0.016/0.016 NO 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 0.016/0.016 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 Confluence Problem: 0.016/0.016 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.016/0.016 (STRATEGY CONTEXTSENSITIVE 0.016/0.016 (U101 1) 0.016/0.016 (U102 1) 0.016/0.016 (U103 1) 0.016/0.016 (U11 1) 0.016/0.016 (U111 1) 0.016/0.016 (U112 1) 0.016/0.016 (U121 1) 0.016/0.016 (U122 1) 0.016/0.016 (U131 1) 0.016/0.016 (U132 1) 0.016/0.016 (U133 1) 0.016/0.016 (U141 1) 0.016/0.016 (U142 1) 0.016/0.016 (U143 1) 0.016/0.016 (U151 1) 0.016/0.016 (U152 1) 0.016/0.016 (U153 1) 0.016/0.016 (U161 1) 0.016/0.016 (U171 1) 0.016/0.016 (U181 1) 0.016/0.016 (U191 1) 0.016/0.016 (U201 1) 0.016/0.016 (U202 1) 0.016/0.016 (U21 1) 0.016/0.016 (U211 1) 0.016/0.016 (U221 1) 0.016/0.016 (U31 1) 0.016/0.016 (U41 1) 0.016/0.016 (U42 1) 0.016/0.016 (U43 1) 0.016/0.016 (U51 1) 0.016/0.016 (U52 1) 0.016/0.016 (U53 1) 0.016/0.016 (U61 1) 0.016/0.016 (U62 1) 0.016/0.016 (U71 1) 0.016/0.016 (U72 1) 0.016/0.016 (U81 1) 0.016/0.016 (U82 1) 0.016/0.016 (U91 1) 0.016/0.016 (U92 1) 0.016/0.016 (afterNth 1 2) 0.016/0.016 (and 1) 0.016/0.016 (fst 1) 0.016/0.016 (head 1) 0.016/0.016 (isLNat) 0.016/0.016 (isLNatKind) 0.016/0.016 (isNatural) 0.016/0.016 (isNaturalKind) 0.016/0.016 (isPLNat) 0.016/0.016 (isPLNatKind) 0.016/0.016 (natsFrom 1) 0.016/0.016 (sel 1 2) 0.016/0.016 (snd 1) 0.016/0.016 (splitAt 1 2) 0.016/0.016 (tail 1) 0.016/0.016 (take 1 2) 0.016/0.016 (0) 0.016/0.016 (cons 1) 0.016/0.016 (fSNonEmpty) 0.016/0.016 (nil) 0.016/0.016 (pair 1 2) 0.016/0.016 (s 1) 0.016/0.016 (tt) 0.016/0.016 ) 0.016/0.016 (RULES 0.016/0.016 U101(tt,V1:S,V2:S) -> U102(isNatural(V1:S),V2:S) 0.016/0.016 U102(tt,V2:S) -> U103(isLNat(V2:S)) 0.016/0.016 U103(tt) -> tt 0.016/0.016 U11(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.016/0.016 U111(tt,V1:S) -> U112(isLNat(V1:S)) 0.016/0.016 U112(tt) -> tt 0.016/0.016 U121(tt,V1:S) -> U122(isNatural(V1:S)) 0.016/0.016 U122(tt) -> tt 0.016/0.016 U131(tt,V1:S,V2:S) -> U132(isNatural(V1:S),V2:S) 0.016/0.016 U132(tt,V2:S) -> U133(isLNat(V2:S)) 0.016/0.016 U133(tt) -> tt 0.016/0.016 U141(tt,V1:S,V2:S) -> U142(isLNat(V1:S),V2:S) 0.016/0.016 U142(tt,V2:S) -> U143(isLNat(V2:S)) 0.016/0.016 U143(tt) -> tt 0.016/0.016 U151(tt,V1:S,V2:S) -> U152(isNatural(V1:S),V2:S) 0.016/0.016 U152(tt,V2:S) -> U153(isLNat(V2:S)) 0.016/0.016 U153(tt) -> tt 0.016/0.016 U161(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.016/0.016 U171(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.016/0.016 U181(tt,Y:S) -> Y:S 0.016/0.016 U191(tt,XS:S) -> pair(nil,XS:S) 0.016/0.016 U201(tt,N:S,X:S,XS:S) -> U202(splitAt(N:S,XS:S),X:S) 0.016/0.016 U202(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.016/0.016 U21(tt,X:S) -> X:S 0.016/0.016 U211(tt,XS:S) -> XS:S 0.016/0.016 U221(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.016/0.016 U31(tt,N:S) -> N:S 0.016/0.016 U41(tt,V1:S,V2:S) -> U42(isNatural(V1:S),V2:S) 0.016/0.016 U42(tt,V2:S) -> U43(isLNat(V2:S)) 0.016/0.016 U43(tt) -> tt 0.016/0.016 U51(tt,V1:S,V2:S) -> U52(isNatural(V1:S),V2:S) 0.016/0.016 U52(tt,V2:S) -> U53(isLNat(V2:S)) 0.016/0.016 U53(tt) -> tt 0.016/0.016 U61(tt,V1:S) -> U62(isPLNat(V1:S)) 0.016/0.016 U62(tt) -> tt 0.016/0.016 U71(tt,V1:S) -> U72(isNatural(V1:S)) 0.016/0.016 U72(tt) -> tt 0.016/0.016 U81(tt,V1:S) -> U82(isPLNat(V1:S)) 0.016/0.016 U82(tt) -> tt 0.016/0.016 U91(tt,V1:S) -> U92(isLNat(V1:S)) 0.016/0.016 U92(tt) -> tt 0.016/0.016 afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 and(tt,X:S) -> X:S 0.016/0.016 fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(nil) -> tt 0.016/0.016 isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(nil) -> tt 0.016/0.016 isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isNatural(0) -> tt 0.016/0.016 isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isNaturalKind(0) -> tt 0.016/0.016 isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 ) 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 0.016/0.016 CleanTRS Processor: 0.016/0.016 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 Confluence Problem: 0.016/0.016 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.016/0.016 (STRATEGY CONTEXTSENSITIVE 0.016/0.016 (U101 1) 0.016/0.016 (U102 1) 0.016/0.016 (U103 1) 0.016/0.016 (U11 1) 0.016/0.016 (U111 1) 0.016/0.016 (U112 1) 0.016/0.016 (U121 1) 0.016/0.016 (U122 1) 0.016/0.016 (U131 1) 0.016/0.016 (U132 1) 0.016/0.016 (U133 1) 0.016/0.016 (U141 1) 0.016/0.016 (U142 1) 0.016/0.016 (U143 1) 0.016/0.016 (U151 1) 0.016/0.016 (U152 1) 0.016/0.016 (U153 1) 0.016/0.016 (U161 1) 0.016/0.016 (U171 1) 0.016/0.016 (U181 1) 0.016/0.016 (U191 1) 0.016/0.016 (U201 1) 0.016/0.016 (U202 1) 0.016/0.016 (U21 1) 0.016/0.016 (U211 1) 0.016/0.016 (U221 1) 0.016/0.016 (U31 1) 0.016/0.016 (U41 1) 0.016/0.016 (U42 1) 0.016/0.016 (U43 1) 0.016/0.016 (U51 1) 0.016/0.016 (U52 1) 0.016/0.016 (U53 1) 0.016/0.016 (U61 1) 0.016/0.016 (U62 1) 0.016/0.016 (U71 1) 0.016/0.016 (U72 1) 0.016/0.016 (U81 1) 0.016/0.016 (U82 1) 0.016/0.016 (U91 1) 0.016/0.016 (U92 1) 0.016/0.016 (afterNth 1 2) 0.016/0.016 (and 1) 0.016/0.016 (fst 1) 0.016/0.016 (head 1) 0.016/0.016 (isLNat) 0.016/0.016 (isLNatKind) 0.016/0.016 (isNatural) 0.016/0.016 (isNaturalKind) 0.016/0.016 (isPLNat) 0.016/0.016 (isPLNatKind) 0.016/0.016 (natsFrom 1) 0.016/0.016 (sel 1 2) 0.016/0.016 (snd 1) 0.016/0.016 (splitAt 1 2) 0.016/0.016 (tail 1) 0.016/0.016 (take 1 2) 0.016/0.016 (0) 0.016/0.016 (cons 1) 0.016/0.016 (fSNonEmpty) 0.016/0.016 (nil) 0.016/0.016 (pair 1 2) 0.016/0.016 (s 1) 0.016/0.016 (tt) 0.016/0.016 ) 0.016/0.016 (RULES 0.016/0.016 U101(tt,V1:S,V2:S) -> U102(isNatural(V1:S),V2:S) 0.016/0.016 U102(tt,V2:S) -> U103(isLNat(V2:S)) 0.016/0.016 U103(tt) -> tt 0.016/0.016 U11(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.016/0.016 U111(tt,V1:S) -> U112(isLNat(V1:S)) 0.016/0.016 U112(tt) -> tt 0.016/0.016 U121(tt,V1:S) -> U122(isNatural(V1:S)) 0.016/0.016 U122(tt) -> tt 0.016/0.016 U131(tt,V1:S,V2:S) -> U132(isNatural(V1:S),V2:S) 0.016/0.016 U132(tt,V2:S) -> U133(isLNat(V2:S)) 0.016/0.016 U133(tt) -> tt 0.016/0.016 U141(tt,V1:S,V2:S) -> U142(isLNat(V1:S),V2:S) 0.016/0.016 U142(tt,V2:S) -> U143(isLNat(V2:S)) 0.016/0.016 U143(tt) -> tt 0.016/0.016 U151(tt,V1:S,V2:S) -> U152(isNatural(V1:S),V2:S) 0.016/0.016 U152(tt,V2:S) -> U153(isLNat(V2:S)) 0.016/0.016 U153(tt) -> tt 0.016/0.016 U161(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.016/0.016 U171(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.016/0.016 U181(tt,Y:S) -> Y:S 0.016/0.016 U191(tt,XS:S) -> pair(nil,XS:S) 0.016/0.016 U201(tt,N:S,X:S,XS:S) -> U202(splitAt(N:S,XS:S),X:S) 0.016/0.016 U202(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.016/0.016 U21(tt,X:S) -> X:S 0.016/0.016 U211(tt,XS:S) -> XS:S 0.016/0.016 U221(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.016/0.016 U31(tt,N:S) -> N:S 0.016/0.016 U41(tt,V1:S,V2:S) -> U42(isNatural(V1:S),V2:S) 0.016/0.016 U42(tt,V2:S) -> U43(isLNat(V2:S)) 0.016/0.016 U43(tt) -> tt 0.016/0.016 U51(tt,V1:S,V2:S) -> U52(isNatural(V1:S),V2:S) 0.016/0.016 U52(tt,V2:S) -> U53(isLNat(V2:S)) 0.016/0.016 U53(tt) -> tt 0.016/0.016 U61(tt,V1:S) -> U62(isPLNat(V1:S)) 0.016/0.016 U62(tt) -> tt 0.016/0.016 U71(tt,V1:S) -> U72(isNatural(V1:S)) 0.016/0.016 U72(tt) -> tt 0.016/0.016 U81(tt,V1:S) -> U82(isPLNat(V1:S)) 0.016/0.016 U82(tt) -> tt 0.016/0.016 U91(tt,V1:S) -> U92(isLNat(V1:S)) 0.016/0.016 U92(tt) -> tt 0.016/0.016 afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 and(tt,X:S) -> X:S 0.016/0.016 fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(nil) -> tt 0.016/0.016 isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(nil) -> tt 0.016/0.016 isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isNatural(0) -> tt 0.016/0.016 isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isNaturalKind(0) -> tt 0.016/0.016 isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 ) 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 0.016/0.016 Modular Confluence Combinations Decomposition Processor: 0.016/0.016 It is a CTRS -> No modular confluence 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 CS-TRS Processor: 0.016/0.016 R is a CS-TRS 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 Confluence Problem: 0.016/0.016 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.016/0.016 (STRATEGY CONTEXTSENSITIVE 0.016/0.016 (U101 1) 0.016/0.016 (U102 1) 0.016/0.016 (U103 1) 0.016/0.016 (U11 1) 0.016/0.016 (U111 1) 0.016/0.016 (U112 1) 0.016/0.016 (U121 1) 0.016/0.016 (U122 1) 0.016/0.016 (U131 1) 0.016/0.016 (U132 1) 0.016/0.016 (U133 1) 0.016/0.016 (U141 1) 0.016/0.016 (U142 1) 0.016/0.016 (U143 1) 0.016/0.016 (U151 1) 0.016/0.016 (U152 1) 0.016/0.016 (U153 1) 0.016/0.016 (U161 1) 0.016/0.016 (U171 1) 0.016/0.016 (U181 1) 0.016/0.016 (U191 1) 0.016/0.016 (U201 1) 0.016/0.016 (U202 1) 0.016/0.016 (U21 1) 0.016/0.016 (U211 1) 0.016/0.016 (U221 1) 0.016/0.016 (U31 1) 0.016/0.016 (U41 1) 0.016/0.016 (U42 1) 0.016/0.016 (U43 1) 0.016/0.016 (U51 1) 0.016/0.016 (U52 1) 0.016/0.016 (U53 1) 0.016/0.016 (U61 1) 0.016/0.016 (U62 1) 0.016/0.016 (U71 1) 0.016/0.016 (U72 1) 0.016/0.016 (U81 1) 0.016/0.016 (U82 1) 0.016/0.016 (U91 1) 0.016/0.016 (U92 1) 0.016/0.016 (afterNth 1 2) 0.016/0.016 (and 1) 0.016/0.016 (fst 1) 0.016/0.016 (head 1) 0.016/0.016 (isLNat) 0.016/0.016 (isLNatKind) 0.016/0.016 (isNatural) 0.016/0.016 (isNaturalKind) 0.016/0.016 (isPLNat) 0.016/0.016 (isPLNatKind) 0.016/0.016 (natsFrom 1) 0.016/0.016 (sel 1 2) 0.016/0.016 (snd 1) 0.016/0.016 (splitAt 1 2) 0.016/0.016 (tail 1) 0.016/0.016 (take 1 2) 0.016/0.016 (0) 0.016/0.016 (cons 1) 0.016/0.016 (fSNonEmpty) 0.016/0.016 (nil) 0.016/0.016 (pair 1 2) 0.016/0.016 (s 1) 0.016/0.016 (tt) 0.016/0.016 ) 0.016/0.016 (RULES 0.016/0.016 U101(tt,V1:S,V2:S) -> U102(isNatural(V1:S),V2:S) 0.016/0.016 U102(tt,V2:S) -> U103(isLNat(V2:S)) 0.016/0.016 U103(tt) -> tt 0.016/0.016 U11(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.016/0.016 U111(tt,V1:S) -> U112(isLNat(V1:S)) 0.016/0.016 U112(tt) -> tt 0.016/0.016 U121(tt,V1:S) -> U122(isNatural(V1:S)) 0.016/0.016 U122(tt) -> tt 0.016/0.016 U131(tt,V1:S,V2:S) -> U132(isNatural(V1:S),V2:S) 0.016/0.016 U132(tt,V2:S) -> U133(isLNat(V2:S)) 0.016/0.016 U133(tt) -> tt 0.016/0.016 U141(tt,V1:S,V2:S) -> U142(isLNat(V1:S),V2:S) 0.016/0.016 U142(tt,V2:S) -> U143(isLNat(V2:S)) 0.016/0.016 U143(tt) -> tt 0.016/0.016 U151(tt,V1:S,V2:S) -> U152(isNatural(V1:S),V2:S) 0.016/0.016 U152(tt,V2:S) -> U153(isLNat(V2:S)) 0.016/0.016 U153(tt) -> tt 0.016/0.016 U161(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.016/0.016 U171(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.016/0.016 U181(tt,Y:S) -> Y:S 0.016/0.016 U191(tt,XS:S) -> pair(nil,XS:S) 0.016/0.016 U201(tt,N:S,X:S,XS:S) -> U202(splitAt(N:S,XS:S),X:S) 0.016/0.016 U202(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.016/0.016 U21(tt,X:S) -> X:S 0.016/0.016 U211(tt,XS:S) -> XS:S 0.016/0.016 U221(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.016/0.016 U31(tt,N:S) -> N:S 0.016/0.016 U41(tt,V1:S,V2:S) -> U42(isNatural(V1:S),V2:S) 0.016/0.016 U42(tt,V2:S) -> U43(isLNat(V2:S)) 0.016/0.016 U43(tt) -> tt 0.016/0.016 U51(tt,V1:S,V2:S) -> U52(isNatural(V1:S),V2:S) 0.016/0.016 U52(tt,V2:S) -> U53(isLNat(V2:S)) 0.016/0.016 U53(tt) -> tt 0.016/0.016 U61(tt,V1:S) -> U62(isPLNat(V1:S)) 0.016/0.016 U62(tt) -> tt 0.016/0.016 U71(tt,V1:S) -> U72(isNatural(V1:S)) 0.016/0.016 U72(tt) -> tt 0.016/0.016 U81(tt,V1:S) -> U82(isPLNat(V1:S)) 0.016/0.016 U82(tt) -> tt 0.016/0.016 U91(tt,V1:S) -> U92(isLNat(V1:S)) 0.016/0.016 U92(tt) -> tt 0.016/0.016 afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 and(tt,X:S) -> X:S 0.016/0.016 fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(nil) -> tt 0.016/0.016 isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(nil) -> tt 0.016/0.016 isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isNatural(0) -> tt 0.016/0.016 isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isNaturalKind(0) -> tt 0.016/0.016 isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 ) 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 0.016/0.016 Extended u-Critical Pairs NonLHRV Processor [JLAMP21]: 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 23 (l' :-> r') => U202(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U202(pair(YS:S,ZS:S),X:S)} 0.016/0.016 s => pair(cons(x33:S,U202(pair(YS:S,ZS:S),X:S)),x35:S) 0.016/0.016 t => U202(pair(pair(cons(X:S,YS:S),ZS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 24 (l' :-> r') => U21(tt,X:S) -> X:S 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U21(tt,X:S)} 0.016/0.016 s => pair(cons(x33:S,U21(tt,X:S)),x35:S) 0.016/0.016 t => U202(pair(X:S,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 25 (l' :-> r') => U211(tt,XS:S) -> XS:S 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U211(tt,XS:S)} 0.016/0.016 s => pair(cons(x33:S,U211(tt,XS:S)),x35:S) 0.016/0.016 t => U202(pair(XS:S,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 26 (l' :-> r') => U221(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U221(tt,N:S,XS:S)} 0.016/0.016 s => pair(cons(x33:S,U221(tt,N:S,XS:S)),x35:S) 0.016/0.016 t => U202(pair(fst(splitAt(N:S,XS:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 27 (l' :-> r') => U31(tt,N:S) -> N:S 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U31(tt,N:S)} 0.016/0.016 s => pair(cons(x33:S,U31(tt,N:S)),x35:S) 0.016/0.016 t => U202(pair(N:S,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 28 (l' :-> r') => U41(tt,V1:S,V2:S) -> U42(isNatural(V1:S),V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U41(tt,V1:S,V2:S)} 0.016/0.016 s => pair(cons(x33:S,U41(tt,V1:S,V2:S)),x35:S) 0.016/0.016 t => U202(pair(U42(isNatural(V1:S),V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 29 (l' :-> r') => U42(tt,V2:S) -> U43(isLNat(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U42(tt,V2:S)} 0.016/0.016 s => pair(cons(x33:S,U42(tt,V2:S)),x35:S) 0.016/0.016 t => U202(pair(U43(isLNat(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 30 (l' :-> r') => U43(tt) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U43(tt)} 0.016/0.016 s => pair(cons(x33:S,U43(tt)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 31 (l' :-> r') => U51(tt,V1:S,V2:S) -> U52(isNatural(V1:S),V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U51(tt,V1:S,V2:S)} 0.016/0.016 s => pair(cons(x33:S,U51(tt,V1:S,V2:S)),x35:S) 0.016/0.016 t => U202(pair(U52(isNatural(V1:S),V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 32 (l' :-> r') => U52(tt,V2:S) -> U53(isLNat(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U52(tt,V2:S)} 0.016/0.016 s => pair(cons(x33:S,U52(tt,V2:S)),x35:S) 0.016/0.016 t => U202(pair(U53(isLNat(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 33 (l' :-> r') => U53(tt) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U53(tt)} 0.016/0.016 s => pair(cons(x33:S,U53(tt)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 34 (l' :-> r') => U61(tt,V1:S) -> U62(isPLNat(V1:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U61(tt,V1:S)} 0.016/0.016 s => pair(cons(x33:S,U61(tt,V1:S)),x35:S) 0.016/0.016 t => U202(pair(U62(isPLNat(V1:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 35 (l' :-> r') => U62(tt) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U62(tt)} 0.016/0.016 s => pair(cons(x33:S,U62(tt)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 36 (l' :-> r') => U71(tt,V1:S) -> U72(isNatural(V1:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U71(tt,V1:S)} 0.016/0.016 s => pair(cons(x33:S,U71(tt,V1:S)),x35:S) 0.016/0.016 t => U202(pair(U72(isNatural(V1:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 37 (l' :-> r') => U72(tt) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U72(tt)} 0.016/0.016 s => pair(cons(x33:S,U72(tt)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 38 (l' :-> r') => U81(tt,V1:S) -> U82(isPLNat(V1:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U81(tt,V1:S)} 0.016/0.016 s => pair(cons(x33:S,U81(tt,V1:S)),x35:S) 0.016/0.016 t => U202(pair(U82(isPLNat(V1:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 39 (l' :-> r') => U82(tt) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U82(tt)} 0.016/0.016 s => pair(cons(x33:S,U82(tt)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 40 (l' :-> r') => U91(tt,V1:S) -> U92(isLNat(V1:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U91(tt,V1:S)} 0.016/0.016 s => pair(cons(x33:S,U91(tt,V1:S)),x35:S) 0.016/0.016 t => U202(pair(U92(isLNat(V1:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 41 (l' :-> r') => U92(tt) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> U92(tt)} 0.016/0.016 s => pair(cons(x33:S,U92(tt)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 42 (l' :-> r') => afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> afterNth(N:S,XS:S)} 0.016/0.016 s => pair(cons(x33:S,afterNth(N:S,XS:S)),x35:S) 0.016/0.016 t => U202(pair(U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 43 (l' :-> r') => and(tt,X:S) -> X:S 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> and(tt,X:S)} 0.016/0.016 s => pair(cons(x33:S,and(tt,X:S)),x35:S) 0.016/0.016 t => U202(pair(X:S,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 44 (l' :-> r') => fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> fst(pair(X:S,Y:S))} 0.016/0.016 s => pair(cons(x33:S,fst(pair(X:S,Y:S))),x35:S) 0.016/0.016 t => U202(pair(U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 45 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> head(cons(N:S,XS:S))} 0.016/0.016 s => pair(cons(x33:S,head(cons(N:S,XS:S))),x35:S) 0.016/0.016 t => U202(pair(U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 46 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(afterNth(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(afterNth(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 47 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(fst(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(fst(V1:S))),x35:S) 0.016/0.016 t => U202(pair(U61(isPLNatKind(V1:S),V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 48 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(natsFrom(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(natsFrom(V1:S))),x35:S) 0.016/0.016 t => U202(pair(U71(isNaturalKind(V1:S),V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 49 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(snd(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(snd(V1:S))),x35:S) 0.016/0.016 t => U202(pair(U81(isPLNatKind(V1:S),V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 50 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(tail(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(tail(V1:S))),x35:S) 0.016/0.016 t => U202(pair(U91(isLNatKind(V1:S),V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 51 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(take(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(take(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 52 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(cons(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isLNat(cons(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 53 (l' :-> r') => isLNat(nil) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNat(nil)} 0.016/0.016 s => pair(cons(x33:S,isLNat(nil)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 54 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(afterNth(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 55 (l' :-> r') => isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(fst(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(fst(V1:S))),x35:S) 0.016/0.016 t => U202(pair(isPLNatKind(V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 56 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(natsFrom(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(natsFrom(V1:S))),x35:S) 0.016/0.016 t => U202(pair(isNaturalKind(V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 57 (l' :-> r') => isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(snd(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(snd(V1:S))),x35:S) 0.016/0.016 t => U202(pair(isPLNatKind(V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 58 (l' :-> r') => isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(tail(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(tail(V1:S))),x35:S) 0.016/0.016 t => U202(pair(isLNatKind(V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 59 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(take(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(take(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 60 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(cons(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(cons(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 61 (l' :-> r') => isLNatKind(nil) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isLNatKind(nil)} 0.016/0.016 s => pair(cons(x33:S,isLNatKind(nil)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 62 (l' :-> r') => isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNatural(head(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isNatural(head(V1:S))),x35:S) 0.016/0.016 t => U202(pair(U111(isLNatKind(V1:S),V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 63 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNatural(sel(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isNatural(sel(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 64 (l' :-> r') => isNatural(0) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNatural(0)} 0.016/0.016 s => pair(cons(x33:S,isNatural(0)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 65 (l' :-> r') => isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNatural(s(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isNatural(s(V1:S))),x35:S) 0.016/0.016 t => U202(pair(U121(isNaturalKind(V1:S),V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 66 (l' :-> r') => isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNaturalKind(head(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isNaturalKind(head(V1:S))),x35:S) 0.016/0.016 t => U202(pair(isLNatKind(V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 67 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNaturalKind(sel(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isNaturalKind(sel(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 68 (l' :-> r') => isNaturalKind(0) -> tt 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNaturalKind(0)} 0.016/0.016 s => pair(cons(x33:S,isNaturalKind(0)),x35:S) 0.016/0.016 t => U202(pair(tt,x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 69 (l' :-> r') => isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isNaturalKind(s(V1:S))} 0.016/0.016 s => pair(cons(x33:S,isNaturalKind(s(V1:S))),x35:S) 0.016/0.016 t => U202(pair(isNaturalKind(V1:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 70 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isPLNat(splitAt(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isPLNat(splitAt(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 71 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isPLNat(pair(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isPLNat(pair(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 72 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isPLNatKind(splitAt(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 73 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> isPLNatKind(pair(V1:S,V2:S))} 0.016/0.016 s => pair(cons(x33:S,isPLNatKind(pair(V1:S,V2:S))),x35:S) 0.016/0.016 t => U202(pair(and(isLNatKind(V1:S),isLNatKind(V2:S)),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 74 (l' :-> r') => natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> natsFrom(N:S)} 0.016/0.016 s => pair(cons(x33:S,natsFrom(N:S)),x35:S) 0.016/0.016 t => U202(pair(U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 75 (l' :-> r') => sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> sel(N:S,XS:S)} 0.016/0.016 s => pair(cons(x33:S,sel(N:S,XS:S)),x35:S) 0.016/0.016 t => U202(pair(U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => pair(cons(x33:S,snd(pair(X:S,Y:S))),x35:S) 0.016/0.016 t => U202(pair(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> splitAt(0,XS:S)} 0.016/0.016 s => pair(cons(x33:S,splitAt(0,XS:S)),x35:S) 0.016/0.016 t => U202(pair(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => pair(cons(x33:S,splitAt(s(N:S),cons(X:S,XS:S))),x35:S) 0.016/0.016 t => U202(pair(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => pair(cons(x33:S,tail(cons(N:S,XS:S))),x35:S) 0.016/0.016 t => U202(pair(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x34:S 0.016/0.016 Pos x34:S in l => [1,1] 0.016/0.016 Sigma => {x34:S -> take(N:S,XS:S)} 0.016/0.016 s => pair(cons(x33:S,take(N:S,XS:S)),x35:S) 0.016/0.016 t => U202(pair(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x35:S),x33:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 42 (l' :-> r') => afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> afterNth(N:S,XS:S)} 0.016/0.016 s => U11(and(and(isNatural(afterNth(N:S,XS:S)),isNaturalKind(afterNth(N:S,XS:S))),and(isLNat(x52:S),isLNatKind(x52:S))),afterNth(N:S,XS:S),x52:S) 0.016/0.016 t => afterNth(U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 43 (l' :-> r') => and(tt,X:S) -> X:S 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> and(tt,X:S)} 0.016/0.016 s => U11(and(and(isNatural(and(tt,X:S)),isNaturalKind(and(tt,X:S))),and(isLNat(x52:S),isLNatKind(x52:S))),and(tt,X:S),x52:S) 0.016/0.016 t => afterNth(X:S,x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 44 (l' :-> r') => fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> fst(pair(X:S,Y:S))} 0.016/0.016 s => U11(and(and(isNatural(fst(pair(X:S,Y:S))),isNaturalKind(fst(pair(X:S,Y:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),fst(pair(X:S,Y:S)),x52:S) 0.016/0.016 t => afterNth(U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 45 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> head(cons(N:S,XS:S))} 0.016/0.016 s => U11(and(and(isNatural(head(cons(N:S,XS:S))),isNaturalKind(head(cons(N:S,XS:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),head(cons(N:S,XS:S)),x52:S) 0.016/0.016 t => afterNth(U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S),x52:S) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 46 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(afterNth(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(afterNth(V1:S,V2:S))),isNaturalKind(isLNat(afterNth(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(afterNth(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 47 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(fst(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(fst(V1:S))),isNaturalKind(isLNat(fst(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(fst(V1:S)),x52:S) 0.016/0.016 t => afterNth(U61(isPLNatKind(V1:S),V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 48 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(natsFrom(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(natsFrom(V1:S))),isNaturalKind(isLNat(natsFrom(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(natsFrom(V1:S)),x52:S) 0.016/0.016 t => afterNth(U71(isNaturalKind(V1:S),V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 49 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(snd(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(snd(V1:S))),isNaturalKind(isLNat(snd(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(snd(V1:S)),x52:S) 0.016/0.016 t => afterNth(U81(isPLNatKind(V1:S),V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 50 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(tail(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(tail(V1:S))),isNaturalKind(isLNat(tail(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(tail(V1:S)),x52:S) 0.016/0.016 t => afterNth(U91(isLNatKind(V1:S),V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 51 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(take(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(take(V1:S,V2:S))),isNaturalKind(isLNat(take(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(take(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 52 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(cons(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNat(cons(V1:S,V2:S))),isNaturalKind(isLNat(cons(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(cons(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 53 (l' :-> r') => isLNat(nil) -> tt 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNat(nil)} 0.016/0.016 s => U11(and(and(isNatural(isLNat(nil)),isNaturalKind(isLNat(nil))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNat(nil),x52:S) 0.016/0.016 t => afterNth(tt,x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 54 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(afterNth(V1:S,V2:S))),isNaturalKind(isLNatKind(afterNth(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(afterNth(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 55 (l' :-> r') => isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(fst(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(fst(V1:S))),isNaturalKind(isLNatKind(fst(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(fst(V1:S)),x52:S) 0.016/0.016 t => afterNth(isPLNatKind(V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 56 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(natsFrom(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(natsFrom(V1:S))),isNaturalKind(isLNatKind(natsFrom(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(natsFrom(V1:S)),x52:S) 0.016/0.016 t => afterNth(isNaturalKind(V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 57 (l' :-> r') => isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(snd(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(snd(V1:S))),isNaturalKind(isLNatKind(snd(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(snd(V1:S)),x52:S) 0.016/0.016 t => afterNth(isPLNatKind(V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 58 (l' :-> r') => isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(tail(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(tail(V1:S))),isNaturalKind(isLNatKind(tail(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(tail(V1:S)),x52:S) 0.016/0.016 t => afterNth(isLNatKind(V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 59 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(take(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(take(V1:S,V2:S))),isNaturalKind(isLNatKind(take(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(take(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 60 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(cons(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(cons(V1:S,V2:S))),isNaturalKind(isLNatKind(cons(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(cons(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 61 (l' :-> r') => isLNatKind(nil) -> tt 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isLNatKind(nil)} 0.016/0.016 s => U11(and(and(isNatural(isLNatKind(nil)),isNaturalKind(isLNatKind(nil))),and(isLNat(x52:S),isLNatKind(x52:S))),isLNatKind(nil),x52:S) 0.016/0.016 t => afterNth(tt,x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 62 (l' :-> r') => isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNatural(head(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isNatural(head(V1:S))),isNaturalKind(isNatural(head(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isNatural(head(V1:S)),x52:S) 0.016/0.016 t => afterNth(U111(isLNatKind(V1:S),V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 63 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNatural(sel(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isNatural(sel(V1:S,V2:S))),isNaturalKind(isNatural(sel(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isNatural(sel(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 64 (l' :-> r') => isNatural(0) -> tt 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNatural(0)} 0.016/0.016 s => U11(and(and(isNatural(isNatural(0)),isNaturalKind(isNatural(0))),and(isLNat(x52:S),isLNatKind(x52:S))),isNatural(0),x52:S) 0.016/0.016 t => afterNth(tt,x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 65 (l' :-> r') => isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNatural(s(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isNatural(s(V1:S))),isNaturalKind(isNatural(s(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isNatural(s(V1:S)),x52:S) 0.016/0.016 t => afterNth(U121(isNaturalKind(V1:S),V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 66 (l' :-> r') => isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNaturalKind(head(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isNaturalKind(head(V1:S))),isNaturalKind(isNaturalKind(head(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isNaturalKind(head(V1:S)),x52:S) 0.016/0.016 t => afterNth(isLNatKind(V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 67 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNaturalKind(sel(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isNaturalKind(sel(V1:S,V2:S))),isNaturalKind(isNaturalKind(sel(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isNaturalKind(sel(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 68 (l' :-> r') => isNaturalKind(0) -> tt 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNaturalKind(0)} 0.016/0.016 s => U11(and(and(isNatural(isNaturalKind(0)),isNaturalKind(isNaturalKind(0))),and(isLNat(x52:S),isLNatKind(x52:S))),isNaturalKind(0),x52:S) 0.016/0.016 t => afterNth(tt,x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 69 (l' :-> r') => isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isNaturalKind(s(V1:S))} 0.016/0.016 s => U11(and(and(isNatural(isNaturalKind(s(V1:S))),isNaturalKind(isNaturalKind(s(V1:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isNaturalKind(s(V1:S)),x52:S) 0.016/0.016 t => afterNth(isNaturalKind(V1:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 70 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isPLNat(splitAt(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isPLNat(splitAt(V1:S,V2:S))),isNaturalKind(isPLNat(splitAt(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isPLNat(splitAt(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 71 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isPLNat(pair(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isPLNat(pair(V1:S,V2:S))),isNaturalKind(isPLNat(pair(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isPLNat(pair(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 72 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isNaturalKind(isPLNatKind(splitAt(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isPLNatKind(splitAt(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 73 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> isPLNatKind(pair(V1:S,V2:S))} 0.016/0.016 s => U11(and(and(isNatural(isPLNatKind(pair(V1:S,V2:S))),isNaturalKind(isPLNatKind(pair(V1:S,V2:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),isPLNatKind(pair(V1:S,V2:S)),x52:S) 0.016/0.016 t => afterNth(and(isLNatKind(V1:S),isLNatKind(V2:S)),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 74 (l' :-> r') => natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> natsFrom(N:S)} 0.016/0.016 s => U11(and(and(isNatural(natsFrom(N:S)),isNaturalKind(natsFrom(N:S))),and(isLNat(x52:S),isLNatKind(x52:S))),natsFrom(N:S),x52:S) 0.016/0.016 t => afterNth(U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 75 (l' :-> r') => sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> sel(N:S,XS:S)} 0.016/0.016 s => U11(and(and(isNatural(sel(N:S,XS:S)),isNaturalKind(sel(N:S,XS:S))),and(isLNat(x52:S),isLNatKind(x52:S))),sel(N:S,XS:S),x52:S) 0.016/0.016 t => afterNth(U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x52:S) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => U11(and(and(isNatural(snd(pair(X:S,Y:S))),isNaturalKind(snd(pair(X:S,Y:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),snd(pair(X:S,Y:S)),x52:S) 0.016/0.016 t => afterNth(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> splitAt(0,XS:S)} 0.016/0.016 s => U11(and(and(isNatural(splitAt(0,XS:S)),isNaturalKind(splitAt(0,XS:S))),and(isLNat(x52:S),isLNatKind(x52:S))),splitAt(0,XS:S),x52:S) 0.016/0.016 t => afterNth(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U11(and(and(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),isNaturalKind(splitAt(s(N:S),cons(X:S,XS:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),splitAt(s(N:S),cons(X:S,XS:S)),x52:S) 0.016/0.016 t => afterNth(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U11(and(and(isNatural(tail(cons(N:S,XS:S))),isNaturalKind(tail(cons(N:S,XS:S)))),and(isLNat(x52:S),isLNatKind(x52:S))),tail(cons(N:S,XS:S)),x52:S) 0.016/0.016 t => afterNth(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x51:S 0.016/0.016 Pos x51:S in l => [1] 0.016/0.016 Sigma => {x51:S -> take(N:S,XS:S)} 0.016/0.016 s => U11(and(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),and(isLNat(x52:S),isLNatKind(x52:S))),take(N:S,XS:S),x52:S) 0.016/0.016 t => afterNth(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x52:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 44 (l' :-> r') => fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> fst(pair(X:S,Y:S))} 0.016/0.016 s => U21(and(and(isLNat(fst(pair(X:S,Y:S))),isLNatKind(fst(pair(X:S,Y:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),fst(pair(X:S,Y:S))) 0.016/0.016 t => fst(pair(U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S),x55:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 45 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> head(cons(N:S,XS:S))} 0.016/0.016 s => U21(and(and(isLNat(head(cons(N:S,XS:S))),isLNatKind(head(cons(N:S,XS:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),head(cons(N:S,XS:S))) 0.016/0.016 t => fst(pair(U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 46 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(afterNth(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(afterNth(V1:S,V2:S))),isLNatKind(isLNat(afterNth(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(afterNth(V1:S,V2:S))) 0.016/0.016 t => fst(pair(U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 47 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(fst(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(fst(V1:S))),isLNatKind(isLNat(fst(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(fst(V1:S))) 0.016/0.016 t => fst(pair(U61(isPLNatKind(V1:S),V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 48 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(natsFrom(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(natsFrom(V1:S))),isLNatKind(isLNat(natsFrom(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(natsFrom(V1:S))) 0.016/0.016 t => fst(pair(U71(isNaturalKind(V1:S),V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 49 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(snd(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(snd(V1:S))),isLNatKind(isLNat(snd(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(snd(V1:S))) 0.016/0.016 t => fst(pair(U81(isPLNatKind(V1:S),V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 50 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(tail(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(tail(V1:S))),isLNatKind(isLNat(tail(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(tail(V1:S))) 0.016/0.016 t => fst(pair(U91(isLNatKind(V1:S),V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 51 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(take(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(take(V1:S,V2:S))),isLNatKind(isLNat(take(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(take(V1:S,V2:S))) 0.016/0.016 t => fst(pair(U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 52 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(cons(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNat(cons(V1:S,V2:S))),isLNatKind(isLNat(cons(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(cons(V1:S,V2:S))) 0.016/0.016 t => fst(pair(U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 53 (l' :-> r') => isLNat(nil) -> tt 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNat(nil)} 0.016/0.016 s => U21(and(and(isLNat(isLNat(nil)),isLNatKind(isLNat(nil))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNat(nil)) 0.016/0.016 t => fst(pair(tt,x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 54 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(afterNth(V1:S,V2:S))),isLNatKind(isLNatKind(afterNth(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(afterNth(V1:S,V2:S))) 0.016/0.016 t => fst(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 55 (l' :-> r') => isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(fst(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(fst(V1:S))),isLNatKind(isLNatKind(fst(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(fst(V1:S))) 0.016/0.016 t => fst(pair(isPLNatKind(V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 56 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(natsFrom(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(natsFrom(V1:S))),isLNatKind(isLNatKind(natsFrom(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(natsFrom(V1:S))) 0.016/0.016 t => fst(pair(isNaturalKind(V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 57 (l' :-> r') => isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(snd(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(snd(V1:S))),isLNatKind(isLNatKind(snd(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(snd(V1:S))) 0.016/0.016 t => fst(pair(isPLNatKind(V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 58 (l' :-> r') => isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(tail(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(tail(V1:S))),isLNatKind(isLNatKind(tail(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(tail(V1:S))) 0.016/0.016 t => fst(pair(isLNatKind(V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 59 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(take(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(take(V1:S,V2:S))),isLNatKind(isLNatKind(take(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(take(V1:S,V2:S))) 0.016/0.016 t => fst(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 60 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(cons(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(cons(V1:S,V2:S))),isLNatKind(isLNatKind(cons(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(cons(V1:S,V2:S))) 0.016/0.016 t => fst(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 61 (l' :-> r') => isLNatKind(nil) -> tt 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isLNatKind(nil)} 0.016/0.016 s => U21(and(and(isLNat(isLNatKind(nil)),isLNatKind(isLNatKind(nil))),and(isLNat(x55:S),isLNatKind(x55:S))),isLNatKind(nil)) 0.016/0.016 t => fst(pair(tt,x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 62 (l' :-> r') => isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNatural(head(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isNatural(head(V1:S))),isLNatKind(isNatural(head(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isNatural(head(V1:S))) 0.016/0.016 t => fst(pair(U111(isLNatKind(V1:S),V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 63 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNatural(sel(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isNatural(sel(V1:S,V2:S))),isLNatKind(isNatural(sel(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isNatural(sel(V1:S,V2:S))) 0.016/0.016 t => fst(pair(U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 64 (l' :-> r') => isNatural(0) -> tt 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNatural(0)} 0.016/0.016 s => U21(and(and(isLNat(isNatural(0)),isLNatKind(isNatural(0))),and(isLNat(x55:S),isLNatKind(x55:S))),isNatural(0)) 0.016/0.016 t => fst(pair(tt,x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 65 (l' :-> r') => isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNatural(s(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isNatural(s(V1:S))),isLNatKind(isNatural(s(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isNatural(s(V1:S))) 0.016/0.016 t => fst(pair(U121(isNaturalKind(V1:S),V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 66 (l' :-> r') => isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNaturalKind(head(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isNaturalKind(head(V1:S))),isLNatKind(isNaturalKind(head(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isNaturalKind(head(V1:S))) 0.016/0.016 t => fst(pair(isLNatKind(V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 67 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNaturalKind(sel(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isNaturalKind(sel(V1:S,V2:S))),isLNatKind(isNaturalKind(sel(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isNaturalKind(sel(V1:S,V2:S))) 0.016/0.016 t => fst(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 68 (l' :-> r') => isNaturalKind(0) -> tt 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNaturalKind(0)} 0.016/0.016 s => U21(and(and(isLNat(isNaturalKind(0)),isLNatKind(isNaturalKind(0))),and(isLNat(x55:S),isLNatKind(x55:S))),isNaturalKind(0)) 0.016/0.016 t => fst(pair(tt,x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 69 (l' :-> r') => isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isNaturalKind(s(V1:S))} 0.016/0.016 s => U21(and(and(isLNat(isNaturalKind(s(V1:S))),isLNatKind(isNaturalKind(s(V1:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isNaturalKind(s(V1:S))) 0.016/0.016 t => fst(pair(isNaturalKind(V1:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 70 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isPLNat(splitAt(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isPLNat(splitAt(V1:S,V2:S))),isLNatKind(isPLNat(splitAt(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isPLNat(splitAt(V1:S,V2:S))) 0.016/0.016 t => fst(pair(U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 71 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isPLNat(pair(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isPLNat(pair(V1:S,V2:S))),isLNatKind(isPLNat(pair(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isPLNat(pair(V1:S,V2:S))) 0.016/0.016 t => fst(pair(U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 72 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isPLNatKind(splitAt(V1:S,V2:S))),isLNatKind(isPLNatKind(splitAt(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isPLNatKind(splitAt(V1:S,V2:S))) 0.016/0.016 t => fst(pair(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 73 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> isPLNatKind(pair(V1:S,V2:S))} 0.016/0.016 s => U21(and(and(isLNat(isPLNatKind(pair(V1:S,V2:S))),isLNatKind(isPLNatKind(pair(V1:S,V2:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),isPLNatKind(pair(V1:S,V2:S))) 0.016/0.016 t => fst(pair(and(isLNatKind(V1:S),isLNatKind(V2:S)),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 74 (l' :-> r') => natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> natsFrom(N:S)} 0.016/0.016 s => U21(and(and(isLNat(natsFrom(N:S)),isLNatKind(natsFrom(N:S))),and(isLNat(x55:S),isLNatKind(x55:S))),natsFrom(N:S)) 0.016/0.016 t => fst(pair(U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S),x55:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 75 (l' :-> r') => sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> sel(N:S,XS:S)} 0.016/0.016 s => U21(and(and(isLNat(sel(N:S,XS:S)),isLNatKind(sel(N:S,XS:S))),and(isLNat(x55:S),isLNatKind(x55:S))),sel(N:S,XS:S)) 0.016/0.016 t => fst(pair(U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => U21(and(and(isLNat(snd(pair(X:S,Y:S))),isLNatKind(snd(pair(X:S,Y:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),snd(pair(X:S,Y:S))) 0.016/0.016 t => fst(pair(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S),x55:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> splitAt(0,XS:S)} 0.016/0.016 s => U21(and(and(isLNat(splitAt(0,XS:S)),isLNatKind(splitAt(0,XS:S))),and(isLNat(x55:S),isLNatKind(x55:S))),splitAt(0,XS:S)) 0.016/0.016 t => fst(pair(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U21(and(and(isLNat(splitAt(s(N:S),cons(X:S,XS:S))),isLNatKind(splitAt(s(N:S),cons(X:S,XS:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),splitAt(s(N:S),cons(X:S,XS:S))) 0.016/0.016 t => fst(pair(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S),x55:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U21(and(and(isLNat(tail(cons(N:S,XS:S))),isLNatKind(tail(cons(N:S,XS:S)))),and(isLNat(x55:S),isLNatKind(x55:S))),tail(cons(N:S,XS:S))) 0.016/0.016 t => fst(pair(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x55:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x54:S 0.016/0.016 Pos x54:S in l => [1,1] 0.016/0.016 Sigma => {x54:S -> take(N:S,XS:S)} 0.016/0.016 s => U21(and(and(isLNat(take(N:S,XS:S)),isLNatKind(take(N:S,XS:S))),and(isLNat(x55:S),isLNatKind(x55:S))),take(N:S,XS:S)) 0.016/0.016 t => fst(pair(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x55:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 45 (l' :-> r') => head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> head(cons(N:S,XS:S))} 0.016/0.016 s => U31(and(and(isNatural(head(cons(N:S,XS:S))),isNaturalKind(head(cons(N:S,XS:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),head(cons(N:S,XS:S))) 0.016/0.016 t => head(cons(U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S),x57:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 46 (l' :-> r') => isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(afterNth(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(afterNth(V1:S,V2:S))),isNaturalKind(isLNat(afterNth(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(afterNth(V1:S,V2:S))) 0.016/0.016 t => head(cons(U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 47 (l' :-> r') => isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(fst(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(fst(V1:S))),isNaturalKind(isLNat(fst(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(fst(V1:S))) 0.016/0.016 t => head(cons(U61(isPLNatKind(V1:S),V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 48 (l' :-> r') => isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(natsFrom(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(natsFrom(V1:S))),isNaturalKind(isLNat(natsFrom(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(natsFrom(V1:S))) 0.016/0.016 t => head(cons(U71(isNaturalKind(V1:S),V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 49 (l' :-> r') => isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(snd(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(snd(V1:S))),isNaturalKind(isLNat(snd(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(snd(V1:S))) 0.016/0.016 t => head(cons(U81(isPLNatKind(V1:S),V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 50 (l' :-> r') => isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(tail(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(tail(V1:S))),isNaturalKind(isLNat(tail(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(tail(V1:S))) 0.016/0.016 t => head(cons(U91(isLNatKind(V1:S),V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 51 (l' :-> r') => isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(take(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(take(V1:S,V2:S))),isNaturalKind(isLNat(take(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(take(V1:S,V2:S))) 0.016/0.016 t => head(cons(U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 52 (l' :-> r') => isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(cons(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNat(cons(V1:S,V2:S))),isNaturalKind(isLNat(cons(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(cons(V1:S,V2:S))) 0.016/0.016 t => head(cons(U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 53 (l' :-> r') => isLNat(nil) -> tt 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNat(nil)} 0.016/0.016 s => U31(and(and(isNatural(isLNat(nil)),isNaturalKind(isLNat(nil))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNat(nil)) 0.016/0.016 t => head(cons(tt,x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 54 (l' :-> r') => isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(afterNth(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(afterNth(V1:S,V2:S))),isNaturalKind(isLNatKind(afterNth(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(afterNth(V1:S,V2:S))) 0.016/0.016 t => head(cons(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 55 (l' :-> r') => isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(fst(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(fst(V1:S))),isNaturalKind(isLNatKind(fst(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(fst(V1:S))) 0.016/0.016 t => head(cons(isPLNatKind(V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 56 (l' :-> r') => isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(natsFrom(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(natsFrom(V1:S))),isNaturalKind(isLNatKind(natsFrom(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(natsFrom(V1:S))) 0.016/0.016 t => head(cons(isNaturalKind(V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 57 (l' :-> r') => isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(snd(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(snd(V1:S))),isNaturalKind(isLNatKind(snd(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(snd(V1:S))) 0.016/0.016 t => head(cons(isPLNatKind(V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 58 (l' :-> r') => isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(tail(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(tail(V1:S))),isNaturalKind(isLNatKind(tail(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(tail(V1:S))) 0.016/0.016 t => head(cons(isLNatKind(V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 59 (l' :-> r') => isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(take(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(take(V1:S,V2:S))),isNaturalKind(isLNatKind(take(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(take(V1:S,V2:S))) 0.016/0.016 t => head(cons(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 60 (l' :-> r') => isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(cons(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(cons(V1:S,V2:S))),isNaturalKind(isLNatKind(cons(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(cons(V1:S,V2:S))) 0.016/0.016 t => head(cons(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 61 (l' :-> r') => isLNatKind(nil) -> tt 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isLNatKind(nil)} 0.016/0.016 s => U31(and(and(isNatural(isLNatKind(nil)),isNaturalKind(isLNatKind(nil))),and(isLNat(x57:S),isLNatKind(x57:S))),isLNatKind(nil)) 0.016/0.016 t => head(cons(tt,x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 62 (l' :-> r') => isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNatural(head(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isNatural(head(V1:S))),isNaturalKind(isNatural(head(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isNatural(head(V1:S))) 0.016/0.016 t => head(cons(U111(isLNatKind(V1:S),V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 63 (l' :-> r') => isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNatural(sel(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isNatural(sel(V1:S,V2:S))),isNaturalKind(isNatural(sel(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isNatural(sel(V1:S,V2:S))) 0.016/0.016 t => head(cons(U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 64 (l' :-> r') => isNatural(0) -> tt 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNatural(0)} 0.016/0.016 s => U31(and(and(isNatural(isNatural(0)),isNaturalKind(isNatural(0))),and(isLNat(x57:S),isLNatKind(x57:S))),isNatural(0)) 0.016/0.016 t => head(cons(tt,x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 65 (l' :-> r') => isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNatural(s(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isNatural(s(V1:S))),isNaturalKind(isNatural(s(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isNatural(s(V1:S))) 0.016/0.016 t => head(cons(U121(isNaturalKind(V1:S),V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 66 (l' :-> r') => isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNaturalKind(head(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isNaturalKind(head(V1:S))),isNaturalKind(isNaturalKind(head(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isNaturalKind(head(V1:S))) 0.016/0.016 t => head(cons(isLNatKind(V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 67 (l' :-> r') => isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNaturalKind(sel(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isNaturalKind(sel(V1:S,V2:S))),isNaturalKind(isNaturalKind(sel(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isNaturalKind(sel(V1:S,V2:S))) 0.016/0.016 t => head(cons(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 68 (l' :-> r') => isNaturalKind(0) -> tt 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNaturalKind(0)} 0.016/0.016 s => U31(and(and(isNatural(isNaturalKind(0)),isNaturalKind(isNaturalKind(0))),and(isLNat(x57:S),isLNatKind(x57:S))),isNaturalKind(0)) 0.016/0.016 t => head(cons(tt,x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 69 (l' :-> r') => isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isNaturalKind(s(V1:S))} 0.016/0.016 s => U31(and(and(isNatural(isNaturalKind(s(V1:S))),isNaturalKind(isNaturalKind(s(V1:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isNaturalKind(s(V1:S))) 0.016/0.016 t => head(cons(isNaturalKind(V1:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 70 (l' :-> r') => isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isPLNat(splitAt(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isPLNat(splitAt(V1:S,V2:S))),isNaturalKind(isPLNat(splitAt(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isPLNat(splitAt(V1:S,V2:S))) 0.016/0.016 t => head(cons(U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 71 (l' :-> r') => isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isPLNat(pair(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isPLNat(pair(V1:S,V2:S))),isNaturalKind(isPLNat(pair(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isPLNat(pair(V1:S,V2:S))) 0.016/0.016 t => head(cons(U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 72 (l' :-> r') => isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isPLNatKind(splitAt(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isPLNatKind(splitAt(V1:S,V2:S))),isNaturalKind(isPLNatKind(splitAt(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isPLNatKind(splitAt(V1:S,V2:S))) 0.016/0.016 t => head(cons(and(isNaturalKind(V1:S),isLNatKind(V2:S)),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 73 (l' :-> r') => isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> isPLNatKind(pair(V1:S,V2:S))} 0.016/0.016 s => U31(and(and(isNatural(isPLNatKind(pair(V1:S,V2:S))),isNaturalKind(isPLNatKind(pair(V1:S,V2:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),isPLNatKind(pair(V1:S,V2:S))) 0.016/0.016 t => head(cons(and(isLNatKind(V1:S),isLNatKind(V2:S)),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 74 (l' :-> r') => natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> natsFrom(N:S)} 0.016/0.016 s => U31(and(and(isNatural(natsFrom(N:S)),isNaturalKind(natsFrom(N:S))),and(isLNat(x57:S),isLNatKind(x57:S))),natsFrom(N:S)) 0.016/0.016 t => head(cons(U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 75 (l' :-> r') => sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> sel(N:S,XS:S)} 0.016/0.016 s => U31(and(and(isNatural(sel(N:S,XS:S)),isNaturalKind(sel(N:S,XS:S))),and(isLNat(x57:S),isLNatKind(x57:S))),sel(N:S,XS:S)) 0.016/0.016 t => head(cons(U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x57:S)) 0.016/0.016 NW => 0 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => U31(and(and(isNatural(snd(pair(X:S,Y:S))),isNaturalKind(snd(pair(X:S,Y:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),snd(pair(X:S,Y:S))) 0.016/0.016 t => head(cons(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> splitAt(0,XS:S)} 0.016/0.016 s => U31(and(and(isNatural(splitAt(0,XS:S)),isNaturalKind(splitAt(0,XS:S))),and(isLNat(x57:S),isLNatKind(x57:S))),splitAt(0,XS:S)) 0.016/0.016 t => head(cons(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U31(and(and(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),isNaturalKind(splitAt(s(N:S),cons(X:S,XS:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),splitAt(s(N:S),cons(X:S,XS:S))) 0.016/0.016 t => head(cons(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U31(and(and(isNatural(tail(cons(N:S,XS:S))),isNaturalKind(tail(cons(N:S,XS:S)))),and(isLNat(x57:S),isLNatKind(x57:S))),tail(cons(N:S,XS:S))) 0.016/0.016 t => head(cons(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x56:S 0.016/0.016 Pos x56:S in l => [1,1] 0.016/0.016 Sigma => {x56:S -> take(N:S,XS:S)} 0.016/0.016 s => U31(and(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),and(isLNat(x57:S),isLNatKind(x57:S))),take(N:S,XS:S)) 0.016/0.016 t => head(cons(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x57:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 74 (l' :-> r') => natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> natsFrom(N:S)} 0.016/0.016 s => U161(and(isNatural(natsFrom(N:S)),isNaturalKind(natsFrom(N:S))),natsFrom(N:S)) 0.016/0.016 t => natsFrom(U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 75 (l' :-> r') => sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> sel(N:S,XS:S)} 0.016/0.016 s => U161(and(isNatural(sel(N:S,XS:S)),isNaturalKind(sel(N:S,XS:S))),sel(N:S,XS:S)) 0.016/0.016 t => natsFrom(U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => U161(and(isNatural(snd(pair(X:S,Y:S))),isNaturalKind(snd(pair(X:S,Y:S)))),snd(pair(X:S,Y:S))) 0.016/0.016 t => natsFrom(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> splitAt(0,XS:S)} 0.016/0.016 s => U161(and(isNatural(splitAt(0,XS:S)),isNaturalKind(splitAt(0,XS:S))),splitAt(0,XS:S)) 0.016/0.016 t => natsFrom(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U161(and(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),isNaturalKind(splitAt(s(N:S),cons(X:S,XS:S)))),splitAt(s(N:S),cons(X:S,XS:S))) 0.016/0.016 t => natsFrom(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U161(and(isNatural(tail(cons(N:S,XS:S))),isNaturalKind(tail(cons(N:S,XS:S)))),tail(cons(N:S,XS:S))) 0.016/0.016 t => natsFrom(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x94:S 0.016/0.016 Pos x94:S in l => [1] 0.016/0.016 Sigma => {x94:S -> take(N:S,XS:S)} 0.016/0.016 s => U161(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),take(N:S,XS:S)) 0.016/0.016 t => natsFrom(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S) 0.016/0.016 Rule 75 (l' :-> r') => sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x95:S 0.016/0.016 Pos x95:S in l => [1] 0.016/0.016 Sigma => {x95:S -> sel(N:S,XS:S)} 0.016/0.016 s => U171(and(and(isNatural(sel(N:S,XS:S)),isNaturalKind(sel(N:S,XS:S))),and(isLNat(x96:S),isLNatKind(x96:S))),sel(N:S,XS:S),x96:S) 0.016/0.016 t => sel(U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x96:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x95:S 0.016/0.016 Pos x95:S in l => [1] 0.016/0.016 Sigma => {x95:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => U171(and(and(isNatural(snd(pair(X:S,Y:S))),isNaturalKind(snd(pair(X:S,Y:S)))),and(isLNat(x96:S),isLNatKind(x96:S))),snd(pair(X:S,Y:S)),x96:S) 0.016/0.016 t => sel(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S),x96:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x95:S 0.016/0.016 Pos x95:S in l => [1] 0.016/0.016 Sigma => {x95:S -> splitAt(0,XS:S)} 0.016/0.016 s => U171(and(and(isNatural(splitAt(0,XS:S)),isNaturalKind(splitAt(0,XS:S))),and(isLNat(x96:S),isLNatKind(x96:S))),splitAt(0,XS:S),x96:S) 0.016/0.016 t => sel(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S),x96:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x95:S 0.016/0.016 Pos x95:S in l => [1] 0.016/0.016 Sigma => {x95:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U171(and(and(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),isNaturalKind(splitAt(s(N:S),cons(X:S,XS:S)))),and(isLNat(x96:S),isLNatKind(x96:S))),splitAt(s(N:S),cons(X:S,XS:S)),x96:S) 0.016/0.016 t => sel(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S),x96:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x95:S 0.016/0.016 Pos x95:S in l => [1] 0.016/0.016 Sigma => {x95:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U171(and(and(isNatural(tail(cons(N:S,XS:S))),isNaturalKind(tail(cons(N:S,XS:S)))),and(isLNat(x96:S),isLNatKind(x96:S))),tail(cons(N:S,XS:S)),x96:S) 0.016/0.016 t => sel(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x96:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x95:S 0.016/0.016 Pos x95:S in l => [1] 0.016/0.016 Sigma => {x95:S -> take(N:S,XS:S)} 0.016/0.016 s => U171(and(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),and(isLNat(x96:S),isLNatKind(x96:S))),take(N:S,XS:S),x96:S) 0.016/0.016 t => sel(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x96:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => snd(pair(x97:S,x98:S)) -> U181(and(and(isLNat(x97:S),isLNatKind(x97:S)),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 Rule 76 (l' :-> r') => snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 Var => x97:S 0.016/0.016 Pos x97:S in l => [1,1] 0.016/0.016 Sigma => {x97:S -> snd(pair(X:S,Y:S))} 0.016/0.016 s => U181(and(and(isLNat(snd(pair(X:S,Y:S))),isLNatKind(snd(pair(X:S,Y:S)))),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 t => snd(pair(U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S),x98:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => snd(pair(x97:S,x98:S)) -> U181(and(and(isLNat(x97:S),isLNatKind(x97:S)),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x97:S 0.016/0.016 Pos x97:S in l => [1,1] 0.016/0.016 Sigma => {x97:S -> splitAt(0,XS:S)} 0.016/0.016 s => U181(and(and(isLNat(splitAt(0,XS:S)),isLNatKind(splitAt(0,XS:S))),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 t => snd(pair(U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S),x98:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => snd(pair(x97:S,x98:S)) -> U181(and(and(isLNat(x97:S),isLNatKind(x97:S)),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x97:S 0.016/0.016 Pos x97:S in l => [1,1] 0.016/0.016 Sigma => {x97:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U181(and(and(isLNat(splitAt(s(N:S),cons(X:S,XS:S))),isLNatKind(splitAt(s(N:S),cons(X:S,XS:S)))),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 t => snd(pair(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S),x98:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => snd(pair(x97:S,x98:S)) -> U181(and(and(isLNat(x97:S),isLNatKind(x97:S)),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x97:S 0.016/0.016 Pos x97:S in l => [1,1] 0.016/0.016 Sigma => {x97:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U181(and(and(isLNat(tail(cons(N:S,XS:S))),isLNatKind(tail(cons(N:S,XS:S)))),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 t => snd(pair(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x98:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => snd(pair(x97:S,x98:S)) -> U181(and(and(isLNat(x97:S),isLNatKind(x97:S)),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x97:S 0.016/0.016 Pos x97:S in l => [1,1] 0.016/0.016 Sigma => {x97:S -> take(N:S,XS:S)} 0.016/0.016 s => U181(and(and(isLNat(take(N:S,XS:S)),isLNatKind(take(N:S,XS:S))),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S) 0.016/0.016 t => snd(pair(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x98:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(0,x99:S) -> U191(and(isLNat(x99:S),isLNatKind(x99:S)),x99:S) 0.016/0.016 Rule 77 (l' :-> r') => splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 Var => x99:S 0.016/0.016 Pos x99:S in l => [2] 0.016/0.016 Sigma => {x99:S -> splitAt(0,XS:S)} 0.016/0.016 s => U191(and(isLNat(splitAt(0,XS:S)),isLNatKind(splitAt(0,XS:S))),splitAt(0,XS:S)) 0.016/0.016 t => splitAt(0,U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(0,x99:S) -> U191(and(isLNat(x99:S),isLNatKind(x99:S)),x99:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x99:S 0.016/0.016 Pos x99:S in l => [2] 0.016/0.016 Sigma => {x99:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U191(and(isLNat(splitAt(s(N:S),cons(X:S,XS:S))),isLNatKind(splitAt(s(N:S),cons(X:S,XS:S)))),splitAt(s(N:S),cons(X:S,XS:S))) 0.016/0.016 t => splitAt(0,U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(0,x99:S) -> U191(and(isLNat(x99:S),isLNatKind(x99:S)),x99:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x99:S 0.016/0.016 Pos x99:S in l => [2] 0.016/0.016 Sigma => {x99:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U191(and(isLNat(tail(cons(N:S,XS:S))),isLNatKind(tail(cons(N:S,XS:S)))),tail(cons(N:S,XS:S))) 0.016/0.016 t => splitAt(0,U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(0,x99:S) -> U191(and(isLNat(x99:S),isLNatKind(x99:S)),x99:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x99:S 0.016/0.016 Pos x99:S in l => [2] 0.016/0.016 Sigma => {x99:S -> take(N:S,XS:S)} 0.016/0.016 s => U191(and(isLNat(take(N:S,XS:S)),isLNatKind(take(N:S,XS:S))),take(N:S,XS:S)) 0.016/0.016 t => splitAt(0,U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(s(x100:S),cons(x101:S,x102:S)) -> U201(and(and(isNatural(x100:S),isNaturalKind(x100:S)),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),x100:S,x101:S,x102:S) 0.016/0.016 Rule 78 (l' :-> r') => splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 Var => x100:S 0.016/0.016 Pos x100:S in l => [1,1] 0.016/0.016 Sigma => {x100:S -> splitAt(s(N:S),cons(X:S,XS:S))} 0.016/0.016 s => U201(and(and(isNatural(splitAt(s(N:S),cons(X:S,XS:S))),isNaturalKind(splitAt(s(N:S),cons(X:S,XS:S)))),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),splitAt(s(N:S),cons(X:S,XS:S)),x101:S,x102:S) 0.016/0.016 t => splitAt(s(U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S)),cons(x101:S,x102:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(s(x100:S),cons(x101:S,x102:S)) -> U201(and(and(isNatural(x100:S),isNaturalKind(x100:S)),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),x100:S,x101:S,x102:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x100:S 0.016/0.016 Pos x100:S in l => [1,1] 0.016/0.016 Sigma => {x100:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U201(and(and(isNatural(tail(cons(N:S,XS:S))),isNaturalKind(tail(cons(N:S,XS:S)))),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),tail(cons(N:S,XS:S)),x101:S,x102:S) 0.016/0.016 t => splitAt(s(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S)),cons(x101:S,x102:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => splitAt(s(x100:S),cons(x101:S,x102:S)) -> U201(and(and(isNatural(x100:S),isNaturalKind(x100:S)),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),x100:S,x101:S,x102:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x100:S 0.016/0.016 Pos x100:S in l => [1,1] 0.016/0.016 Sigma => {x100:S -> take(N:S,XS:S)} 0.016/0.016 s => U201(and(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),take(N:S,XS:S),x101:S,x102:S) 0.016/0.016 t => splitAt(s(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S)),cons(x101:S,x102:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => tail(cons(x103:S,x104:S)) -> U211(and(and(isNatural(x103:S),isNaturalKind(x103:S)),and(isLNat(x104:S),isLNatKind(x104:S))),x104:S) 0.016/0.016 Rule 79 (l' :-> r') => tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 Var => x103:S 0.016/0.016 Pos x103:S in l => [1,1] 0.016/0.016 Sigma => {x103:S -> tail(cons(N:S,XS:S))} 0.016/0.016 s => U211(and(and(isNatural(tail(cons(N:S,XS:S))),isNaturalKind(tail(cons(N:S,XS:S)))),and(isLNat(x104:S),isLNatKind(x104:S))),x104:S) 0.016/0.016 t => tail(cons(U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S),x104:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => tail(cons(x103:S,x104:S)) -> U211(and(and(isNatural(x103:S),isNaturalKind(x103:S)),and(isLNat(x104:S),isLNatKind(x104:S))),x104:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x103:S 0.016/0.016 Pos x103:S in l => [1,1] 0.016/0.016 Sigma => {x103:S -> take(N:S,XS:S)} 0.016/0.016 s => U211(and(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),and(isLNat(x104:S),isLNatKind(x104:S))),x104:S) 0.016/0.016 t => tail(cons(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x104:S)) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 ->Extended u-Critical Pair: 0.016/0.016 Rule 1 (l :-> r) => take(x105:S,x106:S) -> U221(and(and(isNatural(x105:S),isNaturalKind(x105:S)),and(isLNat(x106:S),isLNatKind(x106:S))),x105:S,x106:S) 0.016/0.016 Rule 80 (l' :-> r') => take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 Var => x105:S 0.016/0.016 Pos x105:S in l => [1] 0.016/0.016 Sigma => {x105:S -> take(N:S,XS:S)} 0.016/0.016 s => U221(and(and(isNatural(take(N:S,XS:S)),isNaturalKind(take(N:S,XS:S))),and(isLNat(x106:S),isLNatKind(x106:S))),take(N:S,XS:S),x106:S) 0.016/0.016 t => take(U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S),x106:S) 0.016/0.016 NW => 1 0.016/0.016 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 Confluence Problem: 0.016/0.016 (VAR vNonEmpty:S N:S V1:S V2:S X:S XS:S Y:S YS:S ZS:S) 0.016/0.016 (STRATEGY CONTEXTSENSITIVE 0.016/0.016 (U101 1) 0.016/0.016 (U102 1) 0.016/0.016 (U103 1) 0.016/0.016 (U11 1) 0.016/0.016 (U111 1) 0.016/0.016 (U112 1) 0.016/0.016 (U121 1) 0.016/0.016 (U122 1) 0.016/0.016 (U131 1) 0.016/0.016 (U132 1) 0.016/0.016 (U133 1) 0.016/0.016 (U141 1) 0.016/0.016 (U142 1) 0.016/0.016 (U143 1) 0.016/0.016 (U151 1) 0.016/0.016 (U152 1) 0.016/0.016 (U153 1) 0.016/0.016 (U161 1) 0.016/0.016 (U171 1) 0.016/0.016 (U181 1) 0.016/0.016 (U191 1) 0.016/0.016 (U201 1) 0.016/0.016 (U202 1) 0.016/0.016 (U21 1) 0.016/0.016 (U211 1) 0.016/0.016 (U221 1) 0.016/0.016 (U31 1) 0.016/0.016 (U41 1) 0.016/0.016 (U42 1) 0.016/0.016 (U43 1) 0.016/0.016 (U51 1) 0.016/0.016 (U52 1) 0.016/0.016 (U53 1) 0.016/0.016 (U61 1) 0.016/0.016 (U62 1) 0.016/0.016 (U71 1) 0.016/0.016 (U72 1) 0.016/0.016 (U81 1) 0.016/0.016 (U82 1) 0.016/0.016 (U91 1) 0.016/0.016 (U92 1) 0.016/0.016 (afterNth 1 2) 0.016/0.016 (and 1) 0.016/0.016 (fst 1) 0.016/0.016 (head 1) 0.016/0.016 (isLNat) 0.016/0.016 (isLNatKind) 0.016/0.016 (isNatural) 0.016/0.016 (isNaturalKind) 0.016/0.016 (isPLNat) 0.016/0.016 (isPLNatKind) 0.016/0.016 (natsFrom 1) 0.016/0.016 (sel 1 2) 0.016/0.016 (snd 1) 0.016/0.016 (splitAt 1 2) 0.016/0.016 (tail 1) 0.016/0.016 (take 1 2) 0.016/0.016 (0) 0.016/0.016 (cons 1) 0.016/0.016 (fSNonEmpty) 0.016/0.016 (nil) 0.016/0.016 (pair 1 2) 0.016/0.016 (s 1) 0.016/0.016 (tt) 0.016/0.016 ) 0.016/0.016 (RULES 0.016/0.016 U101(tt,V1:S,V2:S) -> U102(isNatural(V1:S),V2:S) 0.016/0.016 U102(tt,V2:S) -> U103(isLNat(V2:S)) 0.016/0.016 U103(tt) -> tt 0.016/0.016 U11(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.016/0.016 U111(tt,V1:S) -> U112(isLNat(V1:S)) 0.016/0.016 U112(tt) -> tt 0.016/0.016 U121(tt,V1:S) -> U122(isNatural(V1:S)) 0.016/0.016 U122(tt) -> tt 0.016/0.016 U131(tt,V1:S,V2:S) -> U132(isNatural(V1:S),V2:S) 0.016/0.016 U132(tt,V2:S) -> U133(isLNat(V2:S)) 0.016/0.016 U133(tt) -> tt 0.016/0.016 U141(tt,V1:S,V2:S) -> U142(isLNat(V1:S),V2:S) 0.016/0.016 U142(tt,V2:S) -> U143(isLNat(V2:S)) 0.016/0.016 U143(tt) -> tt 0.016/0.016 U151(tt,V1:S,V2:S) -> U152(isNatural(V1:S),V2:S) 0.016/0.016 U152(tt,V2:S) -> U153(isLNat(V2:S)) 0.016/0.016 U153(tt) -> tt 0.016/0.016 U161(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.016/0.016 U171(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.016/0.016 U181(tt,Y:S) -> Y:S 0.016/0.016 U191(tt,XS:S) -> pair(nil,XS:S) 0.016/0.016 U201(tt,N:S,X:S,XS:S) -> U202(splitAt(N:S,XS:S),X:S) 0.016/0.016 U202(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.016/0.016 U21(tt,X:S) -> X:S 0.016/0.016 U211(tt,XS:S) -> XS:S 0.016/0.016 U221(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.016/0.016 U31(tt,N:S) -> N:S 0.016/0.016 U41(tt,V1:S,V2:S) -> U42(isNatural(V1:S),V2:S) 0.016/0.016 U42(tt,V2:S) -> U43(isLNat(V2:S)) 0.016/0.016 U43(tt) -> tt 0.016/0.016 U51(tt,V1:S,V2:S) -> U52(isNatural(V1:S),V2:S) 0.016/0.016 U52(tt,V2:S) -> U53(isLNat(V2:S)) 0.016/0.016 U53(tt) -> tt 0.016/0.016 U61(tt,V1:S) -> U62(isPLNat(V1:S)) 0.016/0.016 U62(tt) -> tt 0.016/0.016 U71(tt,V1:S) -> U72(isNatural(V1:S)) 0.016/0.016 U72(tt) -> tt 0.016/0.016 U81(tt,V1:S) -> U82(isPLNat(V1:S)) 0.016/0.016 U82(tt) -> tt 0.016/0.016 U91(tt,V1:S) -> U92(isLNat(V1:S)) 0.016/0.016 U92(tt) -> tt 0.016/0.016 afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 and(tt,X:S) -> X:S 0.016/0.016 fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(nil) -> tt 0.016/0.016 isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(nil) -> tt 0.016/0.016 isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isNatural(0) -> tt 0.016/0.016 isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isNaturalKind(0) -> tt 0.016/0.016 isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 ) 0.016/0.016 Critical Pairs: 0.016/0.016 => Not trivial, Not overlay, NW1, N1 0.016/0.016 => Not trivial, Not overlay, NW1, N2 0.016/0.016 => Not trivial, Not overlay, NW1, N3 0.016/0.016 => Not trivial, Not overlay, NW1, N4 0.016/0.016 => Not trivial, Not overlay, NW1, N5 0.016/0.016 => Not trivial, Not overlay, NW1, N6 0.016/0.016 => Not trivial, Not overlay, NW1, N7 0.016/0.016 => Not trivial, Not overlay, NW1, N8 0.016/0.016 => Not trivial, Not overlay, NW1, N9 0.016/0.016 => Not trivial, Not overlay, NW1, N10 0.016/0.016 => Not trivial, Not overlay, NW1, N11 0.016/0.016 => Not trivial, Not overlay, NW1, N12 0.016/0.016 => Not trivial, Not overlay, NW1, N13 0.016/0.016 => Not trivial, Not overlay, NW1, N14 0.016/0.016 => Not trivial, Not overlay, NW1, N15 0.016/0.016 => Not trivial, Not overlay, NW1, N16 0.016/0.016 => Not trivial, Not overlay, NW1, N17 0.016/0.016 => Not trivial, Not overlay, NW1, N18 0.016/0.016 => Not trivial, Not overlay, NW1, N19 0.016/0.016 => Not trivial, Not overlay, NW1, N20 0.016/0.016 => Not trivial, Not overlay, NW1, N21 0.016/0.016 => Not trivial, Not overlay, NW1, N22 0.016/0.016 => Not trivial, Not overlay, NW1, N23 0.016/0.016 => Not trivial, Not overlay, NW1, N24 0.016/0.016 => Not trivial, Not overlay, NW1, N25 0.016/0.016 => Not trivial, Not overlay, NW1, N26 0.016/0.016 => Not trivial, Not overlay, NW1, N27 0.016/0.016 => Not trivial, Not overlay, NW1, N28 0.016/0.016 => Not trivial, Not overlay, NW1, N29 0.016/0.016 => Not trivial, Not overlay, NW1, N30 0.016/0.016 => Not trivial, Not overlay, NW1, N31 0.016/0.016 => Not trivial, Not overlay, NW1, N32 0.016/0.016 => Not trivial, Not overlay, NW1, N33 0.016/0.016 => Not trivial, Not overlay, NW1, N34 0.016/0.016 => Not trivial, Not overlay, NW1, N35 0.016/0.016 => Not trivial, Not overlay, NW1, N36 0.016/0.016 => Not trivial, Not overlay, NW1, N37 0.016/0.016 => Not trivial, Not overlay, NW1, N38 0.016/0.016 => Not trivial, Not overlay, NW1, N39 0.016/0.016 => Not trivial, Not overlay, NW1, N40 0.016/0.016 => Not trivial, Not overlay, NW1, N41 0.016/0.016 => Not trivial, Not overlay, NW1, N42 0.016/0.016 => Not trivial, Not overlay, NW1, N43 0.016/0.016 => Not trivial, Not overlay, NW1, N44 0.016/0.016 => Not trivial, Not overlay, NW1, N45 0.016/0.016 => Not trivial, Not overlay, NW1, N46 0.016/0.016 => Not trivial, Not overlay, NW1, N47 0.016/0.016 => Not trivial, Not overlay, NW1, N48 0.016/0.016 => Not trivial, Not overlay, NW1, N49 0.016/0.016 => Not trivial, Not overlay, NW1, N50 0.016/0.016 => Not trivial, Not overlay, NW1, N51 0.016/0.016 => Not trivial, Not overlay, NW1, N52 0.016/0.016 => Not trivial, Not overlay, NW1, N53 0.016/0.016 => Not trivial, Not overlay, NW1, N54 0.016/0.016 => Not trivial, Not overlay, NW1, N55 0.016/0.016 => Not trivial, Not overlay, NW1, N56 0.016/0.016 => Not trivial, Not overlay, NW1, N57 0.016/0.016 => Not trivial, Not overlay, NW1, N58 0.016/0.016 => Not trivial, Not overlay, NW1, N59 0.016/0.016 => Not trivial, Not overlay, NW1, N60 0.016/0.016 => Not trivial, Not overlay, NW1, N61 0.016/0.016 => Not trivial, Not overlay, NW0, N62 0.016/0.016 => Not trivial, Not overlay, NW1, N63 0.016/0.016 => Not trivial, Not overlay, NW1, N64 0.016/0.016 => Not trivial, Not overlay, NW1, N65 0.016/0.016 => Not trivial, Not overlay, NW1, N66 0.016/0.016 => Not trivial, Not overlay, NW1, N67 0.016/0.016 => Not trivial, Not overlay, NW1, N68 0.016/0.016 => Not trivial, Not overlay, NW1, N69 0.016/0.016 => Not trivial, Not overlay, NW1, N70 0.016/0.016 => Not trivial, Not overlay, NW1, N71 0.016/0.016 => Not trivial, Not overlay, NW1, N72 0.016/0.016 => Not trivial, Not overlay, NW1, N73 0.016/0.016 => Not trivial, Not overlay, NW1, N74 0.016/0.016 => Not trivial, Not overlay, NW1, N75 0.016/0.016 => Not trivial, Not overlay, NW1, N76 0.016/0.016 => Not trivial, Not overlay, NW1, N77 0.016/0.016 => Not trivial, Not overlay, NW1, N78 0.016/0.016 => Not trivial, Not overlay, NW1, N79 0.016/0.016 => Not trivial, Not overlay, NW1, N80 0.016/0.016 => Not trivial, Not overlay, NW1, N81 0.016/0.016 => Not trivial, Not overlay, NW1, N82 0.016/0.016 => Not trivial, Not overlay, NW1, N83 0.016/0.016 => Not trivial, Not overlay, NW1, N84 0.016/0.016 => Not trivial, Not overlay, NW1, N85 0.016/0.016 => Not trivial, Not overlay, NW1, N86 0.016/0.016 => Not trivial, Not overlay, NW1, N87 0.016/0.016 => Not trivial, Not overlay, NW1, N88 0.016/0.016 => Not trivial, Not overlay, NW1, N89 0.016/0.016 => Not trivial, Not overlay, NW1, N90 0.016/0.016 => Not trivial, Not overlay, NW1, N91 0.016/0.016 => Not trivial, Not overlay, NW0, N92 0.016/0.016 => Not trivial, Not overlay, NW1, N93 0.016/0.016 => Not trivial, Not overlay, NW1, N94 0.016/0.016 => Not trivial, Not overlay, NW1, N95 0.016/0.016 => Not trivial, Not overlay, NW1, N96 0.016/0.016 => Not trivial, Not overlay, NW1, N97 0.016/0.016 => Not trivial, Not overlay, NW0, N98 0.016/0.016 => Not trivial, Not overlay, NW1, N99 0.016/0.016 => Not trivial, Not overlay, NW1, N100 0.016/0.016 => Not trivial, Not overlay, NW1, N101 0.016/0.016 => Not trivial, Not overlay, NW1, N102 0.016/0.016 => Not trivial, Not overlay, NW1, N103 0.016/0.016 => Not trivial, Not overlay, NW1, N104 0.016/0.016 => Not trivial, Not overlay, NW1, N105 0.016/0.016 => Not trivial, Not overlay, NW1, N106 0.016/0.016 => Not trivial, Not overlay, NW1, N107 0.016/0.016 => Not trivial, Not overlay, NW1, N108 0.016/0.016 => Not trivial, Not overlay, NW1, N109 0.016/0.016 => Not trivial, Not overlay, NW1, N110 0.016/0.016 => Not trivial, Not overlay, NW1, N111 0.016/0.016 => Not trivial, Not overlay, NW1, N112 0.016/0.016 => Not trivial, Not overlay, NW1, N113 0.016/0.016 => Not trivial, Not overlay, NW1, N114 0.016/0.016 => Not trivial, Not overlay, NW1, N115 0.016/0.016 => Not trivial, Not overlay, NW1, N116 0.016/0.016 => Not trivial, Not overlay, NW1, N117 0.016/0.016 => Not trivial, Not overlay, NW1, N118 0.016/0.016 => Not trivial, Not overlay, NW1, N119 0.016/0.016 => Not trivial, Not overlay, NW1, N120 0.016/0.016 => Not trivial, Not overlay, NW1, N121 0.016/0.016 => Not trivial, Not overlay, NW1, N122 0.016/0.016 => Not trivial, Not overlay, NW1, N123 0.016/0.016 => Not trivial, Not overlay, NW1, N124 0.016/0.016 => Not trivial, Not overlay, NW1, N125 0.016/0.016 => Not trivial, Not overlay, NW1, N126 0.016/0.016 => Not trivial, Not overlay, NW1, N127 0.016/0.016 => Not trivial, Not overlay, NW0, N128 0.016/0.016 => Not trivial, Not overlay, NW1, N129 0.016/0.016 => Not trivial, Not overlay, NW0, N130 0.016/0.016 => Not trivial, Not overlay, NW1, N131 0.016/0.016 => Not trivial, Not overlay, NW1, N132 0.016/0.016 => Not trivial, Not overlay, NW0, N133 0.016/0.016 => Not trivial, Not overlay, NW0, N134 0.016/0.016 => Not trivial, Not overlay, NW0, N135 0.016/0.016 => Not trivial, Not overlay, NW1, N136 0.016/0.016 => Not trivial, Not overlay, NW1, N137 0.016/0.016 => Not trivial, Not overlay, NW1, N138 0.016/0.016 => Not trivial, Not overlay, NW1, N139 0.016/0.016 => Not trivial, Not overlay, NW1, N140 0.016/0.016 => Not trivial, Not overlay, NW1, N141 0.016/0.016 => Not trivial, Not overlay, NW1, N142 0.016/0.016 => Not trivial, Not overlay, NW1, N143 0.016/0.016 => Not trivial, Not overlay, NW1, N144 0.016/0.016 => Not trivial, Not overlay, NW1, N145 0.016/0.016 => Not trivial, Not overlay, NW1, N146 0.016/0.016 => Not trivial, Not overlay, NW1, N147 0.016/0.016 => Not trivial, Not overlay, NW1, N148 0.016/0.016 => Not trivial, Not overlay, NW1, N149 0.016/0.016 => Not trivial, Not overlay, NW1, N150 0.016/0.016 => Not trivial, Not overlay, NW1, N151 0.016/0.016 => Not trivial, Not overlay, NW1, N152 0.016/0.016 => Not trivial, Not overlay, NW1, N153 0.016/0.016 => Not trivial, Not overlay, NW1, N154 0.016/0.016 => Not trivial, Not overlay, NW1, N155 0.016/0.016 => Not trivial, Not overlay, NW1, N156 0.016/0.016 => Not trivial, Not overlay, NW1, N157 0.016/0.016 => Not trivial, Not overlay, NW1, N158 0.016/0.016 => Not trivial, Not overlay, NW1, N159 0.016/0.016 => Not trivial, Not overlay, NW1, N160 0.016/0.016 => Not trivial, Not overlay, NW1, N161 0.016/0.016 => Not trivial, Not overlay, NW1, N162 0.016/0.016 => Not trivial, Not overlay, NW1, N163 0.016/0.016 => Not trivial, Not overlay, NW1, N164 0.016/0.016 => Not trivial, Not overlay, NW0, N165 0.016/0.016 => Not trivial, Not overlay, NW1, N166 0.016/0.016 => Not trivial, Not overlay, NW1, N167 0.016/0.016 => Not trivial, Not overlay, NW1, N168 0.016/0.016 => Not trivial, Not overlay, NW1, N169 0.016/0.016 => Not trivial, Not overlay, NW1, N170 0.016/0.016 => Not trivial, Not overlay, NW1, N171 0.016/0.016 => Not trivial, Not overlay, NW1, N172 0.016/0.016 => Not trivial, Not overlay, NW1, N173 0.016/0.016 => Not trivial, Not overlay, NW1, N174 0.016/0.016 => Not trivial, Not overlay, NW1, N175 0.016/0.016 => Not trivial, Not overlay, NW1, N176 0.016/0.016 => Not trivial, Not overlay, NW1, N177 0.016/0.016 => Not trivial, Not overlay, NW1, N178 0.016/0.016 => Not trivial, Not overlay, NW1, N179 0.016/0.016 => Not trivial, Not overlay, NW1, N180 0.016/0.016 => Not trivial, Not overlay, NW1, N181 0.016/0.016 => Not trivial, Not overlay, NW1, N182 0.016/0.016 => Not trivial, Not overlay, NW1, N183 0.016/0.016 => Not trivial, Not overlay, NW1, N184 0.016/0.016 => Not trivial, Not overlay, NW1, N185 0.016/0.016 => Not trivial, Not overlay, NW1, N186 0.016/0.016 => Not trivial, Not overlay, NW1, N187 0.016/0.016 => Not trivial, Not overlay, NW1, N188 0.016/0.016 => Not trivial, Not overlay, NW1, N189 0.016/0.016 => Not trivial, Not overlay, NW1, N190 0.016/0.016 => Not trivial, Not overlay, NW1, N191 0.016/0.016 => Not trivial, Not overlay, NW1, N192 0.016/0.016 => Not trivial, Not overlay, NW1, N193 0.016/0.016 => Not trivial, Not overlay, NW1, N194 0.016/0.016 => Not trivial, Not overlay, NW1, N195 0.016/0.016 => Not trivial, Not overlay, NW1, N196 0.016/0.016 => Not trivial, Not overlay, NW1, N197 0.016/0.016 => Not trivial, Not overlay, NW1, N198 0.016/0.016 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.016/0.016 0.016/0.016 Huet Levy Processor: 0.016/0.016 -> Rules: 0.016/0.016 U101(tt,V1:S,V2:S) -> U102(isNatural(V1:S),V2:S) 0.016/0.016 U102(tt,V2:S) -> U103(isLNat(V2:S)) 0.016/0.016 U103(tt) -> tt 0.016/0.016 U11(tt,N:S,XS:S) -> snd(splitAt(N:S,XS:S)) 0.016/0.016 U111(tt,V1:S) -> U112(isLNat(V1:S)) 0.016/0.016 U112(tt) -> tt 0.016/0.016 U121(tt,V1:S) -> U122(isNatural(V1:S)) 0.016/0.016 U122(tt) -> tt 0.016/0.016 U131(tt,V1:S,V2:S) -> U132(isNatural(V1:S),V2:S) 0.016/0.016 U132(tt,V2:S) -> U133(isLNat(V2:S)) 0.016/0.016 U133(tt) -> tt 0.016/0.016 U141(tt,V1:S,V2:S) -> U142(isLNat(V1:S),V2:S) 0.016/0.016 U142(tt,V2:S) -> U143(isLNat(V2:S)) 0.016/0.016 U143(tt) -> tt 0.016/0.016 U151(tt,V1:S,V2:S) -> U152(isNatural(V1:S),V2:S) 0.016/0.016 U152(tt,V2:S) -> U153(isLNat(V2:S)) 0.016/0.016 U153(tt) -> tt 0.016/0.016 U161(tt,N:S) -> cons(N:S,natsFrom(s(N:S))) 0.016/0.016 U171(tt,N:S,XS:S) -> head(afterNth(N:S,XS:S)) 0.016/0.016 U181(tt,Y:S) -> Y:S 0.016/0.016 U191(tt,XS:S) -> pair(nil,XS:S) 0.016/0.016 U201(tt,N:S,X:S,XS:S) -> U202(splitAt(N:S,XS:S),X:S) 0.016/0.016 U202(pair(YS:S,ZS:S),X:S) -> pair(cons(X:S,YS:S),ZS:S) 0.016/0.016 U21(tt,X:S) -> X:S 0.016/0.016 U211(tt,XS:S) -> XS:S 0.016/0.016 U221(tt,N:S,XS:S) -> fst(splitAt(N:S,XS:S)) 0.016/0.016 U31(tt,N:S) -> N:S 0.016/0.016 U41(tt,V1:S,V2:S) -> U42(isNatural(V1:S),V2:S) 0.016/0.016 U42(tt,V2:S) -> U43(isLNat(V2:S)) 0.016/0.016 U43(tt) -> tt 0.016/0.016 U51(tt,V1:S,V2:S) -> U52(isNatural(V1:S),V2:S) 0.016/0.016 U52(tt,V2:S) -> U53(isLNat(V2:S)) 0.016/0.016 U53(tt) -> tt 0.016/0.016 U61(tt,V1:S) -> U62(isPLNat(V1:S)) 0.016/0.016 U62(tt) -> tt 0.016/0.016 U71(tt,V1:S) -> U72(isNatural(V1:S)) 0.016/0.016 U72(tt) -> tt 0.016/0.016 U81(tt,V1:S) -> U82(isPLNat(V1:S)) 0.016/0.016 U82(tt) -> tt 0.016/0.016 U91(tt,V1:S) -> U92(isLNat(V1:S)) 0.016/0.016 U92(tt) -> tt 0.016/0.016 afterNth(N:S,XS:S) -> U11(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 and(tt,X:S) -> X:S 0.016/0.016 fst(pair(X:S,Y:S)) -> U21(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),X:S) 0.016/0.016 head(cons(N:S,XS:S)) -> U31(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S) 0.016/0.016 isLNat(afterNth(V1:S,V2:S)) -> U41(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(fst(V1:S)) -> U61(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(natsFrom(V1:S)) -> U71(isNaturalKind(V1:S),V1:S) 0.016/0.016 isLNat(snd(V1:S)) -> U81(isPLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(tail(V1:S)) -> U91(isLNatKind(V1:S),V1:S) 0.016/0.016 isLNat(take(V1:S,V2:S)) -> U101(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(cons(V1:S,V2:S)) -> U51(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isLNat(nil) -> tt 0.016/0.016 isLNatKind(afterNth(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(fst(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(natsFrom(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isLNatKind(snd(V1:S)) -> isPLNatKind(V1:S) 0.016/0.016 isLNatKind(tail(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isLNatKind(take(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(cons(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isLNatKind(nil) -> tt 0.016/0.016 isNatural(head(V1:S)) -> U111(isLNatKind(V1:S),V1:S) 0.016/0.016 isNatural(sel(V1:S,V2:S)) -> U131(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isNatural(0) -> tt 0.016/0.016 isNatural(s(V1:S)) -> U121(isNaturalKind(V1:S),V1:S) 0.016/0.016 isNaturalKind(head(V1:S)) -> isLNatKind(V1:S) 0.016/0.016 isNaturalKind(sel(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isNaturalKind(0) -> tt 0.016/0.016 isNaturalKind(s(V1:S)) -> isNaturalKind(V1:S) 0.016/0.016 isPLNat(splitAt(V1:S,V2:S)) -> U151(and(isNaturalKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNat(pair(V1:S,V2:S)) -> U141(and(isLNatKind(V1:S),isLNatKind(V2:S)),V1:S,V2:S) 0.016/0.016 isPLNatKind(splitAt(V1:S,V2:S)) -> and(isNaturalKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 isPLNatKind(pair(V1:S,V2:S)) -> and(isLNatKind(V1:S),isLNatKind(V2:S)) 0.016/0.016 natsFrom(N:S) -> U161(and(isNatural(N:S),isNaturalKind(N:S)),N:S) 0.016/0.016 sel(N:S,XS:S) -> U171(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 snd(pair(X:S,Y:S)) -> U181(and(and(isLNat(X:S),isLNatKind(X:S)),and(isLNat(Y:S),isLNatKind(Y:S))),Y:S) 0.016/0.016 splitAt(0,XS:S) -> U191(and(isLNat(XS:S),isLNatKind(XS:S)),XS:S) 0.016/0.016 splitAt(s(N:S),cons(X:S,XS:S)) -> U201(and(and(isNatural(N:S),isNaturalKind(N:S)),and(and(isNatural(X:S),isNaturalKind(X:S)),and(isLNat(XS:S),isLNatKind(XS:S)))),N:S,X:S,XS:S) 0.016/0.016 tail(cons(N:S,XS:S)) -> U211(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),XS:S) 0.016/0.016 take(N:S,XS:S) -> U221(and(and(isNatural(N:S),isNaturalKind(N:S)),and(isLNat(XS:S),isLNatKind(XS:S))),N:S,XS:S) 0.016/0.016 -> Vars: 0.016/0.016 V1, V2, V2, N, XS, V1, V1, V1, V2, V2, V1, V2, V2, V1, V2, V2, N, N, XS, Y, XS, N, X, XS, X, YS, ZS, X, XS, N, XS, N, V1, V2, V2, V1, V2, V2, V1, V1, V1, V1, N, XS, X, 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 0.016/0.016 -> UVars: 0.016/0.016 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.016/0.016 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, XS], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.016/0.016 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.016/0.016 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.016/0.016 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [N], UV-RFrozen: [N]) 0.016/0.016 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, XS], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 20, UV-LActive: [], UV-RActive: [Y], UV-LFrozen: [Y], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 21, UV-LActive: [], UV-RActive: [XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 22, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, X, XS], UV-RFrozen: [X]) 0.016/0.016 (UV-RuleId: 23, UV-LActive: [YS, ZS], UV-RActive: [X, ZS], UV-LFrozen: [X], UV-RFrozen: [YS]) 0.016/0.016 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 25, UV-LActive: [], UV-RActive: [XS], UV-LFrozen: [XS], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [N, XS], UV-LFrozen: [N, XS], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 27, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [N], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 29, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.016/0.016 (UV-RuleId: 30, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 31, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 32, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.016/0.016 (UV-RuleId: 33, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 34, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 35, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 36, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 37, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 38, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 39, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 40, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 41, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 42, UV-LActive: [N, XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N, XS]) 0.016/0.016 (UV-RuleId: 43, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 44, UV-LActive: [X, Y], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [X, Y]) 0.016/0.016 (UV-RuleId: 45, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [N, XS]) 0.016/0.016 (UV-RuleId: 46, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 47, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 48, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 49, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 50, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 51, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 52, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 53, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 54, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 55, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 56, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 57, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 58, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 59, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 60, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 61, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 62, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 63, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 64, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 65, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 66, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 67, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 68, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.016/0.016 (UV-RuleId: 69, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.016/0.016 (UV-RuleId: 70, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 71, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 72, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 73, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.016/0.016 (UV-RuleId: 74, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N]) 0.016/0.016 (UV-RuleId: 75, UV-LActive: [N, XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N, XS]) 0.016/0.016 (UV-RuleId: 76, UV-LActive: [X, Y], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [X, Y]) 0.016/0.016 (UV-RuleId: 77, UV-LActive: [XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [XS]) 0.016/0.016 (UV-RuleId: 78, UV-LActive: [N, X], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [N, X, XS]) 0.016/0.016 (UV-RuleId: 79, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [XS], UV-RFrozen: [N, XS]) 0.016/0.016 (UV-RuleId: 80, UV-LActive: [N, XS], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N, XS]) 0.016/0.016 -> FVars: 0.016/0.016 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 0.016/0.016 -> PVars: 0.016/0.016 V1: [x9, x14, x15, x16, x19, x22, x41, x44, x47, x48, x49, x50, x58, x60, x61, x62, x63, x64, x66, x68, x70, x71, x72, x73, x74, x76, x78, x79, x81, x82, x83, x85, x86, x88, x90, x92], V2: [x10, x11, x17, x18, x20, x21, x23, x24, x42, x43, x45, x46, x59, x65, x67, x69, x75, x77, x80, x84, x87, x89, x91, x93], N: [x12, x25, x26, x30, x38, x40, x51, x56, x94, x95, x100, x103, x105], XS: [x13, x27, x29, x32, x37, x39, x52, x57, x96, x99, x102, x104, x106], Y: [x28, x55, x98], X: [x31, x33, x36, x53, x54, x97, x101], YS: [x34], ZS: [x35] 0.016/0.016 0.016/0.016 -> Rlps: 0.016/0.016 (rule: U101(tt,x9:S,x10:S) -> U102(isNatural(x9:S),x10:S), id: 1, possubterms: U101(tt,x9:S,x10:S)->[], tt->[1]) 0.016/0.016 (rule: U102(tt,x11:S) -> U103(isLNat(x11:S)), id: 2, possubterms: U102(tt,x11:S)->[], tt->[1]) 0.016/0.016 (rule: U103(tt) -> tt, id: 3, possubterms: U103(tt)->[], tt->[1]) 0.016/0.016 (rule: U11(tt,x12:S,x13:S) -> snd(splitAt(x12:S,x13:S)), id: 4, possubterms: U11(tt,x12:S,x13:S)->[], tt->[1]) 0.016/0.016 (rule: U111(tt,x14:S) -> U112(isLNat(x14:S)), id: 5, possubterms: U111(tt,x14:S)->[], tt->[1]) 0.016/0.016 (rule: U112(tt) -> tt, id: 6, possubterms: U112(tt)->[], tt->[1]) 0.016/0.016 (rule: U121(tt,x15:S) -> U122(isNatural(x15:S)), id: 7, possubterms: U121(tt,x15:S)->[], tt->[1]) 0.016/0.016 (rule: U122(tt) -> tt, id: 8, possubterms: U122(tt)->[], tt->[1]) 0.016/0.016 (rule: U131(tt,x16:S,x17:S) -> U132(isNatural(x16:S),x17:S), id: 9, possubterms: U131(tt,x16:S,x17:S)->[], tt->[1]) 0.016/0.016 (rule: U132(tt,x18:S) -> U133(isLNat(x18:S)), id: 10, possubterms: U132(tt,x18:S)->[], tt->[1]) 0.016/0.016 (rule: U133(tt) -> tt, id: 11, possubterms: U133(tt)->[], tt->[1]) 0.016/0.016 (rule: U141(tt,x19:S,x20:S) -> U142(isLNat(x19:S),x20:S), id: 12, possubterms: U141(tt,x19:S,x20:S)->[], tt->[1]) 0.016/0.016 (rule: U142(tt,x21:S) -> U143(isLNat(x21:S)), id: 13, possubterms: U142(tt,x21:S)->[], tt->[1]) 0.016/0.016 (rule: U143(tt) -> tt, id: 14, possubterms: U143(tt)->[], tt->[1]) 0.016/0.016 (rule: U151(tt,x22:S,x23:S) -> U152(isNatural(x22:S),x23:S), id: 15, possubterms: U151(tt,x22:S,x23:S)->[], tt->[1]) 0.016/0.016 (rule: U152(tt,x24:S) -> U153(isLNat(x24:S)), id: 16, possubterms: U152(tt,x24:S)->[], tt->[1]) 0.016/0.016 (rule: U153(tt) -> tt, id: 17, possubterms: U153(tt)->[], tt->[1]) 0.016/0.016 (rule: U161(tt,x25:S) -> cons(x25:S,natsFrom(s(x25:S))), id: 18, possubterms: U161(tt,x25:S)->[], tt->[1]) 0.016/0.016 (rule: U171(tt,x26:S,x27:S) -> head(afterNth(x26:S,x27:S)), id: 19, possubterms: U171(tt,x26:S,x27:S)->[], tt->[1]) 0.016/0.016 (rule: U181(tt,x28:S) -> x28:S, id: 20, possubterms: U181(tt,x28:S)->[], tt->[1]) 0.016/0.016 (rule: U191(tt,x29:S) -> pair(nil,x29:S), id: 21, possubterms: U191(tt,x29:S)->[], tt->[1]) 0.016/0.016 (rule: U201(tt,x30:S,x31:S,x32:S) -> U202(splitAt(x30:S,x32:S),x31:S), id: 22, possubterms: U201(tt,x30:S,x31:S,x32:S)->[], tt->[1]) 0.016/0.016 (rule: U202(pair(x34:S,x35:S),x33:S) -> pair(cons(x33:S,x34:S),x35:S), id: 23, possubterms: U202(pair(x34:S,x35:S),x33:S)->[], pair(x34:S,x35:S)->[1]) 0.016/0.016 (rule: U21(tt,x36:S) -> x36:S, id: 24, possubterms: U21(tt,x36:S)->[], tt->[1]) 0.016/0.016 (rule: U211(tt,x37:S) -> x37:S, id: 25, possubterms: U211(tt,x37:S)->[], tt->[1]) 0.016/0.016 (rule: U221(tt,x38:S,x39:S) -> fst(splitAt(x38:S,x39:S)), id: 26, possubterms: U221(tt,x38:S,x39:S)->[], tt->[1]) 0.016/0.016 (rule: U31(tt,x40:S) -> x40:S, id: 27, possubterms: U31(tt,x40:S)->[], tt->[1]) 0.016/0.016 (rule: U41(tt,x41:S,x42:S) -> U42(isNatural(x41:S),x42:S), id: 28, possubterms: U41(tt,x41:S,x42:S)->[], tt->[1]) 0.016/0.016 (rule: U42(tt,x43:S) -> U43(isLNat(x43:S)), id: 29, possubterms: U42(tt,x43:S)->[], tt->[1]) 0.016/0.016 (rule: U43(tt) -> tt, id: 30, possubterms: U43(tt)->[], tt->[1]) 0.016/0.016 (rule: U51(tt,x44:S,x45:S) -> U52(isNatural(x44:S),x45:S), id: 31, possubterms: U51(tt,x44:S,x45:S)->[], tt->[1]) 0.016/0.016 (rule: U52(tt,x46:S) -> U53(isLNat(x46:S)), id: 32, possubterms: U52(tt,x46:S)->[], tt->[1]) 0.016/0.016 (rule: U53(tt) -> tt, id: 33, possubterms: U53(tt)->[], tt->[1]) 0.016/0.016 (rule: U61(tt,x47:S) -> U62(isPLNat(x47:S)), id: 34, possubterms: U61(tt,x47:S)->[], tt->[1]) 0.016/0.016 (rule: U62(tt) -> tt, id: 35, possubterms: U62(tt)->[], tt->[1]) 0.016/0.016 (rule: U71(tt,x48:S) -> U72(isNatural(x48:S)), id: 36, possubterms: U71(tt,x48:S)->[], tt->[1]) 0.016/0.016 (rule: U72(tt) -> tt, id: 37, possubterms: U72(tt)->[], tt->[1]) 0.016/0.016 (rule: U81(tt,x49:S) -> U82(isPLNat(x49:S)), id: 38, possubterms: U81(tt,x49:S)->[], tt->[1]) 0.016/0.016 (rule: U82(tt) -> tt, id: 39, possubterms: U82(tt)->[], tt->[1]) 0.016/0.016 (rule: U91(tt,x50:S) -> U92(isLNat(x50:S)), id: 40, possubterms: U91(tt,x50:S)->[], tt->[1]) 0.016/0.016 (rule: U92(tt) -> tt, id: 41, possubterms: U92(tt)->[], tt->[1]) 0.016/0.016 (rule: afterNth(x51:S,x52:S) -> U11(and(and(isNatural(x51:S),isNaturalKind(x51:S)),and(isLNat(x52:S),isLNatKind(x52:S))),x51:S,x52:S), id: 42, possubterms: afterNth(x51:S,x52:S)->[]) 0.016/0.016 (rule: and(tt,x53:S) -> x53:S, id: 43, possubterms: and(tt,x53:S)->[], tt->[1]) 0.016/0.016 (rule: fst(pair(x54:S,x55:S)) -> U21(and(and(isLNat(x54:S),isLNatKind(x54:S)),and(isLNat(x55:S),isLNatKind(x55:S))),x54:S), id: 44, possubterms: fst(pair(x54:S,x55:S))->[], pair(x54:S,x55:S)->[1]) 0.016/0.016 (rule: head(cons(x56:S,x57:S)) -> U31(and(and(isNatural(x56:S),isNaturalKind(x56:S)),and(isLNat(x57:S),isLNatKind(x57:S))),x56:S), id: 45, possubterms: head(cons(x56:S,x57:S))->[], cons(x56:S,x57:S)->[1]) 0.016/0.016 (rule: isLNat(afterNth(x58:S,x59:S)) -> U41(and(isNaturalKind(x58:S),isLNatKind(x59:S)),x58:S,x59:S), id: 46, possubterms: isLNat(afterNth(x58:S,x59:S))->[]) 0.016/0.016 (rule: isLNat(fst(x60:S)) -> U61(isPLNatKind(x60:S),x60:S), id: 47, possubterms: isLNat(fst(x60:S))->[]) 0.016/0.016 (rule: isLNat(natsFrom(x61:S)) -> U71(isNaturalKind(x61:S),x61:S), id: 48, possubterms: isLNat(natsFrom(x61:S))->[]) 0.016/0.016 (rule: isLNat(snd(x62:S)) -> U81(isPLNatKind(x62:S),x62:S), id: 49, possubterms: isLNat(snd(x62:S))->[]) 0.016/0.016 (rule: isLNat(tail(x63:S)) -> U91(isLNatKind(x63:S),x63:S), id: 50, possubterms: isLNat(tail(x63:S))->[]) 0.016/0.016 (rule: isLNat(take(x64:S,x65:S)) -> U101(and(isNaturalKind(x64:S),isLNatKind(x65:S)),x64:S,x65:S), id: 51, possubterms: isLNat(take(x64:S,x65:S))->[]) 0.016/0.016 (rule: isLNat(cons(x66:S,x67:S)) -> U51(and(isNaturalKind(x66:S),isLNatKind(x67:S)),x66:S,x67:S), id: 52, possubterms: isLNat(cons(x66:S,x67:S))->[]) 0.016/0.016 (rule: isLNat(nil) -> tt, id: 53, possubterms: isLNat(nil)->[]) 0.016/0.016 (rule: isLNatKind(afterNth(x68:S,x69:S)) -> and(isNaturalKind(x68:S),isLNatKind(x69:S)), id: 54, possubterms: isLNatKind(afterNth(x68:S,x69:S))->[]) 0.016/0.016 (rule: isLNatKind(fst(x70:S)) -> isPLNatKind(x70:S), id: 55, possubterms: isLNatKind(fst(x70:S))->[]) 0.016/0.016 (rule: isLNatKind(natsFrom(x71:S)) -> isNaturalKind(x71:S), id: 56, possubterms: isLNatKind(natsFrom(x71:S))->[]) 0.016/0.016 (rule: isLNatKind(snd(x72:S)) -> isPLNatKind(x72:S), id: 57, possubterms: isLNatKind(snd(x72:S))->[]) 0.016/0.016 (rule: isLNatKind(tail(x73:S)) -> isLNatKind(x73:S), id: 58, possubterms: isLNatKind(tail(x73:S))->[]) 0.016/0.016 (rule: isLNatKind(take(x74:S,x75:S)) -> and(isNaturalKind(x74:S),isLNatKind(x75:S)), id: 59, possubterms: isLNatKind(take(x74:S,x75:S))->[]) 0.016/0.016 (rule: isLNatKind(cons(x76:S,x77:S)) -> and(isNaturalKind(x76:S),isLNatKind(x77:S)), id: 60, possubterms: isLNatKind(cons(x76:S,x77:S))->[]) 0.016/0.016 (rule: isLNatKind(nil) -> tt, id: 61, possubterms: isLNatKind(nil)->[]) 0.016/0.016 (rule: isNatural(head(x78:S)) -> U111(isLNatKind(x78:S),x78:S), id: 62, possubterms: isNatural(head(x78:S))->[]) 0.016/0.016 (rule: isNatural(sel(x79:S,x80:S)) -> U131(and(isNaturalKind(x79:S),isLNatKind(x80:S)),x79:S,x80:S), id: 63, possubterms: isNatural(sel(x79:S,x80:S))->[]) 0.016/0.016 (rule: isNatural(0) -> tt, id: 64, possubterms: isNatural(0)->[]) 0.016/0.016 (rule: isNatural(s(x81:S)) -> U121(isNaturalKind(x81:S),x81:S), id: 65, possubterms: isNatural(s(x81:S))->[]) 0.016/0.016 (rule: isNaturalKind(head(x82:S)) -> isLNatKind(x82:S), id: 66, possubterms: isNaturalKind(head(x82:S))->[]) 0.016/0.016 (rule: isNaturalKind(sel(x83:S,x84:S)) -> and(isNaturalKind(x83:S),isLNatKind(x84:S)), id: 67, possubterms: isNaturalKind(sel(x83:S,x84:S))->[]) 0.016/0.016 (rule: isNaturalKind(0) -> tt, id: 68, possubterms: isNaturalKind(0)->[]) 0.016/0.016 (rule: isNaturalKind(s(x85:S)) -> isNaturalKind(x85:S), id: 69, possubterms: isNaturalKind(s(x85:S))->[]) 0.016/0.016 (rule: isPLNat(splitAt(x86:S,x87:S)) -> U151(and(isNaturalKind(x86:S),isLNatKind(x87:S)),x86:S,x87:S), id: 70, possubterms: isPLNat(splitAt(x86:S,x87:S))->[]) 0.016/0.016 (rule: isPLNat(pair(x88:S,x89:S)) -> U141(and(isLNatKind(x88:S),isLNatKind(x89:S)),x88:S,x89:S), id: 71, possubterms: isPLNat(pair(x88:S,x89:S))->[]) 0.016/0.016 (rule: isPLNatKind(splitAt(x90:S,x91:S)) -> and(isNaturalKind(x90:S),isLNatKind(x91:S)), id: 72, possubterms: isPLNatKind(splitAt(x90:S,x91:S))->[]) 0.016/0.016 (rule: isPLNatKind(pair(x92:S,x93:S)) -> and(isLNatKind(x92:S),isLNatKind(x93:S)), id: 73, possubterms: isPLNatKind(pair(x92:S,x93:S))->[]) 0.016/0.016 (rule: natsFrom(x94:S) -> U161(and(isNatural(x94:S),isNaturalKind(x94:S)),x94:S), id: 74, possubterms: natsFrom(x94:S)->[]) 0.016/0.016 (rule: sel(x95:S,x96:S) -> U171(and(and(isNatural(x95:S),isNaturalKind(x95:S)),and(isLNat(x96:S),isLNatKind(x96:S))),x95:S,x96:S), id: 75, possubterms: sel(x95:S,x96:S)->[]) 0.016/0.016 (rule: snd(pair(x97:S,x98:S)) -> U181(and(and(isLNat(x97:S),isLNatKind(x97:S)),and(isLNat(x98:S),isLNatKind(x98:S))),x98:S), id: 76, possubterms: snd(pair(x97:S,x98:S))->[], pair(x97:S,x98:S)->[1]) 0.016/0.016 (rule: splitAt(0,x99:S) -> U191(and(isLNat(x99:S),isLNatKind(x99:S)),x99:S), id: 77, possubterms: splitAt(0,x99:S)->[], 0->[1]) 0.016/0.016 (rule: splitAt(s(x100:S),cons(x101:S,x102:S)) -> U201(and(and(isNatural(x100:S),isNaturalKind(x100:S)),and(and(isNatural(x101:S),isNaturalKind(x101:S)),and(isLNat(x102:S),isLNatKind(x102:S)))),x100:S,x101:S,x102:S), id: 78, possubterms: splitAt(s(x100:S),cons(x101:S,x102:S))->[], s(x100:S)->[1], cons(x101:S,x102:S)->[2]) 0.016/0.016 (rule: tail(cons(x103:S,x104:S)) -> U211(and(and(isNatural(x103:S),isNaturalKind(x103:S)),and(isLNat(x104:S),isLNatKind(x104:S))),x104:S), id: 79, possubterms: tail(cons(x103:S,x104:S))->[], cons(x103:S,x104:S)->[1]) 0.016/0.016 (rule: take(x105:S,x106:S) -> U221(and(and(isNatural(x105:S),isNaturalKind(x105:S)),and(isLNat(x106:S),isLNatKind(x106:S))),x105:S,x106:S), id: 80, possubterms: take(x105:S,x106:S)->[]) 0.016/0.016 0.016/0.016 -> Unifications: 0.016/0.016 0.016/0.016 0.016/0.016 -> Critical pairs info: 0.016/0.016 => Not trivial, Not overlay, NW1, N1 0.016/0.016 => Not trivial, Not overlay, NW1, N2 0.016/0.016 => Not trivial, Not overlay, NW1, N3 0.016/0.016 => Not trivial, Not overlay, NW1, N4 0.016/0.016 => Not trivial, Not overlay, NW1, N5 0.016/0.016 => Not trivial, Not overlay, NW1, N6 0.016/0.016 => Not trivial, Not overlay, NW1, N7 0.016/0.016 => Not trivial, Not overlay, NW1, N8 0.016/0.016 => Not trivial, Not overlay, NW1, N9 0.016/0.016 => Not trivial, Not overlay, NW1, N10 0.016/0.016 => Not trivial, Not overlay, NW1, N11 0.016/0.016 => Not trivial, Not overlay, NW1, N12 0.016/0.016 => Not trivial, Not overlay, NW1, N13 0.016/0.016 => Not trivial, Not overlay, NW1, N14 0.016/0.016 => Not trivial, Not overlay, NW1, N15 0.016/0.016 => Not trivial, Not overlay, NW1, N16 0.016/0.016 => Not trivial, Not overlay, NW1, N17 0.016/0.016 => Not trivial, Not overlay, NW1, N18 0.016/0.016 => Not trivial, Not overlay, NW1, N19 0.016/0.016 => Not trivial, Not overlay, NW1, N20 0.016/0.016 => Not trivial, Not overlay, NW1, N21 0.016/0.016 => Not trivial, Not overlay, NW1, N22 0.016/0.016 => Not trivial, Not overlay, NW1, N23 0.016/0.016 => Not trivial, Not overlay, NW1, N24 0.016/0.016 => Not trivial, Not overlay, NW1, N25 0.016/0.016 => Not trivial, Not overlay, NW1, N26 0.016/0.016 => Not trivial, Not overlay, NW1, N27 0.016/0.016 => Not trivial, Not overlay, NW0, N28 0.016/0.016 => Not trivial, Not overlay, NW1, N29 0.016/0.016 => Not trivial, Not overlay, NW1, N30 0.016/0.016 => Not trivial, Not overlay, NW1, N31 0.016/0.016 => Not trivial, Not overlay, NW1, N32 0.016/0.016 => Not trivial, Not overlay, NW1, N33 0.016/0.016 => Not trivial, Not overlay, NW1, N34 0.016/0.016 => Not trivial, Not overlay, NW1, N35 0.016/0.016 => Not trivial, Not overlay, NW1, N36 0.016/0.016 => Not trivial, Not overlay, NW1, N37 0.016/0.016 => Not trivial, Not overlay, NW1, N38 0.016/0.016 => Not trivial, Not overlay, NW1, N39 0.016/0.016 => Not trivial, Not overlay, NW1, N40 0.016/0.016 => Not trivial, Not overlay, NW1, N41 0.016/0.016 => Not trivial, Not overlay, NW1, N42 0.016/0.016 => Not trivial, Not overlay, NW1, N43 0.016/0.016 => Not trivial, Not overlay, NW1, N44 0.016/0.016 => Not trivial, Not overlay, NW1, N45 0.016/0.016 => Not trivial, Not overlay, NW1, N46 0.016/0.016 => Not trivial, Not overlay, NW1, N47 0.016/0.016 => Not trivial, Not overlay, NW1, N48 0.016/0.016 => Not trivial, Not overlay, NW1, N49 0.016/0.016 => Not trivial, Not overlay, NW1, N50 0.016/0.016 => Not trivial, Not overlay, NW1, N51 0.016/0.016 => Not trivial, Not overlay, NW1, N52 0.016/0.016 => Not trivial, Not overlay, NW1, N53 0.016/0.016 => Not trivial, Not overlay, NW1, N54 0.016/0.016 => Not trivial, Not overlay, NW1, N55 0.016/0.016 => Not trivial, Not overlay, NW1, N56 0.016/0.016 => Not trivial, Not overlay, NW1, N57 0.016/0.016 => Not trivial, Not overlay, NW1, N58 0.016/0.016 => Not trivial, Not overlay, NW0, N59 0.016/0.016 => Not trivial, Not overlay, NW1, N60 0.016/0.016 => Not trivial, Not overlay, NW1, N61 0.016/0.016 => Not trivial, Not overlay, NW1, N62 0.016/0.016 => Not trivial, Not overlay, NW1, N63 0.016/0.016 => Not trivial, Not overlay, NW1, N64 0.016/0.016 => Not trivial, Not overlay, NW1, N65 0.016/0.016 => Not trivial, Not overlay, NW1, N66 0.016/0.016 => Not trivial, Not overlay, NW1, N67 0.016/0.016 => Not trivial, Not overlay, NW1, N68 0.016/0.016 => Not trivial, Not overlay, NW1, N69 0.016/0.016 => Not trivial, Not overlay, NW0, N70 0.016/0.016 => Not trivial, Not overlay, NW0, N71 0.016/0.016 => Not trivial, Not overlay, NW1, N72 0.016/0.016 => Not trivial, Not overlay, NW1, N73 0.016/0.016 => Not trivial, Not overlay, NW1, N74 0.016/0.016 => Not trivial, Not overlay, NW1, N75 0.016/0.016 => Not trivial, Not overlay, NW1, N76 0.016/0.016 => Not trivial, Not overlay, NW1, N77 0.016/0.016 => Not trivial, Not overlay, NW1, N78 0.016/0.016 => Not trivial, Not overlay, NW1, N79 0.016/0.016 => Not trivial, Not overlay, NW1, N80 0.016/0.016 => Not trivial, Not overlay, NW1, N81 0.016/0.016 => Not trivial, Not overlay, NW1, N82 0.016/0.016 => Not trivial, Not overlay, NW1, N83 0.016/0.016 => Not trivial, Not overlay, NW1, N84 0.016/0.016 => Not trivial, Not overlay, NW1, N85 0.016/0.016 => Not trivial, Not overlay, NW1, N86 0.016/0.016 => Not trivial, Not overlay, NW1, N87 0.016/0.016 => Not trivial, Not overlay, NW1, N88 0.016/0.016 => Not trivial, Not overlay, NW1, N89 0.016/0.016 => Not trivial, Not overlay, NW1, N90 0.016/0.016 => Not trivial, Not overlay, NW1, N91 0.016/0.016 => Not trivial, Not overlay, NW1, N92 0.016/0.016 => Not trivial, Not overlay, NW1, N93 0.016/0.016 => Not trivial, Not overlay, NW1, N94 0.016/0.016 => Not trivial, Not overlay, NW1, N95 0.016/0.016 => Not trivial, Not overlay, NW1, N96 0.016/0.016 => Not trivial, Not overlay, NW1, N97 0.016/0.016 => Not trivial, Not overlay, NW1, N98 0.016/0.016 => Not trivial, Not overlay, NW1, N99 0.016/0.016 => Not trivial, Not overlay, NW1, N100 0.016/0.016 => Not trivial, Not overlay, NW1, N101 0.016/0.016 => Not trivial, Not overlay, NW1, N102 0.016/0.016 => Not trivial, Not overlay, NW1, N103 0.016/0.016 => Not trivial, Not overlay, NW1, N104 0.016/0.016 => Not trivial, Not overlay, NW1, N105 0.016/0.016 => Not trivial, Not overlay, NW1, N106 0.016/0.016 => Not trivial, Not overlay, NW1, N107 0.016/0.016 => Not trivial, Not overlay, NW1, N108 0.016/0.016 => Not trivial, Not overlay, NW1, N109 0.016/0.016 => Not trivial, Not overlay, NW1, N110 0.016/0.016 => Not trivial, Not overlay, NW1, N111 0.016/0.016 => Not trivial, Not overlay, NW1, N112 0.016/0.016 => Not trivial, Not overlay, NW1, N113 0.016/0.016 => Not trivial, Not overlay, NW1, N114 0.016/0.016 => Not trivial, Not overlay, NW1, N115 0.016/0.016 => Not trivial, Not overlay, NW1, N116 0.016/0.016 => Not trivial, Not overlay, NW1, N117 0.016/0.016 => Not trivial, Not overlay, NW1, N118 0.016/0.016 => Not trivial, Not overlay, NW1, N119 0.016/0.016 => Not trivial, Not overlay, NW1, N120 0.016/0.016 => Not trivial, Not overlay, NW1, N121 0.016/0.016 => Not trivial, Not overlay, NW1, N122 0.016/0.016 => Not trivial, Not overlay, NW1, N123 0.016/0.016 => Not trivial, Not overlay, NW1, N124 0.016/0.016 => Not trivial, Not overlay, NW1, N125 0.016/0.016 => Not trivial, Not overlay, NW1, N126 0.016/0.016 => Not trivial, Not overlay, NW1, N127 0.016/0.016 => Not trivial, Not overlay, NW1, N128 0.016/0.016 => Not trivial, Not overlay, NW1, N129 0.016/0.016 => Not trivial, Not overlay, NW1, N130 0.016/0.016 => Not trivial, Not overlay, NW1, N131 0.016/0.016 => Not trivial, Not overlay, NW1, N132 0.016/0.016 => Not trivial, Not overlay, NW1, N133 0.016/0.016 => Not trivial, Not overlay, NW1, N134 0.016/0.016 => Not trivial, Not overlay, NW0, N135 0.016/0.016 => Not trivial, Not overlay, NW1, N136 0.016/0.016 => Not trivial, Not overlay, NW1, N137 0.016/0.016 => Not trivial, Not overlay, NW1, N138 0.016/0.016 => Not trivial, Not overlay, NW1, N139 0.016/0.016 => Not trivial, Not overlay, NW0, N140 0.016/0.016 => Not trivial, Not overlay, NW1, N141 0.016/0.016 => Not trivial, Not overlay, NW1, N142 0.016/0.016 => Not trivial, Not overlay, NW1, N143 0.016/0.016 => Not trivial, Not overlay, NW1, N144 0.016/0.016 => Not trivial, Not overlay, NW1, N145 0.016/0.016 => Not trivial, Not overlay, NW1, N146 0.016/0.016 => Not trivial, Not overlay, NW1, N147 0.016/0.016 => Not trivial, Not overlay, NW1, N148 0.016/0.016 => Not trivial, Not overlay, NW1, N149 0.016/0.016 => Not trivial, Not overlay, NW1, N150 0.016/0.016 => Not trivial, Not overlay, NW1, N151 0.016/0.016 => Not trivial, Not overlay, NW1, N152 0.016/0.016 => Not trivial, Not overlay, NW1, N153 0.016/0.016 => Not trivial, Not overlay, NW0, N154 0.016/0.016 => Not trivial, Not overlay, NW1, N155 0.016/0.016 => Not trivial, Not overlay, NW1, N156 0.016/0.016 => Not trivial, Not overlay, NW1, N157 0.016/0.016 => Not trivial, Not overlay, NW1, N158 0.016/0.016 => Not trivial, Not overlay, NW1, N159 0.016/0.016 => Not trivial, Not overlay, NW1, N160 0.016/0.016 => Not trivial, Not overlay, NW1, N161 0.016/0.016 => Not trivial, Not overlay, NW1, N162 0.016/0.016 => Not trivial, Not overlay, NW1, N163 0.016/0.016 => Not trivial, Not overlay, NW1, N164 0.016/0.016 => Not trivial, Not overlay, NW1, N165 0.016/0.016 => Not trivial, Not overlay, NW1, N166 0.016/0.016 => Not trivial, Not overlay, NW1, N167 0.016/0.016 => Not trivial, Not overlay, NW1, N168 0.016/0.016 => Not trivial, Not overlay, NW1, N169 0.016/0.016 => Not trivial, Not overlay, NW1, N170 0.016/0.016 => Not trivial, Not overlay, NW1, N171 0.016/0.016 => Not trivial, Not overlay, NW0, N172 0.016/0.016 => Not trivial, Not overlay, NW1, N173 0.016/0.016 => Not trivial, Not overlay, NW0, N174 0.016/0.016 => Not trivial, Not overlay, NW1, N175 0.016/0.016 => Not trivial, Not overlay, NW1, N176 0.016/0.016 => Not trivial, Not overlay, NW1, N177 0.016/0.016 => Not trivial, Not overlay, NW1, N178 0.016/0.016 => Not trivial, Not overlay, NW1, N179 0.016/0.016 => Not trivial, Not overlay, NW1, N180 0.016/0.016 => Not trivial, Not overlay, NW1, N181 0.016/0.016 => Not trivial, Not overlay, NW1, N182 0.016/0.016 => Not trivial, Not overlay, NW1, N183 0.016/0.016 => Not trivial, Not overlay, NW1, N184 0.016/0.016 => Not trivial, Not overlay, NW1, N185 0.016/0.016 => Not trivial, Not overlay, NW1, N186 0.016/0.016 => Not trivial, Not overlay, NW1, N187 0.016/0.016 => Not trivial, Not overlay, NW1, N188 0.016/0.016 => Not trivial, Not overlay, NW1, N189 0.016/0.016 => Not trivial, Not overlay, NW1, N190 0.016/0.016 => Not trivial, Not overlay, NW1, N191 0.016/0.016 => Not trivial, Not overlay, NW1, N192 0.016/0.016 => Not trivial, Not overlay, NW1, N193 0.016/0.016 => Not trivial, Not overlay, NW1, N194 0.016/0.016 => Not trivial, Not overlay, NW1, N195 0.016/0.016 => Not trivial, Not overlay, NW1, N196 0.016/0.016 => Not trivial, Not overlay, NW1, N197 0.016/0.016 => Not trivial, Not overlay, NW1, N198 0.016/0.016 0.016/0.016 -> Problem conclusions: 0.016/0.016 Left linear, Not right linear, Not linear 0.016/0.016 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.016/0.016 Not Huet-Levy confluent, Not Newman confluent 0.016/0.016 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.016/0.016 0.016/0.016 0.016/0.016 Problem 1: 0.016/0.016 No Convergence Brute Force Processor: 0.016/0.016 -> Rewritings: 0.016/0.016 s: U31(and(and(isNatural(isNatural(s(V1:S))),isNaturalKind(isNatural(s(V1:S)))),and(isLNat(XS:S),isLNatKind(XS:S))),isNatural(s(V1:S))) 0.016/0.016 Nodes: [0] 0.016/0.016 Edges: [] 0.016/0.016 ID: 0 => ('U31(and(and(isNatural(isNatural(s(V1:S))),isNaturalKind(isNatural(s(V1:S)))),and(isLNat(XS:S),isLNatKind(XS:S))),isNatural(s(V1:S)))', D0) 0.016/0.016 t: head(cons(U121(isNaturalKind(V1:S),V1:S),XS:S)) 0.016/0.016 Nodes: [0,1] 0.016/0.016 Edges: [(0,1)] 0.016/0.016 ID: 0 => ('head(cons(U121(isNaturalKind(V1:S),V1:S),XS:S))', D0) 0.016/0.016 ID: 1 => ('U31(and(and(isNatural(U121(isNaturalKind(V1:S),V1:S)),isNaturalKind(U121(isNaturalKind(V1:S),V1:S))),and(isLNat(XS:S),isLNatKind(XS:S))),U121(isNaturalKind(V1:S),V1:S))', D1, R45, P[], S{x56:S -> U121(isNaturalKind(V1:S),V1:S), x57:S -> XS:S}), NR: 'U31(and(and(isNatural(U121(isNaturalKind(V1:S),V1:S)),isNaturalKind(U121(isNaturalKind(V1:S),V1:S))),and(isLNat(XS:S),isLNatKind(XS:S))),U121(isNaturalKind(V1:S),V1:S))' 0.016/0.016 U31(and(and(isNatural(isNatural(s(V1:S))),isNaturalKind(isNatural(s(V1:S)))),and(isLNat(XS:S),isLNatKind(XS:S))),isNatural(s(V1:S))) ->* no union *<- head(cons(U121(isNaturalKind(V1:S),V1:S),XS:S)) 0.016/0.016 "Not joinable" 0.016/0.016 0.016/0.016 The problem is not joinable. 0.016/0.016 0.14user 0.00system 0:00.16elapsed 96%CPU (0avgtext+0avgdata 32552maxresident)k 0.016/0.016 0inputs+0outputs (0major+6322minor)pagefaults 0swaps