,V2:S) -> U106(isLNat(V2:S)) 0.019/0.019 U106(tt) -> tt 0.019/0.019 U11(tt,N:S,XS:S) -> U12(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U111(tt,V2:S) -> U112(isLNatKind(V2:S)) 0.019/0.019 U112(tt) -> tt 0.019/0.019 U12(tt,N:S,XS:S) -> U13(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U121(tt,V2:S) -> U122(isLNatKind(V2:S)) 0.019/0.019 U122(tt) -> tt 0.019/0.019 U13(tt,N:S,XS:S) -> U14(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U131(tt) -> tt 0.019/0.019 U14(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.019/0.019 U141(tt) -> tt 0.019/0.019 U151(tt) -> tt 0.019/0.019 U161(tt) -> tt 0.019/0.019 U171(tt,V2:S) -> U172(isLNatKind(V2:S)) 0.019/0.019 U172(tt) -> tt 0.019/0.019 U181(tt,V1:S) -> U182(isLNatKind(V1:S),V1:S) 0.019/0.019 U182(tt,V1:S) -> U183(isLNat(V1:S)) 0.019/0.019 U183(tt) -> tt 0.019/0.019 U191(tt,V1:S) -> U192(isNaturalKind(V1:S),V1:S) 0.019/0.019 U192(tt,V1:S) -> U193(isNatural(V1:S)) 0.019/0.019 U193(tt) -> tt 0.019/0.019 U201(tt,V1:S,V2:S) -> U202(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U202(tt,V1:S,V2:S) -> U203(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U203(tt,V1:S,V2:S) -> U204(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U204(tt,V1:S,V2:S) -> U205(isNatural(V1:S),V2:S) 0.019/0.019 U205(tt,V2:S) -> U206(isLNat(V2:S)) 0.019/0.019 U206(tt) -> tt 0.019/0.019 U21(tt,X:S,Y:S) -> U22(isLNatKind(X:S),X:S,Y:S) 0.019/0.019 U211(tt) -> tt 0.019/0.019 U22(tt,X:S,Y:S) -> U23(isLNat(Y:S),X:S,Y:S) 0.019/0.019 U221(tt) -> tt 0.019/0.019 U23(tt,X:S,Y:S) -> U24(isLNatKind(Y:S),X:S) 0.019/0.019 U231(tt,V2:S) -> U232(isLNatKind(V2:S)) 0.019/0.019 U232(tt) -> tt 0.019/0.019 U24(tt,X:S) -> X:S 0.019/0.019 U241(tt,V1:S,V2:S) -> U242(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 U242(tt,V1:S,V2:S) -> U243(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U243(tt,V1:S,V2:S) -> U244(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U244(tt,V1:S,V2:S) -> U245(isLNat(V1:S),V2:S) 0.019/0.019 U245(tt,V2:S) -> U246(isLNat(V2:S)) 0.019/0.019 U246(tt) -> tt 0.019/0.019 U251(tt,V1:S,V2:S) -> U252(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U252(tt,V1:S,V2:S) -> U253(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U253(tt,V1:S,V2:S) -> U254(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U254(tt,V1:S,V2:S) -> U255(isNatural(V1:S),V2:S) 0.019/0.019 U255(tt,V2:S) -> U256(isLNat(V2:S)) 0.019/0.019 U256(tt) -> tt 0.019/0.019 U261(tt,V2:S) -> U262(isLNatKind(V2:S)) 0.019/0.019 U262(tt) -> tt 0.019/0.019 U271(tt,V2:S) -> U272(isLNatKind(V2:S)) 0.019/0.019 U272(tt) -> tt 0.019/0.019 U281(tt,N:S) -> U282(isNaturalKind(N:S),N:S) 0.019/0.019 U282(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.019/0.019 U291(tt,N:S,XS:S) -> U292(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U292(tt,N:S,XS:S) -> U293(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U293(tt,N:S,XS:S) -> U294(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U294(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.019/0.019 U301(tt,X:S,Y:S) -> U302(isLNatKind(X:S),Y:S) 0.019/0.019 U302(tt,Y:S) -> U303(isLNat(Y:S),Y:S) 0.019/0.019 U303(tt,Y:S) -> U304(isLNatKind(Y:S),Y:S) 0.019/0.019 U304(tt,Y:S) -> Y:S 0.019/0.019 U31(tt,N:S,XS:S) -> U32(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U311(tt,XS:S) -> U312(isLNatKind(XS:S),XS:S) 0.019/0.019 U312(tt,XS:S) -> pair(nil,XS:S) 0.019/0.019 U32(tt,N:S,XS:S) -> U33(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U321(tt,N:S,X:S,XS:S) -> U322(isNaturalKind(N:S),N:S,X:S,XS:S) 0.019/0.019 U322(tt,N:S,X:S,XS:S) -> U323(isNatural(X:S),N:S,X:S,XS:S) 0.019/0.019 U323(tt,N:S,X:S,XS:S) -> U324(isNaturalKind(X:S),N:S,X:S,XS:S) 0.019/0.019 U324(tt,N:S,X:S,XS:S) -> U325(isLNat(XS:S),N:S,X:S,XS:S) 0.019/0.019 U325(tt,N:S,X:S,XS:S) -> U326(isLNatKind(XS:S),N:S,X:S,XS:S) 0.019/0.019 U326(tt,N:S,X:S,XS:S) -> U327(splitAt(N:S,XS:S),X:S) 0.019/0.019 U327(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.019/0.019 U33(tt,N:S,XS:S) -> U34(isLNatKind(XS:S),N:S) 0.019/0.019 U331(tt,N:S,XS:S) -> U332(isNaturalKind(N:S),XS:S) 0.019/0.019 U332(tt,XS:S) -> U333(isLNat(XS:S),XS:S) 0.019/0.019 U333(tt,XS:S) -> U334(isLNatKind(XS:S),XS:S) 0.019/0.019 U334(tt,XS:S) -> XS:S 0.019/0.019 U34(tt,N:S) -> N:S 0.019/0.019 U341(tt,N:S,XS:S) -> U342(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U342(tt,N:S,XS:S) -> U343(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U343(tt,N:S,XS:S) -> U344(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U344(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.019/0.019 U41(tt,V1:S,V2:S) -> U42(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U42(tt,V1:S,V2:S) -> U43(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U43(tt,V1:S,V2:S) -> U44(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U44(tt,V1:S,V2:S) -> U45(isNatural(V1:S),V2:S) 0.019/0.019 U45(tt,V2:S) -> U46(isLNat(V2:S)) 0.019/0.019 U46(tt) -> tt 0.019/0.019 U51(tt,V1:S,V2:S) -> U52(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U52(tt,V1:S,V2:S) -> U53(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U53(tt,V1:S,V2:S) -> U54(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U54(tt,V1:S,V2:S) -> U55(isNatural(V1:S),V2:S) 0.019/0.019 U55(tt,V2:S) -> U56(isLNat(V2:S)) 0.019/0.019 U56(tt) -> tt 0.019/0.019 U61(tt,V1:S) -> U62(isPLNatKind(V1:S),V1:S) 0.019/0.019 U62(tt,V1:S) -> U63(isPLNat(V1:S)) 0.019/0.019 U63(tt) -> tt 0.019/0.019 U71(tt,V1:S) -> U72(isNaturalKind(V1:S),V1:S) 0.019/0.019 U72(tt,V1:S) -> U73(isNatural(V1:S)) 0.019/0.019 U73(tt) -> tt 0.019/0.019 U81(tt,V1:S) -> U82(isPLNatKind(V1:S),V1:S) 0.019/0.019 U82(tt,V1:S) -> U83(isPLNat(V1:S)) 0.019/0.019 U83(tt) -> tt 0.019/0.019 U91(tt,V1:S) -> U92(isLNatKind(V1:S),V1:S) 0.019/0.019 U92(tt,V1:S) -> U93(isLNat(V1:S)) 0.019/0.019 U93(tt) -> tt 0.019/0.019 afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(nil) -> tt 0.019/0.019 isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(nil) -> tt 0.019/0.019 isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isNatural(0) -> tt 0.019/0.019 isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 isNaturalKind(0) -> tt 0.019/0.019 isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 ) 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 0.019/0.019 Modular Confluence Combinations Decomposition Processor: 0.019/0.019 It is a CTRS -> No modular confluence 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 CS-TRS Processor: 0.019/0.019 R is a CS-TRS 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 Confluence Problem: 0.019/0.019 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.019/0.019 (STRATEGY CONTEXTSENSITIVE 0.019/0.019 (U101 1) 0.019/0.019 (U102 1) 0.019/0.019 (U103 1) 0.019/0.019 (U104 1) 0.019/0.019 (U105 1) 0.019/0.019 (U106 1) 0.019/0.019 (U11 1) 0.019/0.019 (U111 1) 0.019/0.019 (U112 1) 0.019/0.019 (U12 1) 0.019/0.019 (U121 1) 0.019/0.019 (U122 1) 0.019/0.019 (U13 1) 0.019/0.019 (U131 1) 0.019/0.019 (U14 1) 0.019/0.019 (U141 1) 0.019/0.019 (U151 1) 0.019/0.019 (U161 1) 0.019/0.019 (U171 1) 0.019/0.019 (U172 1) 0.019/0.019 (U181 1) 0.019/0.019 (U182 1) 0.019/0.019 (U183 1) 0.019/0.019 (U191 1) 0.019/0.019 (U192 1) 0.019/0.019 (U193 1) 0.019/0.019 (U201 1) 0.019/0.019 (U202 1) 0.019/0.019 (U203 1) 0.019/0.019 (U204 1) 0.019/0.019 (U205 1) 0.019/0.019 (U206 1) 0.019/0.019 (U21 1) 0.019/0.019 (U211 1) 0.019/0.019 (U22 1) 0.019/0.019 (U221 1) 0.019/0.019 (U23 1) 0.019/0.019 (U231 1) 0.019/0.019 (U232 1) 0.019/0.019 (U24 1) 0.019/0.019 (U241 1) 0.019/0.019 (U242 1) 0.019/0.019 (U243 1) 0.019/0.019 (U244 1) 0.019/0.019 (U245 1) 0.019/0.019 (U246 1) 0.019/0.019 (U251 1) 0.019/0.019 (U252 1) 0.019/0.019 (U253 1) 0.019/0.019 (U254 1) 0.019/0.019 (U255 1) 0.019/0.019 (U256 1) 0.019/0.019 (U261 1) 0.019/0.019 (U262 1) 0.019/0.019 (U271 1) 0.019/0.019 (U272 1) 0.019/0.019 (U281 1) 0.019/0.019 (U282 1) 0.019/0.019 (U291 1) 0.019/0.019 (U292 1) 0.019/0.019 (U293 1) 0.019/0.019 (U294 1) 0.019/0.019 (U301 1) 0.019/0.019 (U302 1) 0.019/0.019 (U303 1) 0.019/0.019 (U304 1) 0.019/0.019 (U31 1) 0.019/0.019 (U311 1) 0.019/0.019 (U312 1) 0.019/0.019 (U32 1) 0.019/0.019 (U321 1) 0.019/0.019 (U322 1) 0.019/0.019 (U323 1) 0.019/0.019 (U324 1) 0.019/0.019 (U325 1) 0.019/0.019 (U326 1) 0.019/0.019 (U327 1) 0.019/0.019 (U33 1) 0.019/0.019 (U331 1) 0.019/0.019 (U332 1) 0.019/0.019 (U333 1) 0.019/0.019 (U334 1) 0.019/0.019 (U34 1) 0.019/0.019 (U341 1) 0.019/0.019 (U342 1) 0.019/0.019 (U343 1) 0.019/0.019 (U344 1) 0.019/0.019 (U41 1) 0.019/0.019 (U42 1) 0.019/0.019 (U43 1) 0.019/0.019 (U44 1) 0.019/0.019 (U45 1) 0.019/0.019 (U46 1) 0.019/0.019 (U51 1) 0.019/0.019 (U52 1) 0.019/0.019 (U53 1) 0.019/0.019 (U54 1) 0.019/0.019 (U55 1) 0.019/0.019 (U56 1) 0.019/0.019 (U61 1) 0.019/0.019 (U62 1) 0.019/0.019 (U63 1) 0.019/0.019 (U71 1) 0.019/0.019 (U72 1) 0.019/0.019 (U73 1) 0.019/0.019 (U81 1) 0.019/0.019 (U82 1) 0.019/0.019 (U83 1) 0.019/0.019 (U91 1) 0.019/0.019 (U92 1) 0.019/0.019 (U93 1) 0.019/0.019 (afterNth 1 2) 0.019/0.019 (fst 1) 0.019/0.019 (head 1) 0.019/0.019 (isLNat) 0.019/0.019 (isLNatKind) 0.019/0.019 (isNatural) 0.019/0.019 (isNaturalKind) 0.019/0.019 (isPLNat) 0.019/0.019 (isPLNatKind) 0.019/0.019 (natsFrom 1) 0.019/0.019 (sel 1 2) 0.019/0.019 (snd 1) 0.019/0.019 (splitAt 1 2) 0.019/0.019 (tail 1) 0.019/0.019 (take 1 2) 0.019/0.019 (0) 0.019/0.019 (cons 1) 0.019/0.019 (fSNonEmpty) 0.019/0.019 (nil) 0.019/0.019 (pair 1 2) 0.019/0.019 (s 1) 0.019/0.019 (tt) 0.019/0.019 ) 0.019/0.019 (RULES 0.019/0.019 U101(tt,V1:S,V2:S) -> U102(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U102(tt,V1:S,V2:S) -> U103(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U103(tt,V1:S,V2:S) -> U104(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U104(tt,V1:S,V2:S) -> U105(isNatural(V1:S),V2:S) 0.019/0.019 U105(tt,V2:S) -> U106(isLNat(V2:S)) 0.019/0.019 U106(tt) -> tt 0.019/0.019 U11(tt,N:S,XS:S) -> U12(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U111(tt,V2:S) -> U112(isLNatKind(V2:S)) 0.019/0.019 U112(tt) -> tt 0.019/0.019 U12(tt,N:S,XS:S) -> U13(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U121(tt,V2:S) -> U122(isLNatKind(V2:S)) 0.019/0.019 U122(tt) -> tt 0.019/0.019 U13(tt,N:S,XS:S) -> U14(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U131(tt) -> tt 0.019/0.019 U14(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.019/0.019 U141(tt) -> tt 0.019/0.019 U151(tt) -> tt 0.019/0.019 U161(tt) -> tt 0.019/0.019 U171(tt,V2:S) -> U172(isLNatKind(V2:S)) 0.019/0.019 U172(tt) -> tt 0.019/0.019 U181(tt,V1:S) -> U182(isLNatKind(V1:S),V1:S) 0.019/0.019 U182(tt,V1:S) -> U183(isLNat(V1:S)) 0.019/0.019 U183(tt) -> tt 0.019/0.019 U191(tt,V1:S) -> U192(isNaturalKind(V1:S),V1:S) 0.019/0.019 U192(tt,V1:S) -> U193(isNatural(V1:S)) 0.019/0.019 U193(tt) -> tt 0.019/0.019 U201(tt,V1:S,V2:S) -> U202(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U202(tt,V1:S,V2:S) -> U203(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U203(tt,V1:S,V2:S) -> U204(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U204(tt,V1:S,V2:S) -> U205(isNatural(V1:S),V2:S) 0.019/0.019 U205(tt,V2:S) -> U206(isLNat(V2:S)) 0.019/0.019 U206(tt) -> tt 0.019/0.019 U21(tt,X:S,Y:S) -> U22(isLNatKind(X:S),X:S,Y:S) 0.019/0.019 U211(tt) -> tt 0.019/0.019 U22(tt,X:S,Y:S) -> U23(isLNat(Y:S),X:S,Y:S) 0.019/0.019 U221(tt) -> tt 0.019/0.019 U23(tt,X:S,Y:S) -> U24(isLNatKind(Y:S),X:S) 0.019/0.019 U231(tt,V2:S) -> U232(isLNatKind(V2:S)) 0.019/0.019 U232(tt) -> tt 0.019/0.019 U24(tt,X:S) -> X:S 0.019/0.019 U241(tt,V1:S,V2:S) -> U242(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 U242(tt,V1:S,V2:S) -> U243(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U243(tt,V1:S,V2:S) -> U244(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U244(tt,V1:S,V2:S) -> U245(isLNat(V1:S),V2:S) 0.019/0.019 U245(tt,V2:S) -> U246(isLNat(V2:S)) 0.019/0.019 U246(tt) -> tt 0.019/0.019 U251(tt,V1:S,V2:S) -> U252(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U252(tt,V1:S,V2:S) -> U253(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U253(tt,V1:S,V2:S) -> U254(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U254(tt,V1:S,V2:S) -> U255(isNatural(V1:S),V2:S) 0.019/0.019 U255(tt,V2:S) -> U256(isLNat(V2:S)) 0.019/0.019 U256(tt) -> tt 0.019/0.019 U261(tt,V2:S) -> U262(isLNatKind(V2:S)) 0.019/0.019 U262(tt) -> tt 0.019/0.019 U271(tt,V2:S) -> U272(isLNatKind(V2:S)) 0.019/0.019 U272(tt) -> tt 0.019/0.019 U281(tt,N:S) -> U282(isNaturalKind(N:S),N:S) 0.019/0.019 U282(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.019/0.019 U291(tt,N:S,XS:S) -> U292(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U292(tt,N:S,XS:S) -> U293(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U293(tt,N:S,XS:S) -> U294(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U294(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.019/0.019 U301(tt,X:S,Y:S) -> U302(isLNatKind(X:S),Y:S) 0.019/0.019 U302(tt,Y:S) -> U303(isLNat(Y:S),Y:S) 0.019/0.019 U303(tt,Y:S) -> U304(isLNatKind(Y:S),Y:S) 0.019/0.019 U304(tt,Y:S) -> Y:S 0.019/0.019 U31(tt,N:S,XS:S) -> U32(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U311(tt,XS:S) -> U312(isLNatKind(XS:S),XS:S) 0.019/0.019 U312(tt,XS:S) -> pair(nil,XS:S) 0.019/0.019 U32(tt,N:S,XS:S) -> U33(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U321(tt,N:S,X:S,XS:S) -> U322(isNaturalKind(N:S),N:S,X:S,XS:S) 0.019/0.019 U322(tt,N:S,X:S,XS:S) -> U323(isNatural(X:S),N:S,X:S,XS:S) 0.019/0.019 U323(tt,N:S,X:S,XS:S) -> U324(isNaturalKind(X:S),N:S,X:S,XS:S) 0.019/0.019 U324(tt,N:S,X:S,XS:S) -> U325(isLNat(XS:S),N:S,X:S,XS:S) 0.019/0.019 U325(tt,N:S,X:S,XS:S) -> U326(isLNatKind(XS:S),N:S,X:S,XS:S) 0.019/0.019 U326(tt,N:S,X:S,XS:S) -> U327(splitAt(N:S,XS:S),X:S) 0.019/0.019 U327(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.019/0.019 U33(tt,N:S,XS:S) -> U34(isLNatKind(XS:S),N:S) 0.019/0.019 U331(tt,N:S,XS:S) -> U332(isNaturalKind(N:S),XS:S) 0.019/0.019 U332(tt,XS:S) -> U333(isLNat(XS:S),XS:S) 0.019/0.019 U333(tt,XS:S) -> U334(isLNatKind(XS:S),XS:S) 0.019/0.019 U334(tt,XS:S) -> XS:S 0.019/0.019 U34(tt,N:S) -> N:S 0.019/0.019 U341(tt,N:S,XS:S) -> U342(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U342(tt,N:S,XS:S) -> U343(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U343(tt,N:S,XS:S) -> U344(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U344(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.019/0.019 U41(tt,V1:S,V2:S) -> U42(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U42(tt,V1:S,V2:S) -> U43(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U43(tt,V1:S,V2:S) -> U44(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U44(tt,V1:S,V2:S) -> U45(isNatural(V1:S),V2:S) 0.019/0.019 U45(tt,V2:S) -> U46(isLNat(V2:S)) 0.019/0.019 U46(tt) -> tt 0.019/0.019 U51(tt,V1:S,V2:S) -> U52(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U52(tt,V1:S,V2:S) -> U53(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U53(tt,V1:S,V2:S) -> U54(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U54(tt,V1:S,V2:S) -> U55(isNatural(V1:S),V2:S) 0.019/0.019 U55(tt,V2:S) -> U56(isLNat(V2:S)) 0.019/0.019 U56(tt) -> tt 0.019/0.019 U61(tt,V1:S) -> U62(isPLNatKind(V1:S),V1:S) 0.019/0.019 U62(tt,V1:S) -> U63(isPLNat(V1:S)) 0.019/0.019 U63(tt) -> tt 0.019/0.019 U71(tt,V1:S) -> U72(isNaturalKind(V1:S),V1:S) 0.019/0.019 U72(tt,V1:S) -> U73(isNatural(V1:S)) 0.019/0.019 U73(tt) -> tt 0.019/0.019 U81(tt,V1:S) -> U82(isPLNatKind(V1:S),V1:S) 0.019/0.019 U82(tt,V1:S) -> U83(isPLNat(V1:S)) 0.019/0.019 U83(tt) -> tt 0.019/0.019 U91(tt,V1:S) -> U92(isLNatKind(V1:S),V1:S) 0.019/0.019 U92(tt,V1:S) -> U93(isLNat(V1:S)) 0.019/0.019 U93(tt) -> tt 0.019/0.019 afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(nil) -> tt 0.019/0.019 isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(nil) -> tt 0.019/0.019 isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isNatural(0) -> tt 0.019/0.019 isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 isNaturalKind(0) -> tt 0.019/0.019 isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 ) 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 0.019/0.019 Extended u-Critical Pairs NonLHRV Processor [JLAMP21]: 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 77 (l' :-> r') => U327(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U327(pair(YS:S,ZS:S),X:S)} 0.019/0.019 s => pair(cons(x109:S,U327(pair(YS:S,ZS:S),X:S)),x111:S) 0.019/0.019 t => U327(pair(pair(cons(X:S,YS:S),ZS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 78 (l' :-> r') => U33(tt,N:S,XS:S) -> U34(isLNatKind(XS:S),N:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U33(tt,N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U33(tt,N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U34(isLNatKind(XS:S),N:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 79 (l' :-> r') => U331(tt,N:S,XS:S) -> U332(isNaturalKind(N:S),XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U331(tt,N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U331(tt,N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U332(isNaturalKind(N:S),XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 80 (l' :-> r') => U332(tt,XS:S) -> U333(isLNat(XS:S),XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U332(tt,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U332(tt,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U333(isLNat(XS:S),XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 81 (l' :-> r') => U333(tt,XS:S) -> U334(isLNatKind(XS:S),XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U333(tt,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U333(tt,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U334(isLNatKind(XS:S),XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 82 (l' :-> r') => U334(tt,XS:S) -> XS:S 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U334(tt,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U334(tt,XS:S)),x111:S) 0.019/0.019 t => U327(pair(XS:S,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 83 (l' :-> r') => U34(tt,N:S) -> N:S 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U34(tt,N:S)} 0.019/0.019 s => pair(cons(x109:S,U34(tt,N:S)),x111:S) 0.019/0.019 t => U327(pair(N:S,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 84 (l' :-> r') => U341(tt,N:S,XS:S) -> U342(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U341(tt,N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U341(tt,N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U342(isNaturalKind(N:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 85 (l' :-> r') => U342(tt,N:S,XS:S) -> U343(isLNat(XS:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U342(tt,N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U342(tt,N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U343(isLNat(XS:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 86 (l' :-> r') => U343(tt,N:S,XS:S) -> U344(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U343(tt,N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U343(tt,N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U344(isLNatKind(XS:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 87 (l' :-> r') => U344(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U344(tt,N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,U344(tt,N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(fst(splitAt(N:S,XS:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 88 (l' :-> r') => U41(tt,V1:S,V2:S) -> U42(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U41(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U41(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U42(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 89 (l' :-> r') => U42(tt,V1:S,V2:S) -> U43(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U42(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U42(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U43(isLNatKind(V2:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 90 (l' :-> r') => U43(tt,V1:S,V2:S) -> U44(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U43(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U43(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U44(isLNatKind(V2:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 91 (l' :-> r') => U44(tt,V1:S,V2:S) -> U45(isNatural(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U44(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U44(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U45(isNatural(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 92 (l' :-> r') => U45(tt,V2:S) -> U46(isLNat(V2:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U45(tt,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U45(tt,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U46(isLNat(V2:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 93 (l' :-> r') => U46(tt) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U46(tt)} 0.019/0.019 s => pair(cons(x109:S,U46(tt)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 94 (l' :-> r') => U51(tt,V1:S,V2:S) -> U52(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U51(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U51(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U52(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 95 (l' :-> r') => U52(tt,V1:S,V2:S) -> U53(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U52(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U52(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U53(isLNatKind(V2:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 96 (l' :-> r') => U53(tt,V1:S,V2:S) -> U54(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U53(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U53(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U54(isLNatKind(V2:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 97 (l' :-> r') => U54(tt,V1:S,V2:S) -> U55(isNatural(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U54(tt,V1:S,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U54(tt,V1:S,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U55(isNatural(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 98 (l' :-> r') => U55(tt,V2:S) -> U56(isLNat(V2:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U55(tt,V2:S)} 0.019/0.019 s => pair(cons(x109:S,U55(tt,V2:S)),x111:S) 0.019/0.019 t => U327(pair(U56(isLNat(V2:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 99 (l' :-> r') => U56(tt) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U56(tt)} 0.019/0.019 s => pair(cons(x109:S,U56(tt)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 100 (l' :-> r') => U61(tt,V1:S) -> U62(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U61(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U61(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U62(isPLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 101 (l' :-> r') => U62(tt,V1:S) -> U63(isPLNat(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U62(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U62(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U63(isPLNat(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 102 (l' :-> r') => U63(tt) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U63(tt)} 0.019/0.019 s => pair(cons(x109:S,U63(tt)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 103 (l' :-> r') => U71(tt,V1:S) -> U72(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U71(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U71(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U72(isNaturalKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 104 (l' :-> r') => U72(tt,V1:S) -> U73(isNatural(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U72(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U72(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U73(isNatural(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 105 (l' :-> r') => U73(tt) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U73(tt)} 0.019/0.019 s => pair(cons(x109:S,U73(tt)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 106 (l' :-> r') => U81(tt,V1:S) -> U82(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U81(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U81(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U82(isPLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 107 (l' :-> r') => U82(tt,V1:S) -> U83(isPLNat(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U82(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U82(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U83(isPLNat(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 108 (l' :-> r') => U83(tt) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U83(tt)} 0.019/0.019 s => pair(cons(x109:S,U83(tt)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 109 (l' :-> r') => U91(tt,V1:S) -> U92(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U91(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U91(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U92(isLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 110 (l' :-> r') => U92(tt,V1:S) -> U93(isLNat(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U92(tt,V1:S)} 0.019/0.019 s => pair(cons(x109:S,U92(tt,V1:S)),x111:S) 0.019/0.019 t => U327(pair(U93(isLNat(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 111 (l' :-> r') => U93(tt) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> U93(tt)} 0.019/0.019 s => pair(cons(x109:S,U93(tt)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 112 (l' :-> r') => afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> afterNth(N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,afterNth(N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U11(isNatural(N:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 113 (l' :-> r') => fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> fst(pair(X:S,Y:S))} 0.019/0.019 s => pair(cons(x109:S,fst(pair(X:S,Y:S))),x111:S) 0.019/0.019 t => U327(pair(U21(isLNat(X:S),X:S,Y:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 114 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> head(cons(N:S,XS:S))} 0.019/0.019 s => pair(cons(x109:S,head(cons(N:S,XS:S))),x111:S) 0.019/0.019 t => U327(pair(U31(isNatural(N:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 115 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(afterNth(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(afterNth(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U41(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 116 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(fst(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(fst(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U61(isPLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 117 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(natsFrom(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(natsFrom(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U71(isNaturalKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 118 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(snd(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(snd(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U81(isPLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 119 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(tail(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(tail(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U91(isLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 120 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(take(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(take(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U101(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 121 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(cons(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isLNat(cons(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U51(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 122 (l' :-> r') => isLNat(nil) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNat(nil)} 0.019/0.019 s => pair(cons(x109:S,isLNat(nil)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 123 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(afterNth(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U111(isNaturalKind(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 124 (l' :-> r') => isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(fst(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(fst(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U131(isPLNatKind(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 125 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(natsFrom(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(natsFrom(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U141(isNaturalKind(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 126 (l' :-> r') => isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(snd(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(snd(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U151(isPLNatKind(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 127 (l' :-> r') => isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(tail(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(tail(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U161(isLNatKind(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 128 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(take(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(take(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U171(isNaturalKind(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 129 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(cons(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(cons(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U121(isNaturalKind(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 130 (l' :-> r') => isLNatKind(nil) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isLNatKind(nil)} 0.019/0.019 s => pair(cons(x109:S,isLNatKind(nil)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 131 (l' :-> r') => isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNatural(head(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isNatural(head(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U181(isLNatKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 132 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNatural(sel(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isNatural(sel(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U201(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 133 (l' :-> r') => isNatural(0) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNatural(0)} 0.019/0.019 s => pair(cons(x109:S,isNatural(0)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 134 (l' :-> r') => isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNatural(s(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isNatural(s(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U191(isNaturalKind(V1:S),V1:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 135 (l' :-> r') => isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNaturalKind(head(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isNaturalKind(head(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U211(isLNatKind(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 136 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNaturalKind(sel(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isNaturalKind(sel(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U231(isNaturalKind(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 137 (l' :-> r') => isNaturalKind(0) -> tt 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNaturalKind(0)} 0.019/0.019 s => pair(cons(x109:S,isNaturalKind(0)),x111:S) 0.019/0.019 t => U327(pair(tt,x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 138 (l' :-> r') => isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isNaturalKind(s(V1:S))} 0.019/0.019 s => pair(cons(x109:S,isNaturalKind(s(V1:S))),x111:S) 0.019/0.019 t => U327(pair(U221(isNaturalKind(V1:S)),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 139 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isPLNat(splitAt(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isPLNat(splitAt(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U251(isNaturalKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 140 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isPLNat(pair(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isPLNat(pair(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U241(isLNatKind(V1:S),V1:S,V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 141 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isPLNatKind(splitAt(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U271(isNaturalKind(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 142 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> isPLNatKind(pair(V1:S,V2:S))} 0.019/0.019 s => pair(cons(x109:S,isPLNatKind(pair(V1:S,V2:S))),x111:S) 0.019/0.019 t => U327(pair(U261(isLNatKind(V1:S),V2:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 143 (l' :-> r') => natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> natsFrom(N:S)} 0.019/0.019 s => pair(cons(x109:S,natsFrom(N:S)),x111:S) 0.019/0.019 t => U327(pair(U281(isNatural(N:S),N:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 144 (l' :-> r') => sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> sel(N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,sel(N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U291(isNatural(N:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => pair(cons(x109:S,snd(pair(X:S,Y:S))),x111:S) 0.019/0.019 t => U327(pair(U301(isLNat(X:S),X:S,Y:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> splitAt(0,XS:S)} 0.019/0.019 s => pair(cons(x109:S,splitAt(0,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U311(isLNat(XS:S),XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => pair(cons(x109:S,splitAt(s(N:S),cons(X:S,XS:S))),x111:S) 0.019/0.019 t => U327(pair(U321(isNatural(N:S),N:S,X:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => pair(cons(x109:S,tail(cons(N:S,XS:S))),x111:S) 0.019/0.019 t => U327(pair(U331(isNatural(N:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x110:S 0.019/0.019 Pos x110:S in l => [1,1] 0.019/0.019 Sigma => {x110:S -> take(N:S,XS:S)} 0.019/0.019 s => pair(cons(x109:S,take(N:S,XS:S)),x111:S) 0.019/0.019 t => U327(pair(U341(isNatural(N:S),N:S,XS:S),x111:S),x109:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 112 (l' :-> r') => afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> afterNth(N:S,XS:S)} 0.019/0.019 s => U11(isNatural(afterNth(N:S,XS:S)),afterNth(N:S,XS:S),x155:S) 0.019/0.019 t => afterNth(U11(isNatural(N:S),N:S,XS:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 113 (l' :-> r') => fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> fst(pair(X:S,Y:S))} 0.019/0.019 s => U11(isNatural(fst(pair(X:S,Y:S))),fst(pair(X:S,Y:S)),x155:S) 0.019/0.019 t => afterNth(U21(isLNat(X:S),X:S,Y:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 114 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> head(cons(N:S,XS:S))} 0.019/0.019 s => U11(isNatural(head(cons(N:S,XS:S))),head(cons(N:S,XS:S)),x155:S) 0.019/0.019 t => afterNth(U31(isNatural(N:S),N:S,XS:S),x155:S) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 115 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(afterNth(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isLNat(afterNth(V1:S,V2:S))),isLNat(afterNth(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U41(isNaturalKind(V1:S),V1:S,V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 116 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(fst(V1:S))} 0.019/0.019 s => U11(isNatural(isLNat(fst(V1:S))),isLNat(fst(V1:S)),x155:S) 0.019/0.019 t => afterNth(U61(isPLNatKind(V1:S),V1:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 117 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(natsFrom(V1:S))} 0.019/0.019 s => U11(isNatural(isLNat(natsFrom(V1:S))),isLNat(natsFrom(V1:S)),x155:S) 0.019/0.019 t => afterNth(U71(isNaturalKind(V1:S),V1:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 118 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(snd(V1:S))} 0.019/0.019 s => U11(isNatural(isLNat(snd(V1:S))),isLNat(snd(V1:S)),x155:S) 0.019/0.019 t => afterNth(U81(isPLNatKind(V1:S),V1:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 119 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(tail(V1:S))} 0.019/0.019 s => U11(isNatural(isLNat(tail(V1:S))),isLNat(tail(V1:S)),x155:S) 0.019/0.019 t => afterNth(U91(isLNatKind(V1:S),V1:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 120 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(take(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isLNat(take(V1:S,V2:S))),isLNat(take(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U101(isNaturalKind(V1:S),V1:S,V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 121 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(cons(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isLNat(cons(V1:S,V2:S))),isLNat(cons(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U51(isNaturalKind(V1:S),V1:S,V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 122 (l' :-> r') => isLNat(nil) -> tt 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNat(nil)} 0.019/0.019 s => U11(isNatural(isLNat(nil)),isLNat(nil),x155:S) 0.019/0.019 t => afterNth(tt,x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 123 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(afterNth(V1:S,V2:S))),isLNatKind(afterNth(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U111(isNaturalKind(V1:S),V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 124 (l' :-> r') => isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(fst(V1:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(fst(V1:S))),isLNatKind(fst(V1:S)),x155:S) 0.019/0.019 t => afterNth(U131(isPLNatKind(V1:S)),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 125 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(natsFrom(V1:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(natsFrom(V1:S))),isLNatKind(natsFrom(V1:S)),x155:S) 0.019/0.019 t => afterNth(U141(isNaturalKind(V1:S)),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 126 (l' :-> r') => isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(snd(V1:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(snd(V1:S))),isLNatKind(snd(V1:S)),x155:S) 0.019/0.019 t => afterNth(U151(isPLNatKind(V1:S)),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 127 (l' :-> r') => isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(tail(V1:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(tail(V1:S))),isLNatKind(tail(V1:S)),x155:S) 0.019/0.019 t => afterNth(U161(isLNatKind(V1:S)),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 128 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(take(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(take(V1:S,V2:S))),isLNatKind(take(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U171(isNaturalKind(V1:S),V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 129 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(cons(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isLNatKind(cons(V1:S,V2:S))),isLNatKind(cons(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U121(isNaturalKind(V1:S),V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 130 (l' :-> r') => isLNatKind(nil) -> tt 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isLNatKind(nil)} 0.019/0.019 s => U11(isNatural(isLNatKind(nil)),isLNatKind(nil),x155:S) 0.019/0.019 t => afterNth(tt,x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 131 (l' :-> r') => isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNatural(head(V1:S))} 0.019/0.019 s => U11(isNatural(isNatural(head(V1:S))),isNatural(head(V1:S)),x155:S) 0.019/0.019 t => afterNth(U181(isLNatKind(V1:S),V1:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 132 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNatural(sel(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isNatural(sel(V1:S,V2:S))),isNatural(sel(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U201(isNaturalKind(V1:S),V1:S,V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 133 (l' :-> r') => isNatural(0) -> tt 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNatural(0)} 0.019/0.019 s => U11(isNatural(isNatural(0)),isNatural(0),x155:S) 0.019/0.019 t => afterNth(tt,x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 134 (l' :-> r') => isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNatural(s(V1:S))} 0.019/0.019 s => U11(isNatural(isNatural(s(V1:S))),isNatural(s(V1:S)),x155:S) 0.019/0.019 t => afterNth(U191(isNaturalKind(V1:S),V1:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 135 (l' :-> r') => isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNaturalKind(head(V1:S))} 0.019/0.019 s => U11(isNatural(isNaturalKind(head(V1:S))),isNaturalKind(head(V1:S)),x155:S) 0.019/0.019 t => afterNth(U211(isLNatKind(V1:S)),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 136 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNaturalKind(sel(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isNaturalKind(sel(V1:S,V2:S))),isNaturalKind(sel(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U231(isNaturalKind(V1:S),V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 137 (l' :-> r') => isNaturalKind(0) -> tt 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNaturalKind(0)} 0.019/0.019 s => U11(isNatural(isNaturalKind(0)),isNaturalKind(0),x155:S) 0.019/0.019 t => afterNth(tt,x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 138 (l' :-> r') => isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isNaturalKind(s(V1:S))} 0.019/0.019 s => U11(isNatural(isNaturalKind(s(V1:S))),isNaturalKind(s(V1:S)),x155:S) 0.019/0.019 t => afterNth(U221(isNaturalKind(V1:S)),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 139 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isPLNat(splitAt(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isPLNat(splitAt(V1:S,V2:S))),isPLNat(splitAt(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U251(isNaturalKind(V1:S),V1:S,V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 140 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isPLNat(pair(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isPLNat(pair(V1:S,V2:S))),isPLNat(pair(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U241(isLNatKind(V1:S),V1:S,V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 141 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isPLNatKind(splitAt(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U271(isNaturalKind(V1:S),V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 142 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> isPLNatKind(pair(V1:S,V2:S))} 0.019/0.019 s => U11(isNatural(isPLNatKind(pair(V1:S,V2:S))),isPLNatKind(pair(V1:S,V2:S)),x155:S) 0.019/0.019 t => afterNth(U261(isLNatKind(V1:S),V2:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 143 (l' :-> r') => natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> natsFrom(N:S)} 0.019/0.019 s => U11(isNatural(natsFrom(N:S)),natsFrom(N:S),x155:S) 0.019/0.019 t => afterNth(U281(isNatural(N:S),N:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 144 (l' :-> r') => sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> sel(N:S,XS:S)} 0.019/0.019 s => U11(isNatural(sel(N:S,XS:S)),sel(N:S,XS:S),x155:S) 0.019/0.019 t => afterNth(U291(isNatural(N:S),N:S,XS:S),x155:S) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => U11(isNatural(snd(pair(X:S,Y:S))),snd(pair(X:S,Y:S)),x155:S) 0.019/0.019 t => afterNth(U301(isLNat(X:S),X:S,Y:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> splitAt(0,XS:S)} 0.019/0.019 s => U11(isNatural(splitAt(0,XS:S)),splitAt(0,XS:S),x155:S) 0.019/0.019 t => afterNth(U311(isLNat(XS:S),XS:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U11(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S)),x155:S) 0.019/0.019 t => afterNth(U321(isNatural(N:S),N:S,X:S,XS:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U11(isNatural(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x155:S) 0.019/0.019 t => afterNth(U331(isNatural(N:S),N:S,XS:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x154:S 0.019/0.019 Pos x154:S in l => [1] 0.019/0.019 Sigma => {x154:S -> take(N:S,XS:S)} 0.019/0.019 s => U11(isNatural(take(N:S,XS:S)),take(N:S,XS:S),x155:S) 0.019/0.019 t => afterNth(U341(isNatural(N:S),N:S,XS:S),x155:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 113 (l' :-> r') => fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> fst(pair(X:S,Y:S))} 0.019/0.019 s => U21(isLNat(fst(pair(X:S,Y:S))),fst(pair(X:S,Y:S)),x157:S) 0.019/0.019 t => fst(pair(U21(isLNat(X:S),X:S,Y:S),x157:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 114 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> head(cons(N:S,XS:S))} 0.019/0.019 s => U21(isLNat(head(cons(N:S,XS:S))),head(cons(N:S,XS:S)),x157:S) 0.019/0.019 t => fst(pair(U31(isNatural(N:S),N:S,XS:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 115 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(afterNth(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isLNat(afterNth(V1:S,V2:S))),isLNat(afterNth(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U41(isNaturalKind(V1:S),V1:S,V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 116 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(fst(V1:S))} 0.019/0.019 s => U21(isLNat(isLNat(fst(V1:S))),isLNat(fst(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U61(isPLNatKind(V1:S),V1:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 117 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(natsFrom(V1:S))} 0.019/0.019 s => U21(isLNat(isLNat(natsFrom(V1:S))),isLNat(natsFrom(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U71(isNaturalKind(V1:S),V1:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 118 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(snd(V1:S))} 0.019/0.019 s => U21(isLNat(isLNat(snd(V1:S))),isLNat(snd(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U81(isPLNatKind(V1:S),V1:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 119 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(tail(V1:S))} 0.019/0.019 s => U21(isLNat(isLNat(tail(V1:S))),isLNat(tail(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U91(isLNatKind(V1:S),V1:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 120 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(take(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isLNat(take(V1:S,V2:S))),isLNat(take(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U101(isNaturalKind(V1:S),V1:S,V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 121 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(cons(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isLNat(cons(V1:S,V2:S))),isLNat(cons(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U51(isNaturalKind(V1:S),V1:S,V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 122 (l' :-> r') => isLNat(nil) -> tt 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNat(nil)} 0.019/0.019 s => U21(isLNat(isLNat(nil)),isLNat(nil),x157:S) 0.019/0.019 t => fst(pair(tt,x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 123 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(afterNth(V1:S,V2:S))),isLNatKind(afterNth(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U111(isNaturalKind(V1:S),V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 124 (l' :-> r') => isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(fst(V1:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(fst(V1:S))),isLNatKind(fst(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U131(isPLNatKind(V1:S)),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 125 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(natsFrom(V1:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(natsFrom(V1:S))),isLNatKind(natsFrom(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U141(isNaturalKind(V1:S)),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 126 (l' :-> r') => isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(snd(V1:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(snd(V1:S))),isLNatKind(snd(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U151(isPLNatKind(V1:S)),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 127 (l' :-> r') => isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(tail(V1:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(tail(V1:S))),isLNatKind(tail(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U161(isLNatKind(V1:S)),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 128 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(take(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(take(V1:S,V2:S))),isLNatKind(take(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U171(isNaturalKind(V1:S),V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 129 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(cons(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isLNatKind(cons(V1:S,V2:S))),isLNatKind(cons(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U121(isNaturalKind(V1:S),V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 130 (l' :-> r') => isLNatKind(nil) -> tt 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isLNatKind(nil)} 0.019/0.019 s => U21(isLNat(isLNatKind(nil)),isLNatKind(nil),x157:S) 0.019/0.019 t => fst(pair(tt,x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 131 (l' :-> r') => isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNatural(head(V1:S))} 0.019/0.019 s => U21(isLNat(isNatural(head(V1:S))),isNatural(head(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U181(isLNatKind(V1:S),V1:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 132 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNatural(sel(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isNatural(sel(V1:S,V2:S))),isNatural(sel(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U201(isNaturalKind(V1:S),V1:S,V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 133 (l' :-> r') => isNatural(0) -> tt 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNatural(0)} 0.019/0.019 s => U21(isLNat(isNatural(0)),isNatural(0),x157:S) 0.019/0.019 t => fst(pair(tt,x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 134 (l' :-> r') => isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNatural(s(V1:S))} 0.019/0.019 s => U21(isLNat(isNatural(s(V1:S))),isNatural(s(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U191(isNaturalKind(V1:S),V1:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 135 (l' :-> r') => isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNaturalKind(head(V1:S))} 0.019/0.019 s => U21(isLNat(isNaturalKind(head(V1:S))),isNaturalKind(head(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U211(isLNatKind(V1:S)),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 136 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNaturalKind(sel(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isNaturalKind(sel(V1:S,V2:S))),isNaturalKind(sel(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U231(isNaturalKind(V1:S),V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 137 (l' :-> r') => isNaturalKind(0) -> tt 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNaturalKind(0)} 0.019/0.019 s => U21(isLNat(isNaturalKind(0)),isNaturalKind(0),x157:S) 0.019/0.019 t => fst(pair(tt,x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 138 (l' :-> r') => isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isNaturalKind(s(V1:S))} 0.019/0.019 s => U21(isLNat(isNaturalKind(s(V1:S))),isNaturalKind(s(V1:S)),x157:S) 0.019/0.019 t => fst(pair(U221(isNaturalKind(V1:S)),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 139 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isPLNat(splitAt(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isPLNat(splitAt(V1:S,V2:S))),isPLNat(splitAt(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U251(isNaturalKind(V1:S),V1:S,V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 140 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isPLNat(pair(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isPLNat(pair(V1:S,V2:S))),isPLNat(pair(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U241(isLNatKind(V1:S),V1:S,V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 141 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isPLNatKind(splitAt(V1:S,V2:S))),isPLNatKind(splitAt(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U271(isNaturalKind(V1:S),V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 142 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> isPLNatKind(pair(V1:S,V2:S))} 0.019/0.019 s => U21(isLNat(isPLNatKind(pair(V1:S,V2:S))),isPLNatKind(pair(V1:S,V2:S)),x157:S) 0.019/0.019 t => fst(pair(U261(isLNatKind(V1:S),V2:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 143 (l' :-> r') => natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> natsFrom(N:S)} 0.019/0.019 s => U21(isLNat(natsFrom(N:S)),natsFrom(N:S),x157:S) 0.019/0.019 t => fst(pair(U281(isNatural(N:S),N:S),x157:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 144 (l' :-> r') => sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> sel(N:S,XS:S)} 0.019/0.019 s => U21(isLNat(sel(N:S,XS:S)),sel(N:S,XS:S),x157:S) 0.019/0.019 t => fst(pair(U291(isNatural(N:S),N:S,XS:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => U21(isLNat(snd(pair(X:S,Y:S))),snd(pair(X:S,Y:S)),x157:S) 0.019/0.019 t => fst(pair(U301(isLNat(X:S),X:S,Y:S),x157:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> splitAt(0,XS:S)} 0.019/0.019 s => U21(isLNat(splitAt(0,XS:S)),splitAt(0,XS:S),x157:S) 0.019/0.019 t => fst(pair(U311(isLNat(XS:S),XS:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U21(isLNat(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S)),x157:S) 0.019/0.019 t => fst(pair(U321(isNatural(N:S),N:S,X:S,XS:S),x157:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U21(isLNat(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x157:S) 0.019/0.019 t => fst(pair(U331(isNatural(N:S),N:S,XS:S),x157:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x156:S 0.019/0.019 Pos x156:S in l => [1,1] 0.019/0.019 Sigma => {x156:S -> take(N:S,XS:S)} 0.019/0.019 s => U21(isLNat(take(N:S,XS:S)),take(N:S,XS:S),x157:S) 0.019/0.019 t => fst(pair(U341(isNatural(N:S),N:S,XS:S),x157:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 114 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> head(cons(N:S,XS:S))} 0.019/0.019 s => U31(isNatural(head(cons(N:S,XS:S))),head(cons(N:S,XS:S)),x159:S) 0.019/0.019 t => head(cons(U31(isNatural(N:S),N:S,XS:S),x159:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 115 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(afterNth(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isLNat(afterNth(V1:S,V2:S))),isLNat(afterNth(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U41(isNaturalKind(V1:S),V1:S,V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 116 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(fst(V1:S))} 0.019/0.019 s => U31(isNatural(isLNat(fst(V1:S))),isLNat(fst(V1:S)),x159:S) 0.019/0.019 t => head(cons(U61(isPLNatKind(V1:S),V1:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 117 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(natsFrom(V1:S))} 0.019/0.019 s => U31(isNatural(isLNat(natsFrom(V1:S))),isLNat(natsFrom(V1:S)),x159:S) 0.019/0.019 t => head(cons(U71(isNaturalKind(V1:S),V1:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 118 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(snd(V1:S))} 0.019/0.019 s => U31(isNatural(isLNat(snd(V1:S))),isLNat(snd(V1:S)),x159:S) 0.019/0.019 t => head(cons(U81(isPLNatKind(V1:S),V1:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 119 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(tail(V1:S))} 0.019/0.019 s => U31(isNatural(isLNat(tail(V1:S))),isLNat(tail(V1:S)),x159:S) 0.019/0.019 t => head(cons(U91(isLNatKind(V1:S),V1:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 120 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(take(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isLNat(take(V1:S,V2:S))),isLNat(take(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U101(isNaturalKind(V1:S),V1:S,V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 121 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(cons(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isLNat(cons(V1:S,V2:S))),isLNat(cons(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U51(isNaturalKind(V1:S),V1:S,V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 122 (l' :-> r') => isLNat(nil) -> tt 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNat(nil)} 0.019/0.019 s => U31(isNatural(isLNat(nil)),isLNat(nil),x159:S) 0.019/0.019 t => head(cons(tt,x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 123 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(afterNth(V1:S,V2:S))),isLNatKind(afterNth(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U111(isNaturalKind(V1:S),V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 124 (l' :-> r') => isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(fst(V1:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(fst(V1:S))),isLNatKind(fst(V1:S)),x159:S) 0.019/0.019 t => head(cons(U131(isPLNatKind(V1:S)),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 125 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(natsFrom(V1:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(natsFrom(V1:S))),isLNatKind(natsFrom(V1:S)),x159:S) 0.019/0.019 t => head(cons(U141(isNaturalKind(V1:S)),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 126 (l' :-> r') => isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(snd(V1:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(snd(V1:S))),isLNatKind(snd(V1:S)),x159:S) 0.019/0.019 t => head(cons(U151(isPLNatKind(V1:S)),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 127 (l' :-> r') => isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(tail(V1:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(tail(V1:S))),isLNatKind(tail(V1:S)),x159:S) 0.019/0.019 t => head(cons(U161(isLNatKind(V1:S)),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 128 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(take(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(take(V1:S,V2:S))),isLNatKind(take(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U171(isNaturalKind(V1:S),V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 129 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(cons(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isLNatKind(cons(V1:S,V2:S))),isLNatKind(cons(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U121(isNaturalKind(V1:S),V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 130 (l' :-> r') => isLNatKind(nil) -> tt 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isLNatKind(nil)} 0.019/0.019 s => U31(isNatural(isLNatKind(nil)),isLNatKind(nil),x159:S) 0.019/0.019 t => head(cons(tt,x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 131 (l' :-> r') => isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNatural(head(V1:S))} 0.019/0.019 s => U31(isNatural(isNatural(head(V1:S))),isNatural(head(V1:S)),x159:S) 0.019/0.019 t => head(cons(U181(isLNatKind(V1:S),V1:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 132 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNatural(sel(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isNatural(sel(V1:S,V2:S))),isNatural(sel(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U201(isNaturalKind(V1:S),V1:S,V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 133 (l' :-> r') => isNatural(0) -> tt 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNatural(0)} 0.019/0.019 s => U31(isNatural(isNatural(0)),isNatural(0),x159:S) 0.019/0.019 t => head(cons(tt,x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 134 (l' :-> r') => isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNatural(s(V1:S))} 0.019/0.019 s => U31(isNatural(isNatural(s(V1:S))),isNatural(s(V1:S)),x159:S) 0.019/0.019 t => head(cons(U191(isNaturalKind(V1:S),V1:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 135 (l' :-> r') => isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNaturalKind(head(V1:S))} 0.019/0.019 s => U31(isNatural(isNaturalKind(head(V1:S))),isNaturalKind(head(V1:S)),x159:S) 0.019/0.019 t => head(cons(U211(isLNatKind(V1:S)),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 136 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNaturalKind(sel(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isNaturalKind(sel(V1:S,V2:S))),isNaturalKind(sel(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U231(isNaturalKind(V1:S),V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 137 (l' :-> r') => isNaturalKind(0) -> tt 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNaturalKind(0)} 0.019/0.019 s => U31(isNatural(isNaturalKind(0)),isNaturalKind(0),x159:S) 0.019/0.019 t => head(cons(tt,x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 138 (l' :-> r') => isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isNaturalKind(s(V1:S))} 0.019/0.019 s => U31(isNatural(isNaturalKind(s(V1:S))),isNaturalKind(s(V1:S)),x159:S) 0.019/0.019 t => head(cons(U221(isNaturalKind(V1:S)),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 139 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isPLNat(splitAt(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isPLNat(splitAt(V1:S,V2:S))),isPLNat(splitAt(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U251(isNaturalKind(V1:S),V1:S,V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 140 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isPLNat(pair(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isPLNat(pair(V1:S,V2:S))),isPLNat(pair(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U241(isLNatKind(V1:S),V1:S,V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 141 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isPLNatKind(splitAt(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U271(isNaturalKind(V1:S),V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 142 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> isPLNatKind(pair(V1:S,V2:S))} 0.019/0.019 s => U31(isNatural(isPLNatKind(pair(V1:S,V2:S))),isPLNatKind(pair(V1:S,V2:S)),x159:S) 0.019/0.019 t => head(cons(U261(isLNatKind(V1:S),V2:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 143 (l' :-> r') => natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> natsFrom(N:S)} 0.019/0.019 s => U31(isNatural(natsFrom(N:S)),natsFrom(N:S),x159:S) 0.019/0.019 t => head(cons(U281(isNatural(N:S),N:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 144 (l' :-> r') => sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> sel(N:S,XS:S)} 0.019/0.019 s => U31(isNatural(sel(N:S,XS:S)),sel(N:S,XS:S),x159:S) 0.019/0.019 t => head(cons(U291(isNatural(N:S),N:S,XS:S),x159:S)) 0.019/0.019 NW => 0 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => U31(isNatural(snd(pair(X:S,Y:S))),snd(pair(X:S,Y:S)),x159:S) 0.019/0.019 t => head(cons(U301(isLNat(X:S),X:S,Y:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> splitAt(0,XS:S)} 0.019/0.019 s => U31(isNatural(splitAt(0,XS:S)),splitAt(0,XS:S),x159:S) 0.019/0.019 t => head(cons(U311(isLNat(XS:S),XS:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U31(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S)),x159:S) 0.019/0.019 t => head(cons(U321(isNatural(N:S),N:S,X:S,XS:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U31(isNatural(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x159:S) 0.019/0.019 t => head(cons(U331(isNatural(N:S),N:S,XS:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x158:S 0.019/0.019 Pos x158:S in l => [1,1] 0.019/0.019 Sigma => {x158:S -> take(N:S,XS:S)} 0.019/0.019 s => U31(isNatural(take(N:S,XS:S)),take(N:S,XS:S),x159:S) 0.019/0.019 t => head(cons(U341(isNatural(N:S),N:S,XS:S),x159:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 143 (l' :-> r') => natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> natsFrom(N:S)} 0.019/0.019 s => U281(isNatural(natsFrom(N:S)),natsFrom(N:S)) 0.019/0.019 t => natsFrom(U281(isNatural(N:S),N:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 144 (l' :-> r') => sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> sel(N:S,XS:S)} 0.019/0.019 s => U281(isNatural(sel(N:S,XS:S)),sel(N:S,XS:S)) 0.019/0.019 t => natsFrom(U291(isNatural(N:S),N:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => U281(isNatural(snd(pair(X:S,Y:S))),snd(pair(X:S,Y:S))) 0.019/0.019 t => natsFrom(U301(isLNat(X:S),X:S,Y:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> splitAt(0,XS:S)} 0.019/0.019 s => U281(isNatural(splitAt(0,XS:S)),splitAt(0,XS:S)) 0.019/0.019 t => natsFrom(U311(isLNat(XS:S),XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U281(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S))) 0.019/0.019 t => natsFrom(U321(isNatural(N:S),N:S,X:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U281(isNatural(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S))) 0.019/0.019 t => natsFrom(U331(isNatural(N:S),N:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x196:S 0.019/0.019 Pos x196:S in l => [1] 0.019/0.019 Sigma => {x196:S -> take(N:S,XS:S)} 0.019/0.019 s => U281(isNatural(take(N:S,XS:S)),take(N:S,XS:S)) 0.019/0.019 t => natsFrom(U341(isNatural(N:S),N:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S) 0.019/0.019 Rule 144 (l' :-> r') => sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x197:S 0.019/0.019 Pos x197:S in l => [1] 0.019/0.019 Sigma => {x197:S -> sel(N:S,XS:S)} 0.019/0.019 s => U291(isNatural(sel(N:S,XS:S)),sel(N:S,XS:S),x198:S) 0.019/0.019 t => sel(U291(isNatural(N:S),N:S,XS:S),x198:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x197:S 0.019/0.019 Pos x197:S in l => [1] 0.019/0.019 Sigma => {x197:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => U291(isNatural(snd(pair(X:S,Y:S))),snd(pair(X:S,Y:S)),x198:S) 0.019/0.019 t => sel(U301(isLNat(X:S),X:S,Y:S),x198:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x197:S 0.019/0.019 Pos x197:S in l => [1] 0.019/0.019 Sigma => {x197:S -> splitAt(0,XS:S)} 0.019/0.019 s => U291(isNatural(splitAt(0,XS:S)),splitAt(0,XS:S),x198:S) 0.019/0.019 t => sel(U311(isLNat(XS:S),XS:S),x198:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x197:S 0.019/0.019 Pos x197:S in l => [1] 0.019/0.019 Sigma => {x197:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U291(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S)),x198:S) 0.019/0.019 t => sel(U321(isNatural(N:S),N:S,X:S,XS:S),x198:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x197:S 0.019/0.019 Pos x197:S in l => [1] 0.019/0.019 Sigma => {x197:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U291(isNatural(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x198:S) 0.019/0.019 t => sel(U331(isNatural(N:S),N:S,XS:S),x198:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x197:S 0.019/0.019 Pos x197:S in l => [1] 0.019/0.019 Sigma => {x197:S -> take(N:S,XS:S)} 0.019/0.019 s => U291(isNatural(take(N:S,XS:S)),take(N:S,XS:S),x198:S) 0.019/0.019 t => sel(U341(isNatural(N:S),N:S,XS:S),x198:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => snd(pair(x199:S,x200:S)) -> U301(isLNat(x199:S),x199:S,x200:S) 0.019/0.019 Rule 145 (l' :-> r') => snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 Var => x199:S 0.019/0.019 Pos x199:S in l => [1,1] 0.019/0.019 Sigma => {x199:S -> snd(pair(X:S,Y:S))} 0.019/0.019 s => U301(isLNat(snd(pair(X:S,Y:S))),snd(pair(X:S,Y:S)),x200:S) 0.019/0.019 t => snd(pair(U301(isLNat(X:S),X:S,Y:S),x200:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => snd(pair(x199:S,x200:S)) -> U301(isLNat(x199:S),x199:S,x200:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x199:S 0.019/0.019 Pos x199:S in l => [1,1] 0.019/0.019 Sigma => {x199:S -> splitAt(0,XS:S)} 0.019/0.019 s => U301(isLNat(splitAt(0,XS:S)),splitAt(0,XS:S),x200:S) 0.019/0.019 t => snd(pair(U311(isLNat(XS:S),XS:S),x200:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => snd(pair(x199:S,x200:S)) -> U301(isLNat(x199:S),x199:S,x200:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x199:S 0.019/0.019 Pos x199:S in l => [1,1] 0.019/0.019 Sigma => {x199:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U301(isLNat(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S)),x200:S) 0.019/0.019 t => snd(pair(U321(isNatural(N:S),N:S,X:S,XS:S),x200:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => snd(pair(x199:S,x200:S)) -> U301(isLNat(x199:S),x199:S,x200:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x199:S 0.019/0.019 Pos x199:S in l => [1,1] 0.019/0.019 Sigma => {x199:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U301(isLNat(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x200:S) 0.019/0.019 t => snd(pair(U331(isNatural(N:S),N:S,XS:S),x200:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => snd(pair(x199:S,x200:S)) -> U301(isLNat(x199:S),x199:S,x200:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x199:S 0.019/0.019 Pos x199:S in l => [1,1] 0.019/0.019 Sigma => {x199:S -> take(N:S,XS:S)} 0.019/0.019 s => U301(isLNat(take(N:S,XS:S)),take(N:S,XS:S),x200:S) 0.019/0.019 t => snd(pair(U341(isNatural(N:S),N:S,XS:S),x200:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(0,x201:S) -> U311(isLNat(x201:S),x201:S) 0.019/0.019 Rule 146 (l' :-> r') => splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 Var => x201:S 0.019/0.019 Pos x201:S in l => [2] 0.019/0.019 Sigma => {x201:S -> splitAt(0,XS:S)} 0.019/0.019 s => U311(isLNat(splitAt(0,XS:S)),splitAt(0,XS:S)) 0.019/0.019 t => splitAt(0,U311(isLNat(XS:S),XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(0,x201:S) -> U311(isLNat(x201:S),x201:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x201:S 0.019/0.019 Pos x201:S in l => [2] 0.019/0.019 Sigma => {x201:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U311(isLNat(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S))) 0.019/0.019 t => splitAt(0,U321(isNatural(N:S),N:S,X:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(0,x201:S) -> U311(isLNat(x201:S),x201:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x201:S 0.019/0.019 Pos x201:S in l => [2] 0.019/0.019 Sigma => {x201:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U311(isLNat(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S))) 0.019/0.019 t => splitAt(0,U331(isNatural(N:S),N:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(0,x201:S) -> U311(isLNat(x201:S),x201:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x201:S 0.019/0.019 Pos x201:S in l => [2] 0.019/0.019 Sigma => {x201:S -> take(N:S,XS:S)} 0.019/0.019 s => U311(isLNat(take(N:S,XS:S)),take(N:S,XS:S)) 0.019/0.019 t => splitAt(0,U341(isNatural(N:S),N:S,XS:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(s(x202:S),cons(x203:S,x204:S)) -> U321(isNatural(x202:S),x202:S,x203:S,x204:S) 0.019/0.019 Rule 147 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 Var => x202:S 0.019/0.019 Pos x202:S in l => [1,1] 0.019/0.019 Sigma => {x202:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.019/0.019 s => U321(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),splitAt(s(N:S),cons(X:S,XS:S)),x203:S,x204:S) 0.019/0.019 t => splitAt(s(U321(isNatural(N:S),N:S,X:S,XS:S)),cons(x203:S,x204:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(s(x202:S),cons(x203:S,x204:S)) -> U321(isNatural(x202:S),x202:S,x203:S,x204:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x202:S 0.019/0.019 Pos x202:S in l => [1,1] 0.019/0.019 Sigma => {x202:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U321(isNatural(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x203:S,x204:S) 0.019/0.019 t => splitAt(s(U331(isNatural(N:S),N:S,XS:S)),cons(x203:S,x204:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => splitAt(s(x202:S),cons(x203:S,x204:S)) -> U321(isNatural(x202:S),x202:S,x203:S,x204:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x202:S 0.019/0.019 Pos x202:S in l => [1,1] 0.019/0.019 Sigma => {x202:S -> take(N:S,XS:S)} 0.019/0.019 s => U321(isNatural(take(N:S,XS:S)),take(N:S,XS:S),x203:S,x204:S) 0.019/0.019 t => splitAt(s(U341(isNatural(N:S),N:S,XS:S)),cons(x203:S,x204:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => tail(cons(x205:S,x206:S)) -> U331(isNatural(x205:S),x205:S,x206:S) 0.019/0.019 Rule 148 (l' :-> r') => tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x205:S 0.019/0.019 Pos x205:S in l => [1,1] 0.019/0.019 Sigma => {x205:S -> tail(cons(N:S,XS:S))} 0.019/0.019 s => U331(isNatural(tail(cons(N:S,XS:S))),tail(cons(N:S,XS:S)),x206:S) 0.019/0.019 t => tail(cons(U331(isNatural(N:S),N:S,XS:S),x206:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => tail(cons(x205:S,x206:S)) -> U331(isNatural(x205:S),x205:S,x206:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x205:S 0.019/0.019 Pos x205:S in l => [1,1] 0.019/0.019 Sigma => {x205:S -> take(N:S,XS:S)} 0.019/0.019 s => U331(isNatural(take(N:S,XS:S)),take(N:S,XS:S),x206:S) 0.019/0.019 t => tail(cons(U341(isNatural(N:S),N:S,XS:S),x206:S)) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 ->Extended u-Critical Pair: 0.019/0.019 Rule 1 (l :-> r) => take(x207:S,x208:S) -> U341(isNatural(x207:S),x207:S,x208:S) 0.019/0.019 Rule 149 (l' :-> r') => take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 Var => x207:S 0.019/0.019 Pos x207:S in l => [1] 0.019/0.019 Sigma => {x207:S -> take(N:S,XS:S)} 0.019/0.019 s => U341(isNatural(take(N:S,XS:S)),take(N:S,XS:S),x208:S) 0.019/0.019 t => take(U341(isNatural(N:S),N:S,XS:S),x208:S) 0.019/0.019 NW => 1 0.019/0.019 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 Confluence Problem: 0.019/0.019 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.019/0.019 (STRATEGY CONTEXTSENSITIVE 0.019/0.019 (U101 1) 0.019/0.019 (U102 1) 0.019/0.019 (U103 1) 0.019/0.019 (U104 1) 0.019/0.019 (U105 1) 0.019/0.019 (U106 1) 0.019/0.019 (U11 1) 0.019/0.019 (U111 1) 0.019/0.019 (U112 1) 0.019/0.019 (U12 1) 0.019/0.019 (U121 1) 0.019/0.019 (U122 1) 0.019/0.019 (U13 1) 0.019/0.019 (U131 1) 0.019/0.019 (U14 1) 0.019/0.019 (U141 1) 0.019/0.019 (U151 1) 0.019/0.019 (U161 1) 0.019/0.019 (U171 1) 0.019/0.019 (U172 1) 0.019/0.019 (U181 1) 0.019/0.019 (U182 1) 0.019/0.019 (U183 1) 0.019/0.019 (U191 1) 0.019/0.019 (U192 1) 0.019/0.019 (U193 1) 0.019/0.019 (U201 1) 0.019/0.019 (U202 1) 0.019/0.019 (U203 1) 0.019/0.019 (U204 1) 0.019/0.019 (U205 1) 0.019/0.019 (U206 1) 0.019/0.019 (U21 1) 0.019/0.019 (U211 1) 0.019/0.019 (U22 1) 0.019/0.019 (U221 1) 0.019/0.019 (U23 1) 0.019/0.019 (U231 1) 0.019/0.019 (U232 1) 0.019/0.019 (U24 1) 0.019/0.019 (U241 1) 0.019/0.019 (U242 1) 0.019/0.019 (U243 1) 0.019/0.019 (U244 1) 0.019/0.019 (U245 1) 0.019/0.019 (U246 1) 0.019/0.019 (U251 1) 0.019/0.019 (U252 1) 0.019/0.019 (U253 1) 0.019/0.019 (U254 1) 0.019/0.019 (U255 1) 0.019/0.019 (U256 1) 0.019/0.019 (U261 1) 0.019/0.019 (U262 1) 0.019/0.019 (U271 1) 0.019/0.019 (U272 1) 0.019/0.019 (U281 1) 0.019/0.019 (U282 1) 0.019/0.019 (U291 1) 0.019/0.019 (U292 1) 0.019/0.019 (U293 1) 0.019/0.019 (U294 1) 0.019/0.019 (U301 1) 0.019/0.019 (U302 1) 0.019/0.019 (U303 1) 0.019/0.019 (U304 1) 0.019/0.019 (U31 1) 0.019/0.019 (U311 1) 0.019/0.019 (U312 1) 0.019/0.019 (U32 1) 0.019/0.019 (U321 1) 0.019/0.019 (U322 1) 0.019/0.019 (U323 1) 0.019/0.019 (U324 1) 0.019/0.019 (U325 1) 0.019/0.019 (U326 1) 0.019/0.019 (U327 1) 0.019/0.019 (U33 1) 0.019/0.019 (U331 1) 0.019/0.019 (U332 1) 0.019/0.019 (U333 1) 0.019/0.019 (U334 1) 0.019/0.019 (U34 1) 0.019/0.019 (U341 1) 0.019/0.019 (U342 1) 0.019/0.019 (U343 1) 0.019/0.019 (U344 1) 0.019/0.019 (U41 1) 0.019/0.019 (U42 1) 0.019/0.019 (U43 1) 0.019/0.019 (U44 1) 0.019/0.019 (U45 1) 0.019/0.019 (U46 1) 0.019/0.019 (U51 1) 0.019/0.019 (U52 1) 0.019/0.019 (U53 1) 0.019/0.019 (U54 1) 0.019/0.019 (U55 1) 0.019/0.019 (U56 1) 0.019/0.019 (U61 1) 0.019/0.019 (U62 1) 0.019/0.019 (U63 1) 0.019/0.019 (U71 1) 0.019/0.019 (U72 1) 0.019/0.019 (U73 1) 0.019/0.019 (U81 1) 0.019/0.019 (U82 1) 0.019/0.019 (U83 1) 0.019/0.019 (U91 1) 0.019/0.019 (U92 1) 0.019/0.019 (U93 1) 0.019/0.019 (afterNth 1 2) 0.019/0.019 (fst 1) 0.019/0.019 (head 1) 0.019/0.019 (isLNat) 0.019/0.019 (isLNatKind) 0.019/0.019 (isNatural) 0.019/0.019 (isNaturalKind) 0.019/0.019 (isPLNat) 0.019/0.019 (isPLNatKind) 0.019/0.019 (natsFrom 1) 0.019/0.019 (sel 1 2) 0.019/0.019 (snd 1) 0.019/0.019 (splitAt 1 2) 0.019/0.019 (tail 1) 0.019/0.019 (take 1 2) 0.019/0.019 (0) 0.019/0.019 (cons 1) 0.019/0.019 (fSNonEmpty) 0.019/0.019 (nil) 0.019/0.019 (pair 1 2) 0.019/0.019 (s 1) 0.019/0.019 (tt) 0.019/0.019 ) 0.019/0.019 (RULES 0.019/0.019 U101(tt,V1:S,V2:S) -> U102(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U102(tt,V1:S,V2:S) -> U103(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U103(tt,V1:S,V2:S) -> U104(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U104(tt,V1:S,V2:S) -> U105(isNatural(V1:S),V2:S) 0.019/0.019 U105(tt,V2:S) -> U106(isLNat(V2:S)) 0.019/0.019 U106(tt) -> tt 0.019/0.019 U11(tt,N:S,XS:S) -> U12(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U111(tt,V2:S) -> U112(isLNatKind(V2:S)) 0.019/0.019 U112(tt) -> tt 0.019/0.019 U12(tt,N:S,XS:S) -> U13(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U121(tt,V2:S) -> U122(isLNatKind(V2:S)) 0.019/0.019 U122(tt) -> tt 0.019/0.019 U13(tt,N:S,XS:S) -> U14(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U131(tt) -> tt 0.019/0.019 U14(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.019/0.019 U141(tt) -> tt 0.019/0.019 U151(tt) -> tt 0.019/0.019 U161(tt) -> tt 0.019/0.019 U171(tt,V2:S) -> U172(isLNatKind(V2:S)) 0.019/0.019 U172(tt) -> tt 0.019/0.019 U181(tt,V1:S) -> U182(isLNatKind(V1:S),V1:S) 0.019/0.019 U182(tt,V1:S) -> U183(isLNat(V1:S)) 0.019/0.019 U183(tt) -> tt 0.019/0.019 U191(tt,V1:S) -> U192(isNaturalKind(V1:S),V1:S) 0.019/0.019 U192(tt,V1:S) -> U193(isNatural(V1:S)) 0.019/0.019 U193(tt) -> tt 0.019/0.019 U201(tt,V1:S,V2:S) -> U202(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U202(tt,V1:S,V2:S) -> U203(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U203(tt,V1:S,V2:S) -> U204(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U204(tt,V1:S,V2:S) -> U205(isNatural(V1:S),V2:S) 0.019/0.019 U205(tt,V2:S) -> U206(isLNat(V2:S)) 0.019/0.019 U206(tt) -> tt 0.019/0.019 U21(tt,X:S,Y:S) -> U22(isLNatKind(X:S),X:S,Y:S) 0.019/0.019 U211(tt) -> tt 0.019/0.019 U22(tt,X:S,Y:S) -> U23(isLNat(Y:S),X:S,Y:S) 0.019/0.019 U221(tt) -> tt 0.019/0.019 U23(tt,X:S,Y:S) -> U24(isLNatKind(Y:S),X:S) 0.019/0.019 U231(tt,V2:S) -> U232(isLNatKind(V2:S)) 0.019/0.019 U232(tt) -> tt 0.019/0.019 U24(tt,X:S) -> X:S 0.019/0.019 U241(tt,V1:S,V2:S) -> U242(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 U242(tt,V1:S,V2:S) -> U243(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U243(tt,V1:S,V2:S) -> U244(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U244(tt,V1:S,V2:S) -> U245(isLNat(V1:S),V2:S) 0.019/0.019 U245(tt,V2:S) -> U246(isLNat(V2:S)) 0.019/0.019 U246(tt) -> tt 0.019/0.019 U251(tt,V1:S,V2:S) -> U252(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U252(tt,V1:S,V2:S) -> U253(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U253(tt,V1:S,V2:S) -> U254(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U254(tt,V1:S,V2:S) -> U255(isNatural(V1:S),V2:S) 0.019/0.019 U255(tt,V2:S) -> U256(isLNat(V2:S)) 0.019/0.019 U256(tt) -> tt 0.019/0.019 U261(tt,V2:S) -> U262(isLNatKind(V2:S)) 0.019/0.019 U262(tt) -> tt 0.019/0.019 U271(tt,V2:S) -> U272(isLNatKind(V2:S)) 0.019/0.019 U272(tt) -> tt 0.019/0.019 U281(tt,N:S) -> U282(isNaturalKind(N:S),N:S) 0.019/0.019 U282(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.019/0.019 U291(tt,N:S,XS:S) -> U292(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U292(tt,N:S,XS:S) -> U293(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U293(tt,N:S,XS:S) -> U294(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U294(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.019/0.019 U301(tt,X:S,Y:S) -> U302(isLNatKind(X:S),Y:S) 0.019/0.019 U302(tt,Y:S) -> U303(isLNat(Y:S),Y:S) 0.019/0.019 U303(tt,Y:S) -> U304(isLNatKind(Y:S),Y:S) 0.019/0.019 U304(tt,Y:S) -> Y:S 0.019/0.019 U31(tt,N:S,XS:S) -> U32(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U311(tt,XS:S) -> U312(isLNatKind(XS:S),XS:S) 0.019/0.019 U312(tt,XS:S) -> pair(nil,XS:S) 0.019/0.019 U32(tt,N:S,XS:S) -> U33(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U321(tt,N:S,X:S,XS:S) -> U322(isNaturalKind(N:S),N:S,X:S,XS:S) 0.019/0.019 U322(tt,N:S,X:S,XS:S) -> U323(isNatural(X:S),N:S,X:S,XS:S) 0.019/0.019 U323(tt,N:S,X:S,XS:S) -> U324(isNaturalKind(X:S),N:S,X:S,XS:S) 0.019/0.019 U324(tt,N:S,X:S,XS:S) -> U325(isLNat(XS:S),N:S,X:S,XS:S) 0.019/0.019 U325(tt,N:S,X:S,XS:S) -> U326(isLNatKind(XS:S),N:S,X:S,XS:S) 0.019/0.019 U326(tt,N:S,X:S,XS:S) -> U327(splitAt(N:S,XS:S),X:S) 0.019/0.019 U327(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.019/0.019 U33(tt,N:S,XS:S) -> U34(isLNatKind(XS:S),N:S) 0.019/0.019 U331(tt,N:S,XS:S) -> U332(isNaturalKind(N:S),XS:S) 0.019/0.019 U332(tt,XS:S) -> U333(isLNat(XS:S),XS:S) 0.019/0.019 U333(tt,XS:S) -> U334(isLNatKind(XS:S),XS:S) 0.019/0.019 U334(tt,XS:S) -> XS:S 0.019/0.019 U34(tt,N:S) -> N:S 0.019/0.019 U341(tt,N:S,XS:S) -> U342(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U342(tt,N:S,XS:S) -> U343(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U343(tt,N:S,XS:S) -> U344(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U344(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.019/0.019 U41(tt,V1:S,V2:S) -> U42(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U42(tt,V1:S,V2:S) -> U43(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U43(tt,V1:S,V2:S) -> U44(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U44(tt,V1:S,V2:S) -> U45(isNatural(V1:S),V2:S) 0.019/0.019 U45(tt,V2:S) -> U46(isLNat(V2:S)) 0.019/0.019 U46(tt) -> tt 0.019/0.019 U51(tt,V1:S,V2:S) -> U52(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U52(tt,V1:S,V2:S) -> U53(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U53(tt,V1:S,V2:S) -> U54(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U54(tt,V1:S,V2:S) -> U55(isNatural(V1:S),V2:S) 0.019/0.019 U55(tt,V2:S) -> U56(isLNat(V2:S)) 0.019/0.019 U56(tt) -> tt 0.019/0.019 U61(tt,V1:S) -> U62(isPLNatKind(V1:S),V1:S) 0.019/0.019 U62(tt,V1:S) -> U63(isPLNat(V1:S)) 0.019/0.019 U63(tt) -> tt 0.019/0.019 U71(tt,V1:S) -> U72(isNaturalKind(V1:S),V1:S) 0.019/0.019 U72(tt,V1:S) -> U73(isNatural(V1:S)) 0.019/0.019 U73(tt) -> tt 0.019/0.019 U81(tt,V1:S) -> U82(isPLNatKind(V1:S),V1:S) 0.019/0.019 U82(tt,V1:S) -> U83(isPLNat(V1:S)) 0.019/0.019 U83(tt) -> tt 0.019/0.019 U91(tt,V1:S) -> U92(isLNatKind(V1:S),V1:S) 0.019/0.019 U92(tt,V1:S) -> U93(isLNat(V1:S)) 0.019/0.019 U93(tt) -> tt 0.019/0.019 afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(nil) -> tt 0.019/0.019 isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(nil) -> tt 0.019/0.019 isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isNatural(0) -> tt 0.019/0.019 isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 isNaturalKind(0) -> tt 0.019/0.019 isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 ) 0.019/0.019 Critical Pairs: 0.019/0.019 => Not trivial, Not overlay, NW1, N1 0.019/0.019 => Not trivial, Not overlay, NW1, N2 0.019/0.019 => Not trivial, Not overlay, NW1, N3 0.019/0.019 => Not trivial, Not overlay, NW1, N4 0.019/0.019 => Not trivial, Not overlay, NW1, N5 0.019/0.019 => Not trivial, Not overlay, NW1, N6 0.019/0.019 => Not trivial, Not overlay, NW1, N7 0.019/0.019 => Not trivial, Not overlay, NW1, N8 0.019/0.019 => Not trivial, Not overlay, NW1, N9 0.019/0.019 => Not trivial, Not overlay, NW1, N10 0.019/0.019 => Not trivial, Not overlay, NW1, N11 0.019/0.019 => Not trivial, Not overlay, NW1, N12 0.019/0.019 => Not trivial, Not overlay, NW1, N13 0.019/0.019 => Not trivial, Not overlay, NW1, N14 0.019/0.019 => Not trivial, Not overlay, NW1, N15 0.019/0.019 => Not trivial, Not overlay, NW1, N16 0.019/0.019 => Not trivial, Not overlay, NW1, N17 0.019/0.019 => Not trivial, Not overlay, NW1, N18 0.019/0.019 => Not trivial, Not overlay, NW1, N19 0.019/0.019 => Not trivial, Not overlay, NW1, N20 0.019/0.019 => Not trivial, Not overlay, NW1, N21 0.019/0.019 => Not trivial, Not overlay, NW1, N22 0.019/0.019 => Not trivial, Not overlay, NW1, N23 0.019/0.019 => Not trivial, Not overlay, NW1, N24 0.019/0.019 => Not trivial, Not overlay, NW1, N25 0.019/0.019 => Not trivial, Not overlay, NW1, N26 0.019/0.019 => Not trivial, Not overlay, NW1, N27 0.019/0.019 => Not trivial, Not overlay, NW1, N28 0.019/0.019 => Not trivial, Not overlay, NW1, N29 0.019/0.019 => Not trivial, Not overlay, NW1, N30 0.019/0.019 => Not trivial, Not overlay, NW1, N31 0.019/0.019 => Not trivial, Not overlay, NW1, N32 0.019/0.019 => Not trivial, Not overlay, NW1, N33 0.019/0.019 => Not trivial, Not overlay, NW1, N34 0.019/0.019 => Not trivial, Not overlay, NW1, N35 0.019/0.019 => Not trivial, Not overlay, NW1, N36 0.019/0.019 => Not trivial, Not overlay, NW1, N37 0.019/0.019 => Not trivial, Not overlay, NW1, N38 0.019/0.019 => Not trivial, Not overlay, NW1, N39 0.019/0.019 => Not trivial, Not overlay, NW1, N40 0.019/0.019 => Not trivial, Not overlay, NW1, N41 0.019/0.019 => Not trivial, Not overlay, NW1, N42 0.019/0.019 => Not trivial, Not overlay, NW1, N43 0.019/0.019 => Not trivial, Not overlay, NW1, N44 0.019/0.019 => Not trivial, Not overlay, NW1, N45 0.019/0.019 => Not trivial, Not overlay, NW1, N46 0.019/0.019 => Not trivial, Not overlay, NW1, N47 0.019/0.019 => Not trivial, Not overlay, NW1, N48 0.019/0.019 => Not trivial, Not overlay, NW1, N49 0.019/0.019 => Not trivial, Not overlay, NW1, N50 0.019/0.019 => Not trivial, Not overlay, NW1, N51 0.019/0.019 => Not trivial, Not overlay, NW1, N52 0.019/0.019 => Not trivial, Not overlay, NW1, N53 0.019/0.019 => Not trivial, Not overlay, NW1, N54 0.019/0.019 => Not trivial, Not overlay, NW1, N55 0.019/0.019 => Not trivial, Not overlay, NW1, N56 0.019/0.019 => Not trivial, Not overlay, NW1, N57 0.019/0.019 => Not trivial, Not overlay, NW1, N58 0.019/0.019 => Not trivial, Not overlay, NW1, N59 0.019/0.019 => Not trivial, Not overlay, NW1, N60 0.019/0.019 => Not trivial, Not overlay, NW1, N61 0.019/0.019 => Not trivial, Not overlay, NW1, N62 0.019/0.019 => Not trivial, Not overlay, NW1, N63 0.019/0.019 => Not trivial, Not overlay, NW1, N64 0.019/0.019 => Not trivial, Not overlay, NW1, N65 0.019/0.019 => Not trivial, Not overlay, NW1, N66 0.019/0.019 => Not trivial, Not overlay, NW1, N67 0.019/0.019 => Not trivial, Not overlay, NW1, N68 0.019/0.019 => Not trivial, Not overlay, NW1, N69 0.019/0.019 => Not trivial, Not overlay, NW1, N70 0.019/0.019 => Not trivial, Not overlay, NW1, N71 0.019/0.019 => Not trivial, Not overlay, NW1, N72 0.019/0.019 => Not trivial, Not overlay, NW1, N73 0.019/0.019 => Not trivial, Not overlay, NW1, N74 0.019/0.019 => Not trivial, Not overlay, NW1, N75 0.019/0.019 => Not trivial, Not overlay, NW0, N76 0.019/0.019 => Not trivial, Not overlay, NW1, N77 0.019/0.019 => Not trivial, Not overlay, NW1, N78 0.019/0.019 => Not trivial, Not overlay, NW1, N79 0.019/0.019 => Not trivial, Not overlay, NW1, N80 0.019/0.019 => Not trivial, Not overlay, NW1, N81 0.019/0.019 => Not trivial, Not overlay, NW1, N82 0.019/0.019 => Not trivial, Not overlay, NW1, N83 0.019/0.019 => Not trivial, Not overlay, NW1, N84 0.019/0.019 => Not trivial, Not overlay, NW1, N85 0.019/0.019 => Not trivial, Not overlay, NW1, N86 0.019/0.019 => Not trivial, Not overlay, NW1, N87 0.019/0.019 => Not trivial, Not overlay, NW1, N88 0.019/0.019 => Not trivial, Not overlay, NW1, N89 0.019/0.019 => Not trivial, Not overlay, NW1, N90 0.019/0.019 => Not trivial, Not overlay, NW1, N91 0.019/0.019 => Not trivial, Not overlay, NW1, N92 0.019/0.019 => Not trivial, Not overlay, NW1, N93 0.019/0.019 => Not trivial, Not overlay, NW1, N94 0.019/0.019 => Not trivial, Not overlay, NW1, N95 0.019/0.019 => Not trivial, Not overlay, NW1, N96 0.019/0.019 => Not trivial, Not overlay, NW1, N97 0.019/0.019 => Not trivial, Not overlay, NW1, N98 0.019/0.019 => Not trivial, Not overlay, NW1, N99 0.019/0.019 => Not trivial, Not overlay, NW1, N100 0.019/0.019 => Not trivial, Not overlay, NW1, N101 0.019/0.019 => Not trivial, Not overlay, NW1, N102 0.019/0.019 => Not trivial, Not overlay, NW1, N103 0.019/0.019 => Not trivial, Not overlay, NW1, N104 0.019/0.019 => Not trivial, Not overlay, NW1, N105 0.019/0.019 => Not trivial, Not overlay, NW0, N106 0.019/0.019 => Not trivial, Not overlay, NW1, N107 0.019/0.019 => Not trivial, Not overlay, NW1, N108 0.019/0.019 => Not trivial, Not overlay, NW1, N109 0.019/0.019 => Not trivial, Not overlay, NW1, N110 0.019/0.019 => Not trivial, Not overlay, NW1, N111 0.019/0.019 => Not trivial, Not overlay, NW0, N112 0.019/0.019 => Not trivial, Not overlay, NW1, N113 0.019/0.019 => Not trivial, Not overlay, NW1, N114 0.019/0.019 => Not trivial, Not overlay, NW1, N115 0.019/0.019 => Not trivial, Not overlay, NW1, N116 0.019/0.019 => Not trivial, Not overlay, NW1, N117 0.019/0.019 => Not trivial, Not overlay, NW1, N118 0.019/0.019 => Not trivial, Not overlay, NW1, N119 0.019/0.019 => Not trivial, Not overlay, NW1, N120 0.019/0.019 => Not trivial, Not overlay, NW1, N121 0.019/0.019 => Not trivial, Not overlay, NW1, N122 0.019/0.019 => Not trivial, Not overlay, NW1, N123 0.019/0.019 => Not trivial, Not overlay, NW1, N124 0.019/0.019 => Not trivial, Not overlay, NW1, N125 0.019/0.019 => Not trivial, Not overlay, NW1, N126 0.019/0.019 => Not trivial, Not overlay, NW1, N127 0.019/0.019 => Not trivial, Not overlay, NW1, N128 0.019/0.019 => Not trivial, Not overlay, NW1, N129 0.019/0.019 => Not trivial, Not overlay, NW1, N130 0.019/0.019 => Not trivial, Not overlay, NW1, N131 0.019/0.019 => Not trivial, Not overlay, NW1, N132 0.019/0.019 => Not trivial, Not overlay, NW1, N133 0.019/0.019 => Not trivial, Not overlay, NW1, N134 0.019/0.019 => Not trivial, Not overlay, NW1, N135 0.019/0.019 => Not trivial, Not overlay, NW1, N136 0.019/0.019 => Not trivial, Not overlay, NW1, N137 0.019/0.019 => Not trivial, Not overlay, NW1, N138 0.019/0.019 => Not trivial, Not overlay, NW1, N139 0.019/0.019 => Not trivial, Not overlay, NW1, N140 0.019/0.019 => Not trivial, Not overlay, NW1, N141 0.019/0.019 => Not trivial, Not overlay, NW0, N142 0.019/0.019 => Not trivial, Not overlay, NW1, N143 0.019/0.019 => Not trivial, Not overlay, NW0, N144 0.019/0.019 => Not trivial, Not overlay, NW1, N145 0.019/0.019 => Not trivial, Not overlay, NW1, N146 0.019/0.019 => Not trivial, Not overlay, NW0, N147 0.019/0.019 => Not trivial, Not overlay, NW0, N148 0.019/0.019 => Not trivial, Not overlay, NW0, N149 0.019/0.019 => Not trivial, Not overlay, NW1, N150 0.019/0.019 => Not trivial, Not overlay, NW1, N151 0.019/0.019 => Not trivial, Not overlay, NW1, N152 0.019/0.019 => Not trivial, Not overlay, NW1, N153 0.019/0.019 => Not trivial, Not overlay, NW1, N154 0.019/0.019 => Not trivial, Not overlay, NW1, N155 0.019/0.019 => Not trivial, Not overlay, NW1, N156 0.019/0.019 => Not trivial, Not overlay, NW1, N157 0.019/0.019 => Not trivial, Not overlay, NW1, N158 0.019/0.019 => Not trivial, Not overlay, NW1, N159 0.019/0.019 => Not trivial, Not overlay, NW1, N160 0.019/0.019 => Not trivial, Not overlay, NW1, N161 0.019/0.019 => Not trivial, Not overlay, NW1, N162 0.019/0.019 => Not trivial, Not overlay, NW1, N163 0.019/0.019 => Not trivial, Not overlay, NW1, N164 0.019/0.019 => Not trivial, Not overlay, NW1, N165 0.019/0.019 => Not trivial, Not overlay, NW1, N166 0.019/0.019 => Not trivial, Not overlay, NW1, N167 0.019/0.019 => Not trivial, Not overlay, NW1, N168 0.019/0.019 => Not trivial, Not overlay, NW1, N169 0.019/0.019 => Not trivial, Not overlay, NW1, N170 0.019/0.019 => Not trivial, Not overlay, NW1, N171 0.019/0.019 => Not trivial, Not overlay, NW1, N172 0.019/0.019 => Not trivial, Not overlay, NW1, N173 0.019/0.019 => Not trivial, Not overlay, NW1, N174 0.019/0.019 => Not trivial, Not overlay, NW1, N175 0.019/0.019 => Not trivial, Not overlay, NW1, N176 0.019/0.019 => Not trivial, Not overlay, NW1, N177 0.019/0.019 => Not trivial, Not overlay, NW1, N178 0.019/0.019 => Not trivial, Not overlay, NW0, N179 0.019/0.019 => Not trivial, Not overlay, NW1, N180 0.019/0.019 => Not trivial, Not overlay, NW1, N181 0.019/0.019 => Not trivial, Not overlay, NW1, N182 0.019/0.019 => Not trivial, Not overlay, NW1, N183 0.019/0.019 => Not trivial, Not overlay, NW1, N184 0.019/0.019 => Not trivial, Not overlay, NW1, N185 0.019/0.019 => Not trivial, Not overlay, NW1, N186 0.019/0.019 => Not trivial, Not overlay, NW1, N187 0.019/0.019 => Not trivial, Not overlay, NW1, N188 0.019/0.019 => Not trivial, Not overlay, NW1, N189 0.019/0.019 => Not trivial, Not overlay, NW1, N190 0.019/0.019 => Not trivial, Not overlay, NW1, N191 0.019/0.019 => Not trivial, Not overlay, NW1, N192 0.019/0.019 => Not trivial, Not overlay, NW1, N193 0.019/0.019 => Not trivial, Not overlay, NW1, N194 0.019/0.019 => Not trivial, Not overlay, NW1, N195 0.019/0.019 => Not trivial, Not overlay, NW1, N196 0.019/0.019 => Not trivial, Not overlay, NW1, N197 0.019/0.019 => Not trivial, Not overlay, NW1, N198 0.019/0.019 => Not trivial, Not overlay, NW1, N199 0.019/0.019 => Not trivial, Not overlay, NW1, N200 0.019/0.019 => Not trivial, Not overlay, NW1, N201 0.019/0.019 => Not trivial, Not overlay, NW1, N202 0.019/0.019 => Not trivial, Not overlay, NW1, N203 0.019/0.019 => Not trivial, Not overlay, NW1, N204 0.019/0.019 => Not trivial, Not overlay, NW1, N205 0.019/0.019 => Not trivial, Not overlay, NW1, N206 0.019/0.019 => Not trivial, Not overlay, NW1, N207 0.019/0.019 => Not trivial, Not overlay, NW1, N208 0.019/0.019 => Not trivial, Not overlay, NW1, N209 0.019/0.019 => Not trivial, Not overlay, NW1, N210 0.019/0.019 => Not trivial, Not overlay, NW1, N211 0.019/0.019 => Not trivial, Not overlay, NW1, N212 0.019/0.019 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.019/0.019 0.019/0.019 Huet Levy Processor: 0.019/0.019 -> Rules: 0.019/0.019 U101(tt,V1:S,V2:S) -> U102(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U102(tt,V1:S,V2:S) -> U103(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U103(tt,V1:S,V2:S) -> U104(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U104(tt,V1:S,V2:S) -> U105(isNatural(V1:S),V2:S) 0.019/0.019 U105(tt,V2:S) -> U106(isLNat(V2:S)) 0.019/0.019 U106(tt) -> tt 0.019/0.019 U11(tt,N:S,XS:S) -> U12(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U111(tt,V2:S) -> U112(isLNatKind(V2:S)) 0.019/0.019 U112(tt) -> tt 0.019/0.019 U12(tt,N:S,XS:S) -> U13(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U121(tt,V2:S) -> U122(isLNatKind(V2:S)) 0.019/0.019 U122(tt) -> tt 0.019/0.019 U13(tt,N:S,XS:S) -> U14(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U131(tt) -> tt 0.019/0.019 U14(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.019/0.019 U141(tt) -> tt 0.019/0.019 U151(tt) -> tt 0.019/0.019 U161(tt) -> tt 0.019/0.019 U171(tt,V2:S) -> U172(isLNatKind(V2:S)) 0.019/0.019 U172(tt) -> tt 0.019/0.019 U181(tt,V1:S) -> U182(isLNatKind(V1:S),V1:S) 0.019/0.019 U182(tt,V1:S) -> U183(isLNat(V1:S)) 0.019/0.019 U183(tt) -> tt 0.019/0.019 U191(tt,V1:S) -> U192(isNaturalKind(V1:S),V1:S) 0.019/0.019 U192(tt,V1:S) -> U193(isNatural(V1:S)) 0.019/0.019 U193(tt) -> tt 0.019/0.019 U201(tt,V1:S,V2:S) -> U202(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U202(tt,V1:S,V2:S) -> U203(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U203(tt,V1:S,V2:S) -> U204(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U204(tt,V1:S,V2:S) -> U205(isNatural(V1:S),V2:S) 0.019/0.019 U205(tt,V2:S) -> U206(isLNat(V2:S)) 0.019/0.019 U206(tt) -> tt 0.019/0.019 U21(tt,X:S,Y:S) -> U22(isLNatKind(X:S),X:S,Y:S) 0.019/0.019 U211(tt) -> tt 0.019/0.019 U22(tt,X:S,Y:S) -> U23(isLNat(Y:S),X:S,Y:S) 0.019/0.019 U221(tt) -> tt 0.019/0.019 U23(tt,X:S,Y:S) -> U24(isLNatKind(Y:S),X:S) 0.019/0.019 U231(tt,V2:S) -> U232(isLNatKind(V2:S)) 0.019/0.019 U232(tt) -> tt 0.019/0.019 U24(tt,X:S) -> X:S 0.019/0.019 U241(tt,V1:S,V2:S) -> U242(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 U242(tt,V1:S,V2:S) -> U243(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U243(tt,V1:S,V2:S) -> U244(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U244(tt,V1:S,V2:S) -> U245(isLNat(V1:S),V2:S) 0.019/0.019 U245(tt,V2:S) -> U246(isLNat(V2:S)) 0.019/0.019 U246(tt) -> tt 0.019/0.019 U251(tt,V1:S,V2:S) -> U252(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U252(tt,V1:S,V2:S) -> U253(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U253(tt,V1:S,V2:S) -> U254(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U254(tt,V1:S,V2:S) -> U255(isNatural(V1:S),V2:S) 0.019/0.019 U255(tt,V2:S) -> U256(isLNat(V2:S)) 0.019/0.019 U256(tt) -> tt 0.019/0.019 U261(tt,V2:S) -> U262(isLNatKind(V2:S)) 0.019/0.019 U262(tt) -> tt 0.019/0.019 U271(tt,V2:S) -> U272(isLNatKind(V2:S)) 0.019/0.019 U272(tt) -> tt 0.019/0.019 U281(tt,N:S) -> U282(isNaturalKind(N:S),N:S) 0.019/0.019 U282(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.019/0.019 U291(tt,N:S,XS:S) -> U292(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U292(tt,N:S,XS:S) -> U293(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U293(tt,N:S,XS:S) -> U294(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U294(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.019/0.019 U301(tt,X:S,Y:S) -> U302(isLNatKind(X:S),Y:S) 0.019/0.019 U302(tt,Y:S) -> U303(isLNat(Y:S),Y:S) 0.019/0.019 U303(tt,Y:S) -> U304(isLNatKind(Y:S),Y:S) 0.019/0.019 U304(tt,Y:S) -> Y:S 0.019/0.019 U31(tt,N:S,XS:S) -> U32(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U311(tt,XS:S) -> U312(isLNatKind(XS:S),XS:S) 0.019/0.019 U312(tt,XS:S) -> pair(nil,XS:S) 0.019/0.019 U32(tt,N:S,XS:S) -> U33(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U321(tt,N:S,X:S,XS:S) -> U322(isNaturalKind(N:S),N:S,X:S,XS:S) 0.019/0.019 U322(tt,N:S,X:S,XS:S) -> U323(isNatural(X:S),N:S,X:S,XS:S) 0.019/0.019 U323(tt,N:S,X:S,XS:S) -> U324(isNaturalKind(X:S),N:S,X:S,XS:S) 0.019/0.019 U324(tt,N:S,X:S,XS:S) -> U325(isLNat(XS:S),N:S,X:S,XS:S) 0.019/0.019 U325(tt,N:S,X:S,XS:S) -> U326(isLNatKind(XS:S),N:S,X:S,XS:S) 0.019/0.019 U326(tt,N:S,X:S,XS:S) -> U327(splitAt(N:S,XS:S),X:S) 0.019/0.019 U327(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.019/0.019 U33(tt,N:S,XS:S) -> U34(isLNatKind(XS:S),N:S) 0.019/0.019 U331(tt,N:S,XS:S) -> U332(isNaturalKind(N:S),XS:S) 0.019/0.019 U332(tt,XS:S) -> U333(isLNat(XS:S),XS:S) 0.019/0.019 U333(tt,XS:S) -> U334(isLNatKind(XS:S),XS:S) 0.019/0.019 U334(tt,XS:S) -> XS:S 0.019/0.019 U34(tt,N:S) -> N:S 0.019/0.019 U341(tt,N:S,XS:S) -> U342(isNaturalKind(N:S),N:S,XS:S) 0.019/0.019 U342(tt,N:S,XS:S) -> U343(isLNat(XS:S),N:S,XS:S) 0.019/0.019 U343(tt,N:S,XS:S) -> U344(isLNatKind(XS:S),N:S,XS:S) 0.019/0.019 U344(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.019/0.019 U41(tt,V1:S,V2:S) -> U42(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U42(tt,V1:S,V2:S) -> U43(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U43(tt,V1:S,V2:S) -> U44(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U44(tt,V1:S,V2:S) -> U45(isNatural(V1:S),V2:S) 0.019/0.019 U45(tt,V2:S) -> U46(isLNat(V2:S)) 0.019/0.019 U46(tt) -> tt 0.019/0.019 U51(tt,V1:S,V2:S) -> U52(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 U52(tt,V1:S,V2:S) -> U53(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U53(tt,V1:S,V2:S) -> U54(isLNatKind(V2:S),V1:S,V2:S) 0.019/0.019 U54(tt,V1:S,V2:S) -> U55(isNatural(V1:S),V2:S) 0.019/0.019 U55(tt,V2:S) -> U56(isLNat(V2:S)) 0.019/0.019 U56(tt) -> tt 0.019/0.019 U61(tt,V1:S) -> U62(isPLNatKind(V1:S),V1:S) 0.019/0.019 U62(tt,V1:S) -> U63(isPLNat(V1:S)) 0.019/0.019 U63(tt) -> tt 0.019/0.019 U71(tt,V1:S) -> U72(isNaturalKind(V1:S),V1:S) 0.019/0.019 U72(tt,V1:S) -> U73(isNatural(V1:S)) 0.019/0.019 U73(tt) -> tt 0.019/0.019 U81(tt,V1:S) -> U82(isPLNatKind(V1:S),V1:S) 0.019/0.019 U82(tt,V1:S) -> U83(isPLNat(V1:S)) 0.019/0.019 U83(tt) -> tt 0.019/0.019 U91(tt,V1:S) -> U92(isLNatKind(V1:S),V1:S) 0.019/0.019 U92(tt,V1:S) -> U93(isLNat(V1:S)) 0.019/0.019 U93(tt) -> tt 0.019/0.019 afterNth(N:S,XS:S) -> U11(isNatural(N:S),N:S,XS:S) 0.019/0.019 fst(pair(X:S,Y:S)) -> U21(isLNat(X:S),X:S,Y:S) 0.019/0.019 head(cons(N:S,XS:S)) -> U31(isNatural(N:S),N:S,XS:S) 0.019/0.019 isLNat(afterNth(V1:S,V2:S)) -> U41(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.019/0.019 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.019/0.019 isLNat(take(V1:S,V2:S)) -> U101(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(cons(V1:S,V2:S)) -> U51(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isLNat(nil) -> tt 0.019/0.019 isLNatKind(afterNth(V1:S,V2:S)) -> U111(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(fst(V1:S)) -> U131(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(natsFrom(V1:S)) -> U141(isNaturalKind(V1:S)) 0.019/0.019 isLNatKind(snd(V1:S)) -> U151(isPLNatKind(V1:S)) 0.019/0.019 isLNatKind(tail(V1:S)) -> U161(isLNatKind(V1:S)) 0.019/0.019 isLNatKind(take(V1:S,V2:S)) -> U171(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(cons(V1:S,V2:S)) -> U121(isNaturalKind(V1:S),V2:S) 0.019/0.019 isLNatKind(nil) -> tt 0.019/0.019 isNatural(head(V1:S)) -> U181(isLNatKind(V1:S),V1:S) 0.019/0.019 isNatural(sel(V1:S,V2:S)) -> U201(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isNatural(0) -> tt 0.019/0.019 isNatural(s(V1:S)) -> U191(isNaturalKind(V1:S),V1:S) 0.019/0.019 isNaturalKind(head(V1:S)) -> U211(isLNatKind(V1:S)) 0.019/0.019 isNaturalKind(sel(V1:S,V2:S)) -> U231(isNaturalKind(V1:S),V2:S) 0.019/0.019 isNaturalKind(0) -> tt 0.019/0.019 isNaturalKind(s(V1:S)) -> U221(isNaturalKind(V1:S)) 0.019/0.019 isPLNat(splitAt(V1:S,V2:S)) -> U251(isNaturalKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNat(pair(V1:S,V2:S)) -> U241(isLNatKind(V1:S),V1:S,V2:S) 0.019/0.019 isPLNatKind(splitAt(V1:S,V2:S)) -> U271(isNaturalKind(V1:S),V2:S) 0.019/0.019 isPLNatKind(pair(V1:S,V2:S)) -> U261(isLNatKind(V1:S),V2:S) 0.019/0.019 natsFrom(N:S) -> U281(isNatural(N:S),N:S) 0.019/0.019 sel(N:S,XS:S) -> U291(isNatural(N:S),N:S,XS:S) 0.019/0.019 snd(pair(X:S,Y:S)) -> U301(isLNat(X:S),X:S,Y:S) 0.019/0.019 splitAt(0,XS:S) -> U311(isLNat(XS:S),XS:S) 0.019/0.019 splitAt(s(N:S),cons(X:S,XS:S)) -> U321(isNatural(N:S),N:S,X:S,XS:S) 0.019/0.019 tail(cons(N:S,XS:S)) -> U331(isNatural(N:S),N:S,XS:S) 0.019/0.019 take(N:S,XS:S) -> U341(isNatural(N:S),N:S,XS:S) 0.019/0.019 -> Vars: 0.019/0.019 V1, V2, V1, V2, V1, V2, V1, V2, V2, N, XS, V2, N, XS, V2, N, XS, N, XS, V2, V1, V1, V1, V1, V1, V2, V1, V2, V1, V2, V1, V2, V2, X, Y, X, Y, X, Y, V2, X, V1, V2, V1, V2, V1, V2, V1, V2, V2, V1, V2, V1, V2, V1, V2, V1, V2, V2, V2, V2, N, N, N, XS, N, XS, N, XS, N, XS, X, Y, Y, Y, Y, N, XS, XS, XS, N, XS, N, X, XS, N, X, XS, N, X, XS, N, X, XS, N, X, XS, N, X, XS, X, YS, ZS, N, XS, N, XS, XS, XS, XS, N, N, XS, N, XS, N, XS, N, XS, V1, V2, V1, V2, V1, V2, V1, V2, V2, V1, V2, V1, V2, V1, V2, V1, V2, V2, V1, V1, V1, V1, V1, V1, V1, V1, N, XS, X, Y, N, XS, V1, V2, V1, V1, V1, V1, V1, V2, V1, V2, V1, V2, V1, V1, V1, V1, V1, V2, V1, V2, V1, V1, V2, V1, V1, V1, V2, V1, V1, V2, V1, V2, V1, V2, V1, V2, N, N, XS, X, Y, XS, N, X, XS, N, XS, N, XS 0.019/0.019 -> UVars: 0.019/0.019 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, XS], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 20, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 21, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 22, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 23, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 25, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 27, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 29, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 30, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 31, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 32, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 33, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y]) 0.019/0.019 (UV-RuleId: 34, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 35, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y]) 0.019/0.019 (UV-RuleId: 36, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 37, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y]) 0.019/0.019 (UV-RuleId: 38, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 39, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 40, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 41, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 42, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 43, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 44, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 45, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 46, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 47, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 48, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 49, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 50, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 51, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 52, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 53, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 54, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 55, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 56, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 57, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N], UV-RFrozen: [N]) 0.019/0.019 (UV-RuleId: 58, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [N], UV-RFrozen: [N]) 0.019/0.019 (UV-RuleId: 59, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 60, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 61, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 62, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, XS], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 63, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X, Y], UV-RFrozen: [X, Y]) 0.019/0.019 (UV-RuleId: 64, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y], UV-RFrozen: [Y]) 0.019/0.019 (UV-RuleId: 65, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y], UV-RFrozen: [Y]) 0.019/0.019 (UV-RuleId: 66, UV-LActive: [], UV-RActive: [Y], UV-LFrozen: [Y], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 67, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 68, UV-LActive: [], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [XS]) 0.019/0.019 (UV-RuleId: 69, UV-LActive: [], UV-RActive: [XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 70, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 71, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, X, XS], UV-RFrozen: [N, X, XS]) 0.019/0.019 (UV-RuleId: 72, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, X, XS], UV-RFrozen: [N, X, XS]) 0.019/0.019 (UV-RuleId: 73, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, X, XS], UV-RFrozen: [N, X, XS]) 0.019/0.019 (UV-RuleId: 74, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, X, XS], UV-RFrozen: [N, X, XS]) 0.019/0.019 (UV-RuleId: 75, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, X, XS], UV-RFrozen: [N, X, XS]) 0.019/0.019 (UV-RuleId: 76, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, X, XS], UV-RFrozen: [X]) 0.019/0.019 (UV-RuleId: 77, UV-LActive: [YS, ZS], UV-RActive: [X, ZS], UV-LFrozen: [X], UV-RFrozen: [YS]) 0.019/0.019 (UV-RuleId: 78, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 79, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 80, UV-LActive: [], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [XS]) 0.019/0.019 (UV-RuleId: 81, UV-LActive: [], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [XS]) 0.019/0.019 (UV-RuleId: 82, UV-LActive: [], UV-RActive: [XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 83, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [N], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 84, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 85, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 86, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N, XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 87, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, XS], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 88, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 89, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 90, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 91, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 92, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 93, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 94, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 95, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 96, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 97, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 98, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.019/0.019 (UV-RuleId: 99, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 100, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 101, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 102, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 103, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 104, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 105, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 106, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 107, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 108, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 109, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 110, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 111, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 112, UV-LActive: [N, XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 113, UV-LActive: [X, Y], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [X, Y]) 0.019/0.019 (UV-RuleId: 114, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 115, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 116, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 117, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 118, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 119, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 120, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 121, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 122, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 123, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 124, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 125, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 126, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 127, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 128, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 129, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 130, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 131, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 132, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 133, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 134, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 135, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 136, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 137, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.019/0.019 (UV-RuleId: 138, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.019/0.019 (UV-RuleId: 139, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 140, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 141, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 142, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.019/0.019 (UV-RuleId: 143, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N]) 0.019/0.019 (UV-RuleId: 144, UV-LActive: [N, XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 145, UV-LActive: [X, Y], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [X, Y]) 0.019/0.019 (UV-RuleId: 146, UV-LActive: [XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [XS]) 0.019/0.019 (UV-RuleId: 147, UV-LActive: [N, X], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [N, X, XS]) 0.019/0.019 (UV-RuleId: 148, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [N, XS]) 0.019/0.019 (UV-RuleId: 149, UV-LActive: [N, XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N, XS]) 0.019/0.019 -> FVars: 0.019/0.019 x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208 0.019/0.019 -> PVars: 0.019/0.019 V1: [x9, x11, x13, x15, x29, x30, x31, x32, x33, x35, x37, x39, x50, x52, x54, x56, x59, x61, x63, x65, x128, x130, x132, x134, x137, x139, x141, x143, x146, x147, x148, x149, x150, x151, x152, x153, x160, x162, x163, x164, x165, x166, x168, x170, x172, x173, x174, x175, x176, x178, x180, x181, x183, x184, x185, x187, x188, x190, x192, x194], V2: [x10, x12, x14, x16, x17, x20, x23, x28, x34, x36, x38, x40, x41, x48, x51, x53, x55, x57, x58, x60, x62, x64, x66, x67, x68, x69, x129, x131, x133, x135, x136, x138, x140, x142, x144, x145, x161, x167, x169, x171, x177, x179, x182, x186, x189, x191, x193, x195], N: [x18, x21, x24, x26, x70, x71, x72, x74, x76, x78, x85, x89, x91, x94, x97, x100, x103, x106, x112, x114, x119, x120, x122, x124, x126, x154, x158, x196, x197, x202, x205, x207], XS: [x19, x22, x25, x27, x73, x75, x77, x79, x86, x87, x88, x90, x93, x96, x99, x102, x105, x108, x113, x115, x116, x117, x118, x121, x123, x125, x127, x155, x159, x198, x201, x204, x206, x208], X: [x42, x44, x46, x49, x80, x92, x95, x98, x101, x104, x107, x109, x156, x199, x203], Y: [x43, x45, x47, x81, x82, x83, x84, x157, x200], YS: [x110], ZS: [x111] 0.019/0.019 0.019/0.019 -> Rlps: 0.019/0.019 (rule: U101(tt,x9:S,x10:S) -> U102(isNaturalKind(x9:S),x9:S,x10:S), id: 1, possubterms: U101(tt,x9:S,x10:S)->[], tt->[1]) 0.019/0.019 (rule: U102(tt,x11:S,x12:S) -> U103(isLNatKind(x12:S),x11:S,x12:S), id: 2, possubterms: U102(tt,x11:S,x12:S)->[], tt->[1]) 0.019/0.019 (rule: U103(tt,x13:S,x14:S) -> U104(isLNatKind(x14:S),x13:S,x14:S), id: 3, possubterms: U103(tt,x13:S,x14:S)->[], tt->[1]) 0.019/0.019 (rule: U104(tt,x15:S,x16:S) -> U105(isNatural(x15:S),x16:S), id: 4, possubterms: U104(tt,x15:S,x16:S)->[], tt->[1]) 0.019/0.019 (rule: U105(tt,x17:S) -> U106(isLNat(x17:S)), id: 5, possubterms: U105(tt,x17:S)->[], tt->[1]) 0.019/0.019 (rule: U106(tt) -> tt, id: 6, possubterms: U106(tt)->[], tt->[1]) 0.019/0.019 (rule: U11(tt,x18:S,x19:S) -> U12(isNaturalKind(x18:S),x18:S,x19:S), id: 7, possubterms: U11(tt,x18:S,x19:S)->[], tt->[1]) 0.019/0.019 (rule: U111(tt,x20:S) -> U112(isLNatKind(x20:S)), id: 8, possubterms: U111(tt,x20:S)->[], tt->[1]) 0.019/0.019 (rule: U112(tt) -> tt, id: 9, possubterms: U112(tt)->[], tt->[1]) 0.019/0.019 (rule: U12(tt,x21:S,x22:S) -> U13(isLNat(x22:S),x21:S,x22:S), id: 10, possubterms: U12(tt,x21:S,x22:S)->[], tt->[1]) 0.019/0.019 (rule: U121(tt,x23:S) -> U122(isLNatKind(x23:S)), id: 11, possubterms: U121(tt,x23:S)->[], tt->[1]) 0.019/0.019 (rule: U122(tt) -> tt, id: 12, possubterms: U122(tt)->[], tt->[1]) 0.019/0.019 (rule: U13(tt,x24:S,x25:S) -> U14(isLNatKind(x25:S),x24:S,x25:S), id: 13, possubterms: U13(tt,x24:S,x25:S)->[], tt->[1]) 0.019/0.019 (rule: U131(tt) -> tt, id: 14, possubterms: U131(tt)->[], tt->[1]) 0.019/0.019 (rule: U14(tt,x26:S,x27:S) -> snd(splitAt(x26:S,x27:S)), id: 15, possubterms: U14(tt,x26:S,x27:S)->[], tt->[1]) 0.019/0.019 (rule: U141(tt) -> tt, id: 16, possubterms: U141(tt)->[], tt->[1]) 0.019/0.019 (rule: U151(tt) -> tt, id: 17, possubterms: U151(tt)->[], tt->[1]) 0.019/0.019 (rule: U161(tt) -> tt, id: 18, possubterms: U161(tt)->[], tt->[1]) 0.019/0.019 (rule: U171(tt,x28:S) -> U172(isLNatKind(x28:S)), id: 19, possubterms: U171(tt,x28:S)->[], tt->[1]) 0.019/0.019 (rule: U172(tt) -> tt, id: 20, possubterms: U172(tt)->[], tt->[1]) 0.019/0.019 (rule: U181(tt,x29:S) -> U182(isLNatKind(x29:S),x29:S), id: 21, possubterms: U181(tt,x29:S)->[], tt->[1]) 0.019/0.019 (rule: U182(tt,x30:S) -> U183(isLNat(x30:S)), id: 22, possubterms: U182(tt,x30:S)->[], tt->[1]) 0.019/0.019 (rule: U183(tt) -> tt, id: 23, possubterms: U183(tt)->[], tt->[1]) 0.019/0.019 (rule: U191(tt,x31:S) -> U192(isNaturalKind(x31:S),x31:S), id: 24, possubterms: U191(tt,x31:S)->[], tt->[1]) 0.019/0.019 (rule: U192(tt,x32:S) -> U193(isNatural(x32:S)), id: 25, possubterms: U192(tt,x32:S)->[], tt->[1]) 0.019/0.019 (rule: U193(tt) -> tt, id: 26, possubterms: U193(tt)->[], tt->[1]) 0.019/0.019 (rule: U201(tt,x33:S,x34:S) -> U202(isNaturalKind(x33:S),x33:S,x34:S), id: 27, possubterms: U201(tt,x33:S,x34:S)->[], tt->[1]) 0.019/0.019 (rule: U202(tt,x35:S,x36:S) -> U203(isLNatKind(x36:S),x35:S,x36:S), id: 28, possubterms: U202(tt,x35:S,x36:S)->[], tt->[1]) 0.019/0.019 (rule: U203(tt,x37:S,x38:S) -> U204(isLNatKind(x38:S),x37:S,x38:S), id: 29, possubterms: U203(tt,x37:S,x38:S)->[], tt->[1]) 0.019/0.019 (rule: U204(tt,x39:S,x40:S) -> U205(isNatural(x39:S),x40:S), id: 30, possubterms: U204(tt,x39:S,x40:S)->[], tt->[1]) 0.019/0.019 (rule: U205(tt,x41:S) -> U206(isLNat(x41:S)), id: 31, possubterms: U205(tt,x41:S)->[], tt->[1]) 0.019/0.019 (rule: U206(tt) -> tt, id: 32, possubterms: U206(tt)->[], tt->[1]) 0.019/0.019 (rule: U21(tt,x42:S,x43:S) -> U22(isLNatKind(x42:S),x42:S,x43:S), id: 33, possubterms: U21(tt,x42:S,x43:S)->[], tt->[1]) 0.019/0.019 (rule: U211(tt) -> tt, id: 34, possubterms: U211(tt)->[], tt->[1]) 0.019/0.019 (rule: U22(tt,x44:S,x45:S) -> U23(isLNat(x45:S),x44:S,x45:S), id: 35, possubterms: U22(tt,x44:S,x45:S)->[], tt->[1]) 0.019/0.019 (rule: U221(tt) -> tt, id: 36, possubterms: U221(tt)->[], tt->[1]) 0.019/0.019 (rule: U23(tt,x46:S,x47:S) -> U24(isLNatKind(x47:S),x46:S), id: 37, possubterms: U23(tt,x46:S,x47:S)->[], tt->[1]) 0.019/0.019 (rule: U231(tt,x48:S) -> U232(isLNatKind(x48:S)), id: 38, possubterms: U231(tt,x48:S)->[], tt->[1]) 0.019/0.019 (rule: U232(tt) -> tt, id: 39, possubterms: U232(tt)->[], tt->[1]) 0.019/0.019 (rule: U24(tt,x49:S) -> x49:S, id: 40, possubterms: U24(tt,x49:S)->[], tt->[1]) 0.019/0.019 (rule: U241(tt,x50:S,x51:S) -> U242(isLNatKind(x50:S),x50:S,x51:S), id: 41, possubterms: U241(tt,x50:S,x51:S)->[], tt->[1]) 0.019/0.019 (rule: U242(tt,x52:S,x53:S) -> U243(isLNatKind(x53:S),x52:S,x53:S), id: 42, possubterms: U242(tt,x52:S,x53:S)->[], tt->[1]) 0.019/0.019 (rule: U243(tt,x54:S,x55:S) -> U244(isLNatKind(x55:S),x54:S,x55:S), id: 43, possubterms: U243(tt,x54:S,x55:S)->[], tt->[1]) 0.019/0.019 (rule: U244(tt,x56:S,x57:S) -> U245(isLNat(x56:S),x57:S), id: 44, possubterms: U244(tt,x56:S,x57:S)->[], tt->[1]) 0.019/0.019 (rule: U245(tt,x58:S) -> U246(isLNat(x58:S)), id: 45, possubterms: U245(tt,x58:S)->[], tt->[1]) 0.019/0.019 (rule: U246(tt) -> tt, id: 46, possubterms: U246(tt)->[], tt->[1]) 0.019/0.019 (rule: U251(tt,x59:S,x60:S) -> U252(isNaturalKind(x59:S),x59:S,x60:S), id: 47, possubterms: U251(tt,x59:S,x60:S)->[], tt->[1]) 0.019/0.019 (rule: U252(tt,x61:S,x62:S) -> U253(isLNatKind(x62:S),x61:S,x62:S), id: 48, possubterms: U252(tt,x61:S,x62:S)->[], tt->[1]) 0.019/0.019 (rule: U253(tt,x63:S,x64:S) -> U254(isLNatKind(x64:S),x63:S,x64:S), id: 49, possubterms: U253(tt,x63:S,x64:S)->[], tt->[1]) 0.019/0.019 (rule: U254(tt,x65:S,x66:S) -> U255(isNatural(x65:S),x66:S), id: 50, possubterms: U254(tt,x65:S,x66:S)->[], tt->[1]) 0.019/0.019 (rule: U255(tt,x67:S) -> U256(isLNat(x67:S)), id: 51, possubterms: U255(tt,x67:S)->[], tt->[1]) 0.019/0.019 (rule: U256(tt) -> tt, id: 52, possubterms: U256(tt)->[], tt->[1]) 0.019/0.019 (rule: U261(tt,x68:S) -> U262(isLNatKind(x68:S)), id: 53, possubterms: U261(tt,x68:S)->[], tt->[1]) 0.019/0.019 (rule: U262(tt) -> tt, id: 54, possubterms: U262(tt)->[], tt->[1]) 0.019/0.019 (rule: U271(tt,x69:S) -> U272(isLNatKind(x69:S)), id: 55, possubterms: U271(tt,x69:S)->[], tt->[1]) 0.019/0.019 (rule: U272(tt) -> tt, id: 56, possubterms: U272(tt)->[], tt->[1]) 0.019/0.019 (rule: U281(tt,x70:S) -> U282(isNaturalKind(x70:S),x70:S), id: 57, possubterms: U281(tt,x70:S)->[], tt->[1]) 0.019/0.019 (rule: U282(tt,x71:S) -> cons(x71:S,natsFrom(s(x71:S))), id: 58, possubterms: U282(tt,x71:S)->[], tt->[1]) 0.019/0.019 (rule: U291(tt,x72:S,x73:S) -> U292(isNaturalKind(x72:S),x72:S,x73:S), id: 59, possubterms: U291(tt,x72:S,x73:S)->[], tt->[1]) 0.019/0.019 (rule: U292(tt,x74:S,x75:S) -> U293(isLNat(x75:S),x74:S,x75:S), id: 60, possubterms: U292(tt,x74:S,x75:S)->[], tt->[1]) 0.019/0.019 (rule: U293(tt,x76:S,x77:S) -> U294(isLNatKind(x77:S),x76:S,x77:S), id: 61, possubterms: U293(tt,x76:S,x77:S)->[], tt->[1]) 0.019/0.019 (rule: U294(tt,x78:S,x79:S) -> head(afterNth(x78:S,x79:S)), id: 62, possubterms: U294(tt,x78:S,x79:S)->[], tt->[1]) 0.019/0.019 (rule: U301(tt,x80:S,x81:S) -> U302(isLNatKind(x80:S),x81:S), id: 63, possubterms: U301(tt,x80:S,x81:S)->[], tt->[1]) 0.019/0.019 (rule: U302(tt,x82:S) -> U303(isLNat(x82:S),x82:S), id: 64, possubterms: U302(tt,x82:S)->[], tt->[1]) 0.019/0.019 (rule: U303(tt,x83:S) -> U304(isLNatKind(x83:S),x83:S), id: 65, possubterms: U303(tt,x83:S)->[], tt->[1]) 0.019/0.019 (rule: U304(tt,x84:S) -> x84:S, id: 66, possubterms: U304(tt,x84:S)->[], tt->[1]) 0.019/0.019 (rule: U31(tt,x85:S,x86:S) -> U32(isNaturalKind(x85:S),x85:S,x86:S), id: 67, possubterms: U31(tt,x85:S,x86:S)->[], tt->[1]) 0.019/0.019 (rule: U311(tt,x87:S) -> U312(isLNatKind(x87:S),x87:S), id: 68, possubterms: U311(tt,x87:S)->[], tt->[1]) 0.019/0.019 (rule: U312(tt,x88:S) -> pair(nil,x88:S), id: 69, possubterms: U312(tt,x88:S)->[], tt->[1]) 0.019/0.019 (rule: U32(tt,x89:S,x90:S) -> U33(isLNat(x90:S),x89:S,x90:S), id: 70, possubterms: U32(tt,x89:S,x90:S)->[], tt->[1]) 0.019/0.019 (rule: U321(tt,x91:S,x92:S,x93:S) -> U322(isNaturalKind(x91:S),x91:S,x92:S,x93:S), id: 71, possubterms: U321(tt,x91:S,x92:S,x93:S)->[], tt->[1]) 0.019/0.019 (rule: U322(tt,x94:S,x95:S,x96:S) -> U323(isNatural(x95:S),x94:S,x95:S,x96:S), id: 72, possubterms: U322(tt,x94:S,x95:S,x96:S)->[], tt->[1]) 0.019/0.019 (rule: U323(tt,x97:S,x98:S,x99:S) -> U324(isNaturalKind(x98:S),x97:S,x98:S,x99:S), id: 73, possubterms: U323(tt,x97:S,x98:S,x99:S)->[], tt->[1]) 0.019/0.019 (rule: U324(tt,x100:S,x101:S,x102:S) -> U325(isLNat(x102:S),x100:S,x101:S,x102:S), id: 74, possubterms: U324(tt,x100:S,x101:S,x102:S)->[], tt->[1]) 0.019/0.019 (rule: U325(tt,x103:S,x104:S,x105:S) -> U326(isLNatKind(x105:S),x103:S,x104:S,x105:S), id: 75, possubterms: U325(tt,x103:S,x104:S,x105:S)->[], tt->[1]) 0.019/0.019 (rule: U326(tt,x106:S,x107:S,x108:S) -> U327(splitAt(x106:S,x108:S),x107:S), id: 76, possubterms: U326(tt,x106:S,x107:S,x108:S)->[], tt->[1]) 0.019/0.019 (rule: U327(pair(x110:S,x111:S),x109:S) -> pair(cons(x109:S,x110:S),x111:S), id: 77, possubterms: U327(pair(x110:S,x111:S),x109:S)->[], pair(x110:S,x111:S)->[1]) 0.019/0.019 (rule: U33(tt,x112:S,x113:S) -> U34(isLNatKind(x113:S),x112:S), id: 78, possubterms: U33(tt,x112:S,x113:S)->[], tt->[1]) 0.019/0.019 (rule: U331(tt,x114:S,x115:S) -> U332(isNaturalKind(x114:S),x115:S), id: 79, possubterms: U331(tt,x114:S,x115:S)->[], tt->[1]) 0.019/0.019 (rule: U332(tt,x116:S) -> U333(isLNat(x116:S),x116:S), id: 80, possubterms: U332(tt,x116:S)->[], tt->[1]) 0.019/0.019 (rule: U333(tt,x117:S) -> U334(isLNatKind(x117:S),x117:S), id: 81, possubterms: U333(tt,x117:S)->[], tt->[1]) 0.019/0.019 (rule: U334(tt,x118:S) -> x118:S, id: 82, possubterms: U334(tt,x118:S)->[], tt->[1]) 0.019/0.019 (rule: U34(tt,x119:S) -> x119:S, id: 83, possubterms: U34(tt,x119:S)->[], tt->[1]) 0.019/0.019 (rule: U341(tt,x120:S,x121:S) -> U342(isNaturalKind(x120:S),x120:S,x121:S), id: 84, possubterms: U341(tt,x120:S,x121:S)->[], tt->[1]) 0.019/0.019 (rule: U342(tt,x122:S,x123:S) -> U343(isLNat(x123:S),x122:S,x123:S), id: 85, possubterms: U342(tt,x122:S,x123:S)->[], tt->[1]) 0.019/0.019 (rule: U343(tt,x124:S,x125:S) -> U344(isLNatKind(x125:S),x124:S,x125:S), id: 86, possubterms: U343(tt,x124:S,x125:S)->[], tt->[1]) 0.019/0.019 (rule: U344(tt,x126:S,x127:S) -> fst(splitAt(x126:S,x127:S)), id: 87, possubterms: U344(tt,x126:S,x127:S)->[], tt->[1]) 0.019/0.019 (rule: U41(tt,x128:S,x129:S) -> U42(isNaturalKind(x128:S),x128:S,x129:S), id: 88, possubterms: U41(tt,x128:S,x129:S)->[], tt->[1]) 0.019/0.019 (rule: U42(tt,x130:S,x131:S) -> U43(isLNatKind(x131:S),x130:S,x131:S), id: 89, possubterms: U42(tt,x130:S,x131:S)->[], tt->[1]) 0.019/0.019 (rule: U43(tt,x132:S,x133:S) -> U44(isLNatKind(x133:S),x132:S,x133:S), id: 90, possubterms: U43(tt,x132:S,x133:S)->[], tt->[1]) 0.019/0.019 (rule: U44(tt,x134:S,x135:S) -> U45(isNatural(x134:S),x135:S), id: 91, possubterms: U44(tt,x134:S,x135:S)->[], tt->[1]) 0.019/0.019 (rule: U45(tt,x136:S) -> U46(isLNat(x136:S)), id: 92, possubterms: U45(tt,x136:S)->[], tt->[1]) 0.019/0.019 (rule: U46(tt) -> tt, id: 93, possubterms: U46(tt)->[], tt->[1]) 0.019/0.019 (rule: U51(tt,x137:S,x138:S) -> U52(isNaturalKind(x137:S),x137:S,x138:S), id: 94, possubterms: U51(tt,x137:S,x138:S)->[], tt->[1]) 0.019/0.019 (rule: U52(tt,x139:S,x140:S) -> U53(isLNatKind(x140:S),x139:S,x140:S), id: 95, possubterms: U52(tt,x139:S,x140:S)->[], tt->[1]) 0.019/0.019 (rule: U53(tt,x141:S,x142:S) -> U54(isLNatKind(x142:S),x141:S,x142:S), id: 96, possubterms: U53(tt,x141:S,x142:S)->[], tt->[1]) 0.019/0.019 (rule: U54(tt,x143:S,x144:S) -> U55(isNatural(x143:S),x144:S), id: 97, possubterms: U54(tt,x143:S,x144:S)->[], tt->[1]) 0.019/0.019 (rule: U55(tt,x145:S) -> U56(isLNat(x145:S)), id: 98, possubterms: U55(tt,x145:S)->[], tt->[1]) 0.019/0.019 (rule: U56(tt) -> tt, id: 99, possubterms: U56(tt)->[], tt->[1]) 0.019/0.019 (rule: U61(tt,x146:S) -> U62(isPLNatKind(x146:S),x146:S), id: 100, possubterms: U61(tt,x146:S)->[], tt->[1]) 0.019/0.019 (rule: U62(tt,x147:S) -> U63(isPLNat(x147:S)), id: 101, possubterms: U62(tt,x147:S)->[], tt->[1]) 0.019/0.019 (rule: U63(tt) -> tt, id: 102, possubterms: U63(tt)->[], tt->[1]) 0.019/0.019 (rule: U71(tt,x148:S) -> U72(isNaturalKind(x148:S),x148:S), id: 103, possubterms: U71(tt,x148:S)->[], tt->[1]) 0.019/0.019 (rule: U72(tt,x149:S) -> U73(isNatural(x149:S)), id: 104, possubterms: U72(tt,x149:S)->[], tt->[1]) 0.019/0.019 (rule: U73(tt) -> tt, id: 105, possubterms: U73(tt)->[], tt->[1]) 0.019/0.019 (rule: U81(tt,x150:S) -> U82(isPLNatKind(x150:S),x150:S), id: 106, possubterms: U81(tt,x150:S)->[], tt->[1]) 0.019/0.019 (rule: U82(tt,x151:S) -> U83(isPLNat(x151:S)), id: 107, possubterms: U82(tt,x151:S)->[], tt->[1]) 0.019/0.019 (rule: U83(tt) -> tt, id: 108, possubterms: U83(tt)->[], tt->[1]) 0.019/0.019 (rule: U91(tt,x152:S) -> U92(isLNatKind(x152:S),x152:S), id: 109, possubterms: U91(tt,x152:S)->[], tt->[1]) 0.019/0.019 (rule: U92(tt,x153:S) -> U93(isLNat(x153:S)), id: 110, possubterms: U92(tt,x153:S)->[], tt->[1]) 0.019/0.019 (rule: U93(tt) -> tt, id: 111, possubterms: U93(tt)->[], tt->[1]) 0.019/0.019 (rule: afterNth(x154:S,x155:S) -> U11(isNatural(x154:S),x154:S,x155:S), id: 112, possubterms: afterNth(x154:S,x155:S)->[]) 0.019/0.019 (rule: fst(pair(x156:S,x157:S)) -> U21(isLNat(x156:S),x156:S,x157:S), id: 113, possubterms: fst(pair(x156:S,x157:S))->[], pair(x156:S,x157:S)->[1]) 0.019/0.019 (rule: head(cons(x158:S,x159:S)) -> U31(isNatural(x158:S),x158:S,x159:S), id: 114, possubterms: head(cons(x158:S,x159:S))->[], cons(x158:S,x159:S)->[1]) 0.019/0.019 (rule: isLNat(afterNth(x160:S,x161:S)) -> U41(isNaturalKind(x160:S),x160:S,x161:S), id: 115, possubterms: isLNat(afterNth(x160:S,x161:S))->[]) 0.019/0.019 (rule: isLNat(fst(x162:S)) -> U61(isPLNatKind(x162:S),x162:S), id: 116, possubterms: isLNat(fst(x162:S))->[]) 0.019/0.019 (rule: isLNat(natsFrom(x163:S)) -> U71(isNaturalKind(x163:S),x163:S), id: 117, possubterms: isLNat(natsFrom(x163:S))->[]) 0.019/0.019 (rule: isLNat(snd(x164:S)) -> U81(isPLNatKind(x164:S),x164:S), id: 118, possubterms: isLNat(snd(x164:S))->[]) 0.019/0.019 (rule: isLNat(tail(x165:S)) -> U91(isLNatKind(x165:S),x165:S), id: 119, possubterms: isLNat(tail(x165:S))->[]) 0.019/0.019 (rule: isLNat(take(x166:S,x167:S)) -> U101(isNaturalKind(x166:S),x166:S,x167:S), id: 120, possubterms: isLNat(take(x166:S,x167:S))->[]) 0.019/0.019 (rule: isLNat(cons(x168:S,x169:S)) -> U51(isNaturalKind(x168:S),x168:S,x169:S), id: 121, possubterms: isLNat(cons(x168:S,x169:S))->[]) 0.019/0.019 (rule: isLNat(nil) -> tt, id: 122, possubterms: isLNat(nil)->[]) 0.019/0.019 (rule: isLNatKind(afterNth(x170:S,x171:S)) -> U111(isNaturalKind(x170:S),x171:S), id: 123, possubterms: isLNatKind(afterNth(x170:S,x171:S))->[]) 0.019/0.019 (rule: isLNatKind(fst(x172:S)) -> U131(isPLNatKind(x172:S)), id: 124, possubterms: isLNatKind(fst(x172:S))->[]) 0.019/0.019 (rule: isLNatKind(natsFrom(x173:S)) -> U141(isNaturalKind(x173:S)), id: 125, possubterms: isLNatKind(natsFrom(x173:S))->[]) 0.019/0.019 (rule: isLNatKind(snd(x174:S)) -> U151(isPLNatKind(x174:S)), id: 126, possubterms: isLNatKind(snd(x174:S))->[]) 0.019/0.019 (rule: isLNatKind(tail(x175:S)) -> U161(isLNatKind(x175:S)), id: 127, possubterms: isLNatKind(tail(x175:S))->[]) 0.019/0.019 (rule: isLNatKind(take(x176:S,x177:S)) -> U171(isNaturalKind(x176:S),x177:S), id: 128, possubterms: isLNatKind(take(x176:S,x177:S))->[]) 0.019/0.019 (rule: isLNatKind(cons(x178:S,x179:S)) -> U121(isNaturalKind(x178:S),x179:S), id: 129, possubterms: isLNatKind(cons(x178:S,x179:S))->[]) 0.019/0.019 (rule: isLNatKind(nil) -> tt, id: 130, possubterms: isLNatKind(nil)->[]) 0.019/0.019 (rule: isNatural(head(x180:S)) -> U181(isLNatKind(x180:S),x180:S), id: 131, possubterms: isNatural(head(x180:S))->[]) 0.019/0.019 (rule: isNatural(sel(x181:S,x182:S)) -> U201(isNaturalKind(x181:S),x181:S,x182:S), id: 132, possubterms: isNatural(sel(x181:S,x182:S))->[]) 0.019/0.019 (rule: isNatural(0) -> tt, id: 133, possubterms: isNatural(0)->[]) 0.019/0.019 (rule: isNatural(s(x183:S)) -> U191(isNaturalKind(x183:S),x183:S), id: 134, possubterms: isNatural(s(x183:S))->[]) 0.019/0.019 (rule: isNaturalKind(head(x184:S)) -> U211(isLNatKind(x184:S)), id: 135, possubterms: isNaturalKind(head(x184:S))->[]) 0.019/0.019 (rule: isNaturalKind(sel(x185:S,x186:S)) -> U231(isNaturalKind(x185:S),x186:S), id: 136, possubterms: isNaturalKind(sel(x185:S,x186:S))->[]) 0.019/0.019 (rule: isNaturalKind(0) -> tt, id: 137, possubterms: isNaturalKind(0)->[]) 0.019/0.019 (rule: isNaturalKind(s(x187:S)) -> U221(isNaturalKind(x187:S)), id: 138, possubterms: isNaturalKind(s(x187:S))->[]) 0.019/0.019 (rule: isPLNat(splitAt(x188:S,x189:S)) -> U251(isNaturalKind(x188:S),x188:S,x189:S), id: 139, possubterms: isPLNat(splitAt(x188:S,x189:S))->[]) 0.019/0.019 (rule: isPLNat(pair(x190:S,x191:S)) -> U241(isLNatKind(x190:S),x190:S,x191:S), id: 140, possubterms: isPLNat(pair(x190:S,x191:S))->[]) 0.019/0.019 (rule: isPLNatKind(splitAt(x192:S,x193:S)) -> U271(isNaturalKind(x192:S),x193:S), id: 141, possubterms: isPLNatKind(splitAt(x192:S,x193:S))->[]) 0.019/0.019 (rule: isPLNatKind(pair(x194:S,x195:S)) -> U261(isLNatKind(x194:S),x195:S), id: 142, possubterms: isPLNatKind(pair(x194:S,x195:S))->[]) 0.019/0.019 (rule: natsFrom(x196:S) -> U281(isNatural(x196:S),x196:S), id: 143, possubterms: natsFrom(x196:S)->[]) 0.019/0.019 (rule: sel(x197:S,x198:S) -> U291(isNatural(x197:S),x197:S,x198:S), id: 144, possubterms: sel(x197:S,x198:S)->[]) 0.019/0.019 (rule: snd(pair(x199:S,x200:S)) -> U301(isLNat(x199:S),x199:S,x200:S), id: 145, possubterms: snd(pair(x199:S,x200:S))->[], pair(x199:S,x200:S)->[1]) 0.019/0.019 (rule: splitAt(0,x201:S) -> U311(isLNat(x201:S),x201:S), id: 146, possubterms: splitAt(0,x201:S)->[], 0->[1]) 0.019/0.019 (rule: splitAt(s(x202:S),cons(x203:S,x204:S)) -> U321(isNatural(x202:S),x202:S,x203:S,x204:S), id: 147, possubterms: splitAt(s(x202:S),cons(x203:S,x204:S))->[], s(x202:S)->[1], cons(x203:S,x204:S)->[2]) 0.019/0.019 (rule: tail(cons(x205:S,x206:S)) -> U331(isNatural(x205:S),x205:S,x206:S), id: 148, possubterms: tail(cons(x205:S,x206:S))->[], cons(x205:S,x206:S)->[1]) 0.019/0.019 (rule: take(x207:S,x208:S) -> U341(isNatural(x207:S),x207:S,x208:S), id: 149, possubterms: take(x207:S,x208:S)->[]) 0.019/0.019 0.019/0.019 -> Unifications: 0.019/0.019 0.019/0.019 0.019/0.019 -> Critical pairs info: 0.019/0.019 => Not trivial, Not overlay, NW1, N1 0.019/0.019 => Not trivial, Not overlay, NW1, N2 0.019/0.019 => Not trivial, Not overlay, NW1, N3 0.019/0.019 => Not trivial, Not overlay, NW1, N4 0.019/0.019 => Not trivial, Not overlay, NW1, N5 0.019/0.019 => Not trivial, Not overlay, NW1, N6 0.019/0.019 => Not trivial, Not overlay, NW1, N7 0.019/0.019 => Not trivial, Not overlay, NW0, N8 0.019/0.019 => Not trivial, Not overlay, NW1, N9 0.019/0.019 => Not trivial, Not overlay, NW1, N10 0.019/0.019 => Not trivial, Not overlay, NW1, N11 0.019/0.019 => Not trivial, Not overlay, NW1, N12 0.019/0.019 => Not trivial, Not overlay, NW1, N13 0.019/0.019 => Not trivial, Not overlay, NW1, N14 0.019/0.019 => Not trivial, Not overlay, NW1, N15 0.019/0.019 => Not trivial, Not overlay, NW1, N16 0.019/0.019 => Not trivial, Not overlay, NW1, N17 0.019/0.019 => Not trivial, Not overlay, NW1, N18 0.019/0.019 => Not trivial, Not overlay, NW1, N19 0.019/0.019 => Not trivial, Not overlay, NW1, N20 0.019/0.019 => Not trivial, Not overlay, NW1, N21 0.019/0.019 => Not trivial, Not overlay, NW1, N22 0.019/0.019 => Not trivial, Not overlay, NW1, N23 0.019/0.019 => Not trivial, Not overlay, NW1, N24 0.019/0.019 => Not trivial, Not overlay, NW1, N25 0.019/0.019 => Not trivial, Not overlay, NW1, N26 0.019/0.019 => Not trivial, Not overlay, NW1, N27 0.019/0.019 => Not trivial, Not overlay, NW1, N28 0.019/0.019 => Not trivial, Not overlay, NW1, N29 0.019/0.019 => Not trivial, Not overlay, NW1, N30 0.019/0.019 => Not trivial, Not overlay, NW1, N31 0.019/0.019 => Not trivial, Not overlay, NW1, N32 0.019/0.019 => Not trivial, Not overlay, NW1, N33 0.019/0.019 => Not trivial, Not overlay, NW1, N34 0.019/0.019 => Not trivial, Not overlay, NW1, N35 0.019/0.019 => Not trivial, Not overlay, NW1, N36 0.019/0.019 => Not trivial, Not overlay, NW1, N37 0.019/0.019 => Not trivial, Not overlay, NW1, N38 0.019/0.019 => Not trivial, Not overlay, NW1, N39 0.019/0.019 => Not trivial, Not overlay, NW1, N40 0.019/0.019 => Not trivial, Not overlay, NW1, N41 0.019/0.019 => Not trivial, Not overlay, NW1, N42 0.019/0.019 => Not trivial, Not overlay, NW0, N43 0.019/0.019 => Not trivial, Not overlay, NW1, N44 0.019/0.019 => Not trivial, Not overlay, NW1, N45 0.019/0.019 => Not trivial, Not overlay, NW1, N46 0.019/0.019 => Not trivial, Not overlay, NW1, N47 0.019/0.019 => Not trivial, Not overlay, NW1, N48 0.019/0.019 => Not trivial, Not overlay, NW1, N49 0.019/0.019 => Not trivial, Not overlay, NW1, N50 0.019/0.019 => Not trivial, Not overlay, NW1, N51 0.019/0.019 => Not trivial, Not overlay, NW1, N52 0.019/0.019 => Not trivial, Not overlay, NW1, N53 0.019/0.019 => Not trivial, Not overlay, NW1, N54 0.019/0.019 => Not trivial, Not overlay, NW1, N55 0.019/0.019 => Not trivial, Not overlay, NW1, N56 0.019/0.019 => Not trivial, Not overlay, NW1, N57 0.019/0.019 => Not trivial, Not overlay, NW1, N58 0.019/0.019 => Not trivial, Not overlay, NW1, N59 0.019/0.019 => Not trivial, Not overlay, NW1, N60 0.019/0.019 => Not trivial, Not overlay, NW1, N61 0.019/0.019 => Not trivial, Not overlay, NW1, N62 0.019/0.019 => Not trivial, Not overlay, NW1, N63 0.019/0.019 => Not trivial, Not overlay, NW1, N64 0.019/0.019 => Not trivial, Not overlay, NW1, N65 0.019/0.019 => Not trivial, Not overlay, NW1, N66 0.019/0.019 => Not trivial, Not overlay, NW1, N67 0.019/0.019 => Not trivial, Not overlay, NW1, N68 0.019/0.019 => Not trivial, Not overlay, NW1, N69 0.019/0.019 => Not trivial, Not overlay, NW1, N70 0.019/0.019 => Not trivial, Not overlay, NW1, N71 0.019/0.019 => Not trivial, Not overlay, NW1, N72 0.019/0.019 => Not trivial, Not overlay, NW1, N73 0.019/0.019 => Not trivial, Not overlay, NW1, N74 0.019/0.019 => Not trivial, Not overlay, NW1, N75 0.019/0.019 => Not trivial, Not overlay, NW1, N76 0.019/0.019 => Not trivial, Not overlay, NW1, N77 0.019/0.019 => Not trivial, Not overlay, NW1, N78 0.019/0.019 => Not trivial, Not overlay, NW0, N79 0.019/0.019 => Not trivial, Not overlay, NW1, N80 0.019/0.019 => Not trivial, Not overlay, NW1, N81 0.019/0.019 => Not trivial, Not overlay, NW1, N82 0.019/0.019 => Not trivial, Not overlay, NW1, N83 0.019/0.019 => Not trivial, Not overlay, NW1, N84 0.019/0.019 => Not trivial, Not overlay, NW1, N85 0.019/0.019 => Not trivial, Not overlay, NW1, N86 0.019/0.019 => Not trivial, Not overlay, NW1, N87 0.019/0.019 => Not trivial, Not overlay, NW1, N88 0.019/0.019 => Not trivial, Not overlay, NW1, N89 0.019/0.019 => Not trivial, Not overlay, NW1, N90 0.019/0.019 => Not trivial, Not overlay, NW1, N91 0.019/0.019 => Not trivial, Not overlay, NW0, N92 0.019/0.019 => Not trivial, Not overlay, NW1, N93 0.019/0.019 => Not trivial, Not overlay, NW1, N94 0.019/0.019 => Not trivial, Not overlay, NW1, N95 0.019/0.019 => Not trivial, Not overlay, NW1, N96 0.019/0.019 => Not trivial, Not overlay, NW1, N97 0.019/0.019 => Not trivial, Not overlay, NW1, N98 0.019/0.019 => Not trivial, Not overlay, NW1, N99 0.019/0.019 => Not trivial, Not overlay, NW0, N100 0.019/0.019 => Not trivial, Not overlay, NW1, N101 0.019/0.019 => Not trivial, Not overlay, NW1, N102 0.019/0.019 => Not trivial, Not overlay, NW1, N103 0.019/0.019 => Not trivial, Not overlay, NW1, N104 0.019/0.019 => Not trivial, Not overlay, NW1, N105 0.019/0.019 => Not trivial, Not overlay, NW1, N106 0.019/0.019 => Not trivial, Not overlay, NW1, N107 0.019/0.019 => Not trivial, Not overlay, NW1, N108 0.019/0.019 => Not trivial, Not overlay, NW1, N109 0.019/0.019 => Not trivial, Not overlay, NW1, N110 0.019/0.019 => Not trivial, Not overlay, NW1, N111 0.019/0.019 => Not trivial, Not overlay, NW1, N112 0.019/0.019 => Not trivial, Not overlay, NW1, N113 0.019/0.019 => Not trivial, Not overlay, NW1, N114 0.019/0.019 => Not trivial, Not overlay, NW1, N115 0.019/0.019 => Not trivial, Not overlay, NW1, N116 0.019/0.019 => Not trivial, Not overlay, NW1, N117 0.019/0.019 => Not trivial, Not overlay, NW1, N118 0.019/0.019 => Not trivial, Not overlay, NW1, N119 0.019/0.019 => Not trivial, Not overlay, NW1, N120 0.019/0.019 => Not trivial, Not overlay, NW1, N121 0.019/0.019 => Not trivial, Not overlay, NW1, N122 0.019/0.019 => Not trivial, Not overlay, NW1, N123 0.019/0.019 => Not trivial, Not overlay, NW1, N124 0.019/0.019 => Not trivial, Not overlay, NW1, N125 0.019/0.019 => Not trivial, Not overlay, NW1, N126 0.019/0.019 => Not trivial, Not overlay, NW1, N127 0.019/0.019 => Not trivial, Not overlay, NW1, N128 0.019/0.019 => Not trivial, Not overlay, NW1, N129 0.019/0.019 => Not trivial, Not overlay, NW1, N130 0.019/0.019 => Not trivial, Not overlay, NW1, N131 0.019/0.019 => Not trivial, Not overlay, NW1, N132 0.019/0.019 => Not trivial, Not overlay, NW1, N133 0.019/0.019 => Not trivial, Not overlay, NW1, N134 0.019/0.019 => Not trivial, Not overlay, NW0, N135 0.019/0.019 => Not trivial, Not overlay, NW1, N136 0.019/0.019 => Not trivial, Not overlay, NW1, N137 0.019/0.019 => Not trivial, Not overlay, NW1, N138 0.019/0.019 => Not trivial, Not overlay, NW1, N139 0.019/0.019 => Not trivial, Not overlay, NW1, N140 0.019/0.019 => Not trivial, Not overlay, NW1, N141 0.019/0.019 => Not trivial, Not overlay, NW1, N142 0.019/0.019 => Not trivial, Not overlay, NW1, N143 0.019/0.019 => Not trivial, Not overlay, NW1, N144 0.019/0.019 => Not trivial, Not overlay, NW1, N145 0.019/0.019 => Not trivial, Not overlay, NW1, N146 0.019/0.019 => Not trivial, Not overlay, NW1, N147 0.019/0.019 => Not trivial, Not overlay, NW1, N148 0.019/0.019 => Not trivial, Not overlay, NW1, N149 0.019/0.019 => Not trivial, Not overlay, NW1, N150 0.019/0.019 => Not trivial, Not overlay, NW1, N151 0.019/0.019 => Not trivial, Not overlay, NW1, N152 0.019/0.019 => Not trivial, Not overlay, NW1, N153 0.019/0.019 => Not trivial, Not overlay, NW1, N154 0.019/0.019 => Not trivial, Not overlay, NW1, N155 0.019/0.019 => Not trivial, Not overlay, NW1, N156 0.019/0.019 => Not trivial, Not overlay, NW1, N157 0.019/0.019 => Not trivial, Not overlay, NW1, N158 0.019/0.019 => Not trivial, Not overlay, NW1, N159 0.019/0.019 => Not trivial, Not overlay, NW1, N160 0.019/0.019 => Not trivial, Not overlay, NW1, N161 0.019/0.019 => Not trivial, Not overlay, NW1, N162 0.019/0.019 => Not trivial, Not overlay, NW1, N163 0.019/0.019 => Not trivial, Not overlay, NW1, N164 0.019/0.019 => Not trivial, Not overlay, NW1, N165 0.019/0.019 => Not trivial, Not overlay, NW1, N166 0.019/0.019 => Not trivial, Not overlay, NW1, N167 0.019/0.019 => Not trivial, Not overlay, NW1, N168 0.019/0.019 => Not trivial, Not overlay, NW1, N169 0.019/0.019 => Not trivial, Not overlay, NW1, N170 0.019/0.019 => Not trivial, Not overlay, NW1, N171 0.019/0.019 => Not trivial, Not overlay, NW1, N172 0.019/0.019 => Not trivial, Not overlay, NW1, N173 0.019/0.019 => Not trivial, Not overlay, NW0, N174 0.019/0.019 => Not trivial, Not overlay, NW1, N175 0.019/0.019 => Not trivial, Not overlay, NW1, N176 0.019/0.019 => Not trivial, Not overlay, NW1, N177 0.019/0.019 => Not trivial, Not overlay, NW1, N178 0.019/0.019 => Not trivial, Not overlay, NW1, N179 0.019/0.019 => Not trivial, Not overlay, NW1, N180 0.019/0.019 => Not trivial, Not overlay, NW1, N181 0.019/0.019 => Not trivial, Not overlay, NW1, N182 0.019/0.019 => Not trivial, Not overlay, NW1, N183 0.019/0.019 => Not trivial, Not overlay, NW1, N184 0.019/0.019 => Not trivial, Not overlay, NW1, N185 0.019/0.019 => Not trivial, Not overlay, NW1, N186 0.019/0.019 => Not trivial, Not overlay, NW1, N187 0.019/0.019 => Not trivial, Not overlay, NW0, N188 0.019/0.019 => Not trivial, Not overlay, NW1, N189 0.019/0.019 => Not trivial, Not overlay, NW1, N190 0.019/0.019 => Not trivial, Not overlay, NW1, N191 0.019/0.019 => Not trivial, Not overlay, NW1, N192 0.019/0.019 => Not trivial, Not overlay, NW1, N193 0.019/0.019 => Not trivial, Not overlay, NW1, N194 0.019/0.019 => Not trivial, Not overlay, NW1, N195 0.019/0.019 => Not trivial, Not overlay, NW1, N196 0.019/0.019 => Not trivial, Not overlay, NW1, N197 0.019/0.019 => Not trivial, Not overlay, NW1, N198 0.019/0.019 => Not trivial, Not overlay, NW1, N199 0.019/0.019 => Not trivial, Not overlay, NW1, N200 0.019/0.019 => Not trivial, Not overlay, NW1, N201 0.019/0.019 => Not trivial, Not overlay, NW1, N202 0.019/0.019 => Not trivial, Not overlay, NW1, N203 0.019/0.019 => Not trivial, Not overlay, NW1, N204 0.019/0.019 => Not trivial, Not overlay, NW1, N205 0.019/0.019 => Not trivial, Not overlay, NW1, N206 0.019/0.019 => Not trivial, Not overlay, NW1, N207 0.019/0.019 => Not trivial, Not overlay, NW1, N208 0.019/0.019 => Not trivial, Not overlay, NW1, N209 0.019/0.019 => Not trivial, Not overlay, NW1, N210 0.019/0.019 => Not trivial, Not overlay, NW1, N211 0.019/0.019 => Not trivial, Not overlay, NW0, N212 0.019/0.019 0.019/0.019 -> Problem conclusions: 0.019/0.019 Left linear, Not right linear, Not linear 0.019/0.019 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.019/0.019 Not Huet-Levy confluent, Not Newman confluent 0.019/0.019 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.019/0.019 0.019/0.019 0.019/0.019 Problem 1: 0.019/0.019 No Convergence Brute Force Processor: 0.019/0.019 -> Rewritings: 0.019/0.019 s: U31(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isPLNatKind(splitAt(V1:S,V2:S)),XS:S) 0.019/0.019 Nodes: [0] 0.019/0.019 Edges: [] 0.019/0.019 ID: 0 => ('U31(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isPLNatKind(splitAt(V1:S,V2:S)),XS:S)', D0) 0.019/0.019 t: head(cons(U271(isNaturalKind(V1:S),V2:S),XS:S)) 0.019/0.019 Nodes: [0,1] 0.019/0.019 Edges: [(0,1)] 0.019/0.019 ID: 0 => ('head(cons(U271(isNaturalKind(V1:S),V2:S),XS:S))', D0) 0.019/0.019 ID: 1 => ('U31(isNatural(U271(isNaturalKind(V1:S),V2:S)),U271(isNaturalKind(V1:S),V2:S),XS:S)', D1, R114, P[], S{x158:S -> U271(isNaturalKind(V1:S),V2:S), x159:S -> XS:S}), NR: 'U31(isNatural(U271(isNaturalKind(V1:S),V2:S)),U271(isNaturalKind(V1:S),V2:S),XS:S)' 0.019/0.019 U31(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isPLNatKind(splitAt(V1:S,V2:S)),XS:S) ->* no union *<- head(cons(U271(isNaturalKind(V1:S),V2:S),XS:S)) 0.019/0.019 "Not joinable" 0.019/0.019 0.019/0.019 The problem is not joinable. 0.019/0.019 0.17user 0.00system 0:00.19elapsed 94%CPU (0avgtext+0avgdata 29492maxresident)k 0.019/0.019 0inputs+0outputs (0major+5566minor)pagefaults 0swaps