0.002/0.002 NO 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S IL:S L:S M:S N:S V:S V1:S V2:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U101 1) 0.002/0.002 (U102 1) 0.002/0.002 (U103 1) 0.002/0.002 (U104 1) 0.002/0.002 (U105 1) 0.002/0.002 (U106 1) 0.002/0.002 (U11 1) 0.002/0.002 (U111 1) 0.002/0.002 (U112 1) 0.002/0.002 (U113 1) 0.002/0.002 (U114 1) 0.002/0.002 (U12 1) 0.002/0.002 (U121 1) 0.002/0.002 (U122 1) 0.002/0.002 (U13 1) 0.002/0.002 (U131 1) 0.002/0.002 (U132 1) 0.002/0.002 (U133 1) 0.002/0.002 (U134 1) 0.002/0.002 (U135 1) 0.002/0.002 (U136 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U23 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U33 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U43 1) 0.002/0.002 (U44 1) 0.002/0.002 (U45 1) 0.002/0.002 (U46 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U71 1) 0.002/0.002 (U81 1) 0.002/0.002 (U91 1) 0.002/0.002 (U92 1) 0.002/0.002 (U93 1) 0.002/0.002 (U94 1) 0.002/0.002 (U95 1) 0.002/0.002 (U96 1) 0.002/0.002 (isNat) 0.002/0.002 (isNatIList) 0.002/0.002 (isNatIListKind) 0.002/0.002 (isNatKind) 0.002/0.002 (isNatList) 0.002/0.002 (length 1) 0.002/0.002 (take 1 2) 0.002/0.002 (zeros) 0.002/0.002 (0) 0.002/0.002 (cons 1) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U101(tt,V1:S,V2:S) -> U102(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U102(tt,V1:S,V2:S) -> U103(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U103(tt,V1:S,V2:S) -> U104(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U104(tt,V1:S,V2:S) -> U105(isNat(V1:S),V2:S) 0.002/0.002 U105(tt,V2:S) -> U106(isNatIList(V2:S)) 0.002/0.002 U106(tt) -> tt 0.002/0.002 U11(tt,V1:S) -> U12(isNatIListKind(V1:S),V1:S) 0.002/0.002 U111(tt,L:S,N:S) -> U112(isNatIListKind(L:S),L:S,N:S) 0.002/0.002 U112(tt,L:S,N:S) -> U113(isNat(N:S),L:S,N:S) 0.002/0.002 U113(tt,L:S,N:S) -> U114(isNatKind(N:S),L:S) 0.002/0.002 U114(tt,L:S) -> s(length(L:S)) 0.002/0.002 U12(tt,V1:S) -> U13(isNatList(V1:S)) 0.002/0.002 U121(tt,IL:S) -> U122(isNatIListKind(IL:S)) 0.002/0.002 U122(tt) -> nil 0.002/0.002 U13(tt) -> tt 0.002/0.002 U131(tt,IL:S,M:S,N:S) -> U132(isNatIListKind(IL:S),IL:S,M:S,N:S) 0.002/0.002 U132(tt,IL:S,M:S,N:S) -> U133(isNat(M:S),IL:S,M:S,N:S) 0.002/0.002 U133(tt,IL:S,M:S,N:S) -> U134(isNatKind(M:S),IL:S,M:S,N:S) 0.002/0.002 U134(tt,IL:S,M:S,N:S) -> U135(isNat(N:S),IL:S,M:S,N:S) 0.002/0.002 U135(tt,IL:S,M:S,N:S) -> U136(isNatKind(N:S),IL:S,M:S,N:S) 0.002/0.002 U136(tt,IL:S,M:S,N:S) -> cons(N:S,take(M:S,IL:S)) 0.002/0.002 U21(tt,V1:S) -> U22(isNatKind(V1:S),V1:S) 0.002/0.002 U22(tt,V1:S) -> U23(isNat(V1:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isNatIListKind(V:S),V:S) 0.002/0.002 U32(tt,V:S) -> U33(isNatList(V:S)) 0.002/0.002 U33(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U42(tt,V1:S,V2:S) -> U43(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U43(tt,V1:S,V2:S) -> U44(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U44(tt,V1:S,V2:S) -> U45(isNat(V1:S),V2:S) 0.002/0.002 U45(tt,V2:S) -> U46(isNatIList(V2:S)) 0.002/0.002 U46(tt) -> tt 0.002/0.002 U51(tt,V2:S) -> U52(isNatIListKind(V2:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S) -> U62(isNatIListKind(V2:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 U91(tt,V1:S,V2:S) -> U92(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U92(tt,V1:S,V2:S) -> U93(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U93(tt,V1:S,V2:S) -> U94(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U94(tt,V1:S,V2:S) -> U95(isNat(V1:S),V2:S) 0.002/0.002 U95(tt,V2:S) -> U96(isNatList(V2:S)) 0.002/0.002 U96(tt) -> tt 0.002/0.002 isNat(length(V1:S)) -> U11(isNatIListKind(V1:S),V1:S) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> U21(isNatKind(V1:S),V1:S) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S,V2:S)) -> U41(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatIList(V:S) -> U31(isNatIListKind(V:S),V:S) 0.002/0.002 isNatIListKind(take(V1:S,V2:S)) -> U61(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(zeros) -> tt 0.002/0.002 isNatIListKind(cons(V1:S,V2:S)) -> U51(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(nil) -> tt 0.002/0.002 isNatKind(length(V1:S)) -> U71(isNatIListKind(V1:S)) 0.002/0.002 isNatKind(0) -> tt 0.002/0.002 isNatKind(s(V1:S)) -> U81(isNatKind(V1:S)) 0.002/0.002 isNatList(take(V1:S,V2:S)) -> U101(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(cons(V1:S,V2:S)) -> U91(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S,L:S)) -> U111(isNatList(L:S),L:S,N:S) 0.002/0.002 length(nil) -> 0 0.002/0.002 take(0,IL:S) -> U121(isNatIList(IL:S),IL:S) 0.002/0.002 take(s(M:S),cons(N:S,IL:S)) -> U131(isNatIList(IL:S),IL:S,M:S,N:S) 0.002/0.002 zeros -> cons(0,zeros) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 CleanTRS Processor: 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S IL:S L:S M:S N:S V:S V1:S V2:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U101 1) 0.002/0.002 (U102 1) 0.002/0.002 (U103 1) 0.002/0.002 (U104 1) 0.002/0.002 (U105 1) 0.002/0.002 (U106 1) 0.002/0.002 (U11 1) 0.002/0.002 (U111 1) 0.002/0.002 (U112 1) 0.002/0.002 (U113 1) 0.002/0.002 (U114 1) 0.002/0.002 (U12 1) 0.002/0.002 (U121 1) 0.002/0.002 (U122 1) 0.002/0.002 (U13 1) 0.002/0.002 (U131 1) 0.002/0.002 (U132 1) 0.002/0.002 (U133 1) 0.002/0.002 (U134 1) 0.002/0.002 (U135 1) 0.002/0.002 (U136 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U23 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U33 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U43 1) 0.002/0.002 (U44 1) 0.002/0.002 (U45 1) 0.002/0.002 (U46 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U71 1) 0.002/0.002 (U81 1) 0.002/0.002 (U91 1) 0.002/0.002 (U92 1) 0.002/0.002 (U93 1) 0.002/0.002 (U94 1) 0.002/0.002 (U95 1) 0.002/0.002 (U96 1) 0.002/0.002 (isNat) 0.002/0.002 (isNatIList) 0.002/0.002 (isNatIListKind) 0.002/0.002 (isNatKind) 0.002/0.002 (isNatList) 0.002/0.002 (length 1) 0.002/0.002 (take 1 2) 0.002/0.002 (zeros) 0.002/0.002 (0) 0.002/0.002 (cons 1) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U101(tt,V1:S,V2:S) -> U102(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U102(tt,V1:S,V2:S) -> U103(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U103(tt,V1:S,V2:S) -> U104(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U104(tt,V1:S,V2:S) -> U105(isNat(V1:S),V2:S) 0.002/0.002 U105(tt,V2:S) -> U106(isNatIList(V2:S)) 0.002/0.002 U106(tt) -> tt 0.002/0.002 U11(tt,V1:S) -> U12(isNatIListKind(V1:S),V1:S) 0.002/0.002 U111(tt,L:S,N:S) -> U112(isNatIListKind(L:S),L:S,N:S) 0.002/0.002 U112(tt,L:S,N:S) -> U113(isNat(N:S),L:S,N:S) 0.002/0.002 U113(tt,L:S,N:S) -> U114(isNatKind(N:S),L:S) 0.002/0.002 U114(tt,L:S) -> s(length(L:S)) 0.002/0.002 U12(tt,V1:S) -> U13(isNatList(V1:S)) 0.002/0.002 U121(tt,IL:S) -> U122(isNatIListKind(IL:S)) 0.002/0.002 U122(tt) -> nil 0.002/0.002 U13(tt) -> tt 0.002/0.002 U131(tt,IL:S,M:S,N:S) -> U132(isNatIListKind(IL:S),IL:S,M:S,N:S) 0.002/0.002 U132(tt,IL:S,M:S,N:S) -> U133(isNat(M:S),IL:S,M:S,N:S) 0.002/0.002 U133(tt,IL:S,M:S,N:S) -> U134(isNatKind(M:S),IL:S,M:S,N:S) 0.002/0.002 U134(tt,IL:S,M:S,N:S) -> U135(isNat(N:S),IL:S,M:S,N:S) 0.002/0.002 U135(tt,IL:S,M:S,N:S) -> U136(isNatKind(N:S),IL:S,M:S,N:S) 0.002/0.002 U136(tt,IL:S,M:S,N:S) -> cons(N:S,take(M:S,IL:S)) 0.002/0.002 U21(tt,V1:S) -> U22(isNatKind(V1:S),V1:S) 0.002/0.002 U22(tt,V1:S) -> U23(isNat(V1:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isNatIListKind(V:S),V:S) 0.002/0.002 U32(tt,V:S) -> U33(isNatList(V:S)) 0.002/0.002 U33(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U42(tt,V1:S,V2:S) -> U43(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U43(tt,V1:S,V2:S) -> U44(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U44(tt,V1:S,V2:S) -> U45(isNat(V1:S),V2:S) 0.002/0.002 U45(tt,V2:S) -> U46(isNatIList(V2:S)) 0.002/0.002 U46(tt) -> tt 0.002/0.002 U51(tt,V2:S) -> U52(isNatIListKind(V2:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S) -> U62(isNatIListKind(V2:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 U91(tt,V1:S,V2:S) -> U92(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U92(tt,V1:S,V2:S) -> U93(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U93(tt,V1:S,V2:S) -> U94(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U94(tt,V1:S,V2:S) -> U95(isNat(V1:S),V2:S) 0.002/0.002 U95(tt,V2:S) -> U96(isNatList(V2:S)) 0.002/0.002 U96(tt) -> tt 0.002/0.002 isNat(length(V1:S)) -> U11(isNatIListKind(V1:S),V1:S) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> U21(isNatKind(V1:S),V1:S) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S,V2:S)) -> U41(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatIList(V:S) -> U31(isNatIListKind(V:S),V:S) 0.002/0.002 isNatIListKind(take(V1:S,V2:S)) -> U61(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(zeros) -> tt 0.002/0.002 isNatIListKind(cons(V1:S,V2:S)) -> U51(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(nil) -> tt 0.002/0.002 isNatKind(length(V1:S)) -> U71(isNatIListKind(V1:S)) 0.002/0.002 isNatKind(0) -> tt 0.002/0.002 isNatKind(s(V1:S)) -> U81(isNatKind(V1:S)) 0.002/0.002 isNatList(take(V1:S,V2:S)) -> U101(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(cons(V1:S,V2:S)) -> U91(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S,L:S)) -> U111(isNatList(L:S),L:S,N:S) 0.002/0.002 length(nil) -> 0 0.002/0.002 take(0,IL:S) -> U121(isNatIList(IL:S),IL:S) 0.002/0.002 take(s(M:S),cons(N:S,IL:S)) -> U131(isNatIList(IL:S),IL:S,M:S,N:S) 0.002/0.002 zeros -> cons(0,zeros) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 Modular Confluence Combinations Decomposition Processor: 0.002/0.002 It is a CTRS -> No modular confluence 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 CS-TRS Processor: 0.002/0.002 R is a CS-TRS 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S IL:S L:S M:S N:S V:S V1:S V2:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U101 1) 0.002/0.002 (U102 1) 0.002/0.002 (U103 1) 0.002/0.002 (U104 1) 0.002/0.002 (U105 1) 0.002/0.002 (U106 1) 0.002/0.002 (U11 1) 0.002/0.002 (U111 1) 0.002/0.002 (U112 1) 0.002/0.002 (U113 1) 0.002/0.002 (U114 1) 0.002/0.002 (U12 1) 0.002/0.002 (U121 1) 0.002/0.002 (U122 1) 0.002/0.002 (U13 1) 0.002/0.002 (U131 1) 0.002/0.002 (U132 1) 0.002/0.002 (U133 1) 0.002/0.002 (U134 1) 0.002/0.002 (U135 1) 0.002/0.002 (U136 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U23 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U33 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U43 1) 0.002/0.002 (U44 1) 0.002/0.002 (U45 1) 0.002/0.002 (U46 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U71 1) 0.002/0.002 (U81 1) 0.002/0.002 (U91 1) 0.002/0.002 (U92 1) 0.002/0.002 (U93 1) 0.002/0.002 (U94 1) 0.002/0.002 (U95 1) 0.002/0.002 (U96 1) 0.002/0.002 (isNat) 0.002/0.002 (isNatIList) 0.002/0.002 (isNatIListKind) 0.002/0.002 (isNatKind) 0.002/0.002 (isNatList) 0.002/0.002 (length 1) 0.002/0.002 (take 1 2) 0.002/0.002 (zeros) 0.002/0.002 (0) 0.002/0.002 (cons 1) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U101(tt,V1:S,V2:S) -> U102(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U102(tt,V1:S,V2:S) -> U103(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U103(tt,V1:S,V2:S) -> U104(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U104(tt,V1:S,V2:S) -> U105(isNat(V1:S),V2:S) 0.002/0.002 U105(tt,V2:S) -> U106(isNatIList(V2:S)) 0.002/0.002 U106(tt) -> tt 0.002/0.002 U11(tt,V1:S) -> U12(isNatIListKind(V1:S),V1:S) 0.002/0.002 U111(tt,L:S,N:S) -> U112(isNatIListKind(L:S),L:S,N:S) 0.002/0.002 U112(tt,L:S,N:S) -> U113(isNat(N:S),L:S,N:S) 0.002/0.002 U113(tt,L:S,N:S) -> U114(isNatKind(N:S),L:S) 0.002/0.002 U114(tt,L:S) -> s(length(L:S)) 0.002/0.002 U12(tt,V1:S) -> U13(isNatList(V1:S)) 0.002/0.002 U121(tt,IL:S) -> U122(isNatIListKind(IL:S)) 0.002/0.002 U122(tt) -> nil 0.002/0.002 U13(tt) -> tt 0.002/0.002 U131(tt,IL:S,M:S,N:S) -> U132(isNatIListKind(IL:S),IL:S,M:S,N:S) 0.002/0.002 U132(tt,IL:S,M:S,N:S) -> U133(isNat(M:S),IL:S,M:S,N:S) 0.002/0.002 U133(tt,IL:S,M:S,N:S) -> U134(isNatKind(M:S),IL:S,M:S,N:S) 0.002/0.002 U134(tt,IL:S,M:S,N:S) -> U135(isNat(N:S),IL:S,M:S,N:S) 0.002/0.002 U135(tt,IL:S,M:S,N:S) -> U136(isNatKind(N:S),IL:S,M:S,N:S) 0.002/0.002 U136(tt,IL:S,M:S,N:S) -> cons(N:S,take(M:S,IL:S)) 0.002/0.002 U21(tt,V1:S) -> U22(isNatKind(V1:S),V1:S) 0.002/0.002 U22(tt,V1:S) -> U23(isNat(V1:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isNatIListKind(V:S),V:S) 0.002/0.002 U32(tt,V:S) -> U33(isNatList(V:S)) 0.002/0.002 U33(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U42(tt,V1:S,V2:S) -> U43(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U43(tt,V1:S,V2:S) -> U44(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U44(tt,V1:S,V2:S) -> U45(isNat(V1:S),V2:S) 0.002/0.002 U45(tt,V2:S) -> U46(isNatIList(V2:S)) 0.002/0.002 U46(tt) -> tt 0.002/0.002 U51(tt,V2:S) -> U52(isNatIListKind(V2:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S) -> U62(isNatIListKind(V2:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 U91(tt,V1:S,V2:S) -> U92(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U92(tt,V1:S,V2:S) -> U93(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U93(tt,V1:S,V2:S) -> U94(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U94(tt,V1:S,V2:S) -> U95(isNat(V1:S),V2:S) 0.002/0.002 U95(tt,V2:S) -> U96(isNatList(V2:S)) 0.002/0.002 U96(tt) -> tt 0.002/0.002 isNat(length(V1:S)) -> U11(isNatIListKind(V1:S),V1:S) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> U21(isNatKind(V1:S),V1:S) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S,V2:S)) -> U41(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatIList(V:S) -> U31(isNatIListKind(V:S),V:S) 0.002/0.002 isNatIListKind(take(V1:S,V2:S)) -> U61(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(zeros) -> tt 0.002/0.002 isNatIListKind(cons(V1:S,V2:S)) -> U51(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(nil) -> tt 0.002/0.002 isNatKind(length(V1:S)) -> U71(isNatIListKind(V1:S)) 0.002/0.002 isNatKind(0) -> tt 0.002/0.002 isNatKind(s(V1:S)) -> U81(isNatKind(V1:S)) 0.002/0.002 isNatList(take(V1:S,V2:S)) -> U101(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(cons(V1:S,V2:S)) -> U91(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S,L:S)) -> U111(isNatList(L:S),L:S,N:S) 0.002/0.002 length(nil) -> 0 0.002/0.002 take(0,IL:S) -> U121(isNatIList(IL:S),IL:S) 0.002/0.002 take(s(M:S),cons(N:S,IL:S)) -> U131(isNatIList(IL:S),IL:S,M:S,N:S) 0.002/0.002 zeros -> cons(0,zeros) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 Huet Levy Processor: 0.002/0.002 -> Rules: 0.002/0.002 U101(tt,V1:S,V2:S) -> U102(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U102(tt,V1:S,V2:S) -> U103(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U103(tt,V1:S,V2:S) -> U104(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U104(tt,V1:S,V2:S) -> U105(isNat(V1:S),V2:S) 0.002/0.002 U105(tt,V2:S) -> U106(isNatIList(V2:S)) 0.002/0.002 U106(tt) -> tt 0.002/0.002 U11(tt,V1:S) -> U12(isNatIListKind(V1:S),V1:S) 0.002/0.002 U111(tt,L:S,N:S) -> U112(isNatIListKind(L:S),L:S,N:S) 0.002/0.002 U112(tt,L:S,N:S) -> U113(isNat(N:S),L:S,N:S) 0.002/0.002 U113(tt,L:S,N:S) -> U114(isNatKind(N:S),L:S) 0.002/0.002 U114(tt,L:S) -> s(length(L:S)) 0.002/0.002 U12(tt,V1:S) -> U13(isNatList(V1:S)) 0.002/0.002 U121(tt,IL:S) -> U122(isNatIListKind(IL:S)) 0.002/0.002 U122(tt) -> nil 0.002/0.002 U13(tt) -> tt 0.002/0.002 U131(tt,IL:S,M:S,N:S) -> U132(isNatIListKind(IL:S),IL:S,M:S,N:S) 0.002/0.002 U132(tt,IL:S,M:S,N:S) -> U133(isNat(M:S),IL:S,M:S,N:S) 0.002/0.002 U133(tt,IL:S,M:S,N:S) -> U134(isNatKind(M:S),IL:S,M:S,N:S) 0.002/0.002 U134(tt,IL:S,M:S,N:S) -> U135(isNat(N:S),IL:S,M:S,N:S) 0.002/0.002 U135(tt,IL:S,M:S,N:S) -> U136(isNatKind(N:S),IL:S,M:S,N:S) 0.002/0.002 U136(tt,IL:S,M:S,N:S) -> cons(N:S,take(M:S,IL:S)) 0.002/0.002 U21(tt,V1:S) -> U22(isNatKind(V1:S),V1:S) 0.002/0.002 U22(tt,V1:S) -> U23(isNat(V1:S)) 0.002/0.002 U23(tt) -> tt 0.002/0.002 U31(tt,V:S) -> U32(isNatIListKind(V:S),V:S) 0.002/0.002 U32(tt,V:S) -> U33(isNatList(V:S)) 0.002/0.002 U33(tt) -> tt 0.002/0.002 U41(tt,V1:S,V2:S) -> U42(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U42(tt,V1:S,V2:S) -> U43(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U43(tt,V1:S,V2:S) -> U44(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U44(tt,V1:S,V2:S) -> U45(isNat(V1:S),V2:S) 0.002/0.002 U45(tt,V2:S) -> U46(isNatIList(V2:S)) 0.002/0.002 U46(tt) -> tt 0.002/0.002 U51(tt,V2:S) -> U52(isNatIListKind(V2:S)) 0.002/0.002 U52(tt) -> tt 0.002/0.002 U61(tt,V2:S) -> U62(isNatIListKind(V2:S)) 0.002/0.002 U62(tt) -> tt 0.002/0.002 U71(tt) -> tt 0.002/0.002 U81(tt) -> tt 0.002/0.002 U91(tt,V1:S,V2:S) -> U92(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 U92(tt,V1:S,V2:S) -> U93(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U93(tt,V1:S,V2:S) -> U94(isNatIListKind(V2:S),V1:S,V2:S) 0.002/0.002 U94(tt,V1:S,V2:S) -> U95(isNat(V1:S),V2:S) 0.002/0.002 U95(tt,V2:S) -> U96(isNatList(V2:S)) 0.002/0.002 U96(tt) -> tt 0.002/0.002 isNat(length(V1:S)) -> U11(isNatIListKind(V1:S),V1:S) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> U21(isNatKind(V1:S),V1:S) 0.002/0.002 isNatIList(zeros) -> tt 0.002/0.002 isNatIList(cons(V1:S,V2:S)) -> U41(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatIList(V:S) -> U31(isNatIListKind(V:S),V:S) 0.002/0.002 isNatIListKind(take(V1:S,V2:S)) -> U61(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(zeros) -> tt 0.002/0.002 isNatIListKind(cons(V1:S,V2:S)) -> U51(isNatKind(V1:S),V2:S) 0.002/0.002 isNatIListKind(nil) -> tt 0.002/0.002 isNatKind(length(V1:S)) -> U71(isNatIListKind(V1:S)) 0.002/0.002 isNatKind(0) -> tt 0.002/0.002 isNatKind(s(V1:S)) -> U81(isNatKind(V1:S)) 0.002/0.002 isNatList(take(V1:S,V2:S)) -> U101(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(cons(V1:S,V2:S)) -> U91(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 isNatList(nil) -> tt 0.002/0.002 length(cons(N:S,L:S)) -> U111(isNatList(L:S),L:S,N:S) 0.002/0.002 length(nil) -> 0 0.002/0.002 take(0,IL:S) -> U121(isNatIList(IL:S),IL:S) 0.002/0.002 take(s(M:S),cons(N:S,IL:S)) -> U131(isNatIList(IL:S),IL:S,M:S,N:S) 0.002/0.002 zeros -> cons(0,zeros) 0.002/0.002 -> Vars: 0.002/0.002 V1, V2, V1, V2, V1, V2, V1, V2, V2, V1, L, N, L, N, L, N, L, V1, IL, IL, M, N, IL, M, N, IL, M, N, IL, M, N, IL, M, N, IL, M, N, V1, V1, V, V, V1, V2, V1, V2, V1, V2, V1, V2, V2, V2, V2, V1, V2, V1, V2, V1, V2, V1, V2, V2, V1, V1, V1, V2, V, V1, V2, V1, V2, V1, V1, V1, V2, V1, V2, L, N, IL, IL, M, N 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, N], UV-RFrozen: [L, N]) 0.002/0.002 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, N], UV-RFrozen: [L, N]) 0.002/0.002 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [L, N], UV-RFrozen: [L, N]) 0.002/0.002 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [L], UV-LFrozen: [L], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL], UV-RFrozen: [IL]) 0.002/0.002 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M, N]) 0.002/0.002 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M, N]) 0.002/0.002 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M, N]) 0.002/0.002 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M, N]) 0.002/0.002 (UV-RuleId: 20, UV-LActive: [], UV-RActive: [], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M, N]) 0.002/0.002 (UV-RuleId: 21, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [IL, M, N], UV-RFrozen: [IL, M]) 0.002/0.002 (UV-RuleId: 22, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 23, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 25, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 27, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 29, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 30, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 31, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 32, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 33, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 34, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 35, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 36, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 37, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 38, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 39, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 40, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 41, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 42, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 43, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 44, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V2], UV-RFrozen: [V2]) 0.002/0.002 (UV-RuleId: 45, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 46, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 47, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 48, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 49, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 50, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 51, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V], UV-RFrozen: [V]) 0.002/0.002 (UV-RuleId: 52, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 53, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 54, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 55, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 56, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 57, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 58, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 59, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 60, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 61, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 62, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [L], UV-RFrozen: [L, N]) 0.002/0.002 (UV-RuleId: 63, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 64, UV-LActive: [IL], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [IL]) 0.002/0.002 (UV-RuleId: 65, UV-LActive: [M, N], UV-RActive: [], UV-LFrozen: [IL], UV-RFrozen: [IL, M, N]) 0.002/0.002 (UV-RuleId: 66, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 -> FVars: 0.002/0.002 x8, 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 0.002/0.002 -> PVars: 0.002/0.002 V1: [x8, x10, x12, x14, x17, x25, x45, x46, x49, x51, x53, x55, x60, x62, x64, x66, x69, x70, x71, x74, x76, x78, x79, x80, x82], V2: [x9, x11, x13, x15, x16, x50, x52, x54, x56, x57, x58, x59, x61, x63, x65, x67, x68, x72, x75, x77, x81, x83], L: [x18, x20, x22, x24, x84], N: [x19, x21, x23, x29, x32, x35, x38, x41, x44, x85, x89], IL: [x26, x27, x30, x33, x36, x39, x42, x86, x87], M: [x28, x31, x34, x37, x40, x43, x88], V: [x47, x48, x73] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: U101(tt,x8:S,x9:S) -> U102(isNatKind(x8:S),x8:S,x9:S), id: 1, possubterms: U101(tt,x8:S,x9:S)->[], tt->[1]) 0.002/0.002 (rule: U102(tt,x10:S,x11:S) -> U103(isNatIListKind(x11:S),x10:S,x11:S), id: 2, possubterms: U102(tt,x10:S,x11:S)->[], tt->[1]) 0.002/0.002 (rule: U103(tt,x12:S,x13:S) -> U104(isNatIListKind(x13:S),x12:S,x13:S), id: 3, possubterms: U103(tt,x12:S,x13:S)->[], tt->[1]) 0.002/0.002 (rule: U104(tt,x14:S,x15:S) -> U105(isNat(x14:S),x15:S), id: 4, possubterms: U104(tt,x14:S,x15:S)->[], tt->[1]) 0.002/0.002 (rule: U105(tt,x16:S) -> U106(isNatIList(x16:S)), id: 5, possubterms: U105(tt,x16:S)->[], tt->[1]) 0.002/0.002 (rule: U106(tt) -> tt, id: 6, possubterms: U106(tt)->[], tt->[1]) 0.002/0.002 (rule: U11(tt,x17:S) -> U12(isNatIListKind(x17:S),x17:S), id: 7, possubterms: U11(tt,x17:S)->[], tt->[1]) 0.002/0.002 (rule: U111(tt,x18:S,x19:S) -> U112(isNatIListKind(x18:S),x18:S,x19:S), id: 8, possubterms: U111(tt,x18:S,x19:S)->[], tt->[1]) 0.002/0.002 (rule: U112(tt,x20:S,x21:S) -> U113(isNat(x21:S),x20:S,x21:S), id: 9, possubterms: U112(tt,x20:S,x21:S)->[], tt->[1]) 0.002/0.002 (rule: U113(tt,x22:S,x23:S) -> U114(isNatKind(x23:S),x22:S), id: 10, possubterms: U113(tt,x22:S,x23:S)->[], tt->[1]) 0.002/0.002 (rule: U114(tt,x24:S) -> s(length(x24:S)), id: 11, possubterms: U114(tt,x24:S)->[], tt->[1]) 0.002/0.002 (rule: U12(tt,x25:S) -> U13(isNatList(x25:S)), id: 12, possubterms: U12(tt,x25:S)->[], tt->[1]) 0.002/0.002 (rule: U121(tt,x26:S) -> U122(isNatIListKind(x26:S)), id: 13, possubterms: U121(tt,x26:S)->[], tt->[1]) 0.002/0.002 (rule: U122(tt) -> nil, id: 14, possubterms: U122(tt)->[], tt->[1]) 0.002/0.002 (rule: U13(tt) -> tt, id: 15, possubterms: U13(tt)->[], tt->[1]) 0.002/0.002 (rule: U131(tt,x27:S,x28:S,x29:S) -> U132(isNatIListKind(x27:S),x27:S,x28:S,x29:S), id: 16, possubterms: U131(tt,x27:S,x28:S,x29:S)->[], tt->[1]) 0.002/0.002 (rule: U132(tt,x30:S,x31:S,x32:S) -> U133(isNat(x31:S),x30:S,x31:S,x32:S), id: 17, possubterms: U132(tt,x30:S,x31:S,x32:S)->[], tt->[1]) 0.002/0.002 (rule: U133(tt,x33:S,x34:S,x35:S) -> U134(isNatKind(x34:S),x33:S,x34:S,x35:S), id: 18, possubterms: U133(tt,x33:S,x34:S,x35:S)->[], tt->[1]) 0.002/0.002 (rule: U134(tt,x36:S,x37:S,x38:S) -> U135(isNat(x38:S),x36:S,x37:S,x38:S), id: 19, possubterms: U134(tt,x36:S,x37:S,x38:S)->[], tt->[1]) 0.002/0.002 (rule: U135(tt,x39:S,x40:S,x41:S) -> U136(isNatKind(x41:S),x39:S,x40:S,x41:S), id: 20, possubterms: U135(tt,x39:S,x40:S,x41:S)->[], tt->[1]) 0.002/0.002 (rule: U136(tt,x42:S,x43:S,x44:S) -> cons(x44:S,take(x43:S,x42:S)), id: 21, possubterms: U136(tt,x42:S,x43:S,x44:S)->[], tt->[1]) 0.002/0.002 (rule: U21(tt,x45:S) -> U22(isNatKind(x45:S),x45:S), id: 22, possubterms: U21(tt,x45:S)->[], tt->[1]) 0.002/0.002 (rule: U22(tt,x46:S) -> U23(isNat(x46:S)), id: 23, possubterms: U22(tt,x46:S)->[], tt->[1]) 0.002/0.002 (rule: U23(tt) -> tt, id: 24, possubterms: U23(tt)->[], tt->[1]) 0.002/0.002 (rule: U31(tt,x47:S) -> U32(isNatIListKind(x47:S),x47:S), id: 25, possubterms: U31(tt,x47:S)->[], tt->[1]) 0.002/0.002 (rule: U32(tt,x48:S) -> U33(isNatList(x48:S)), id: 26, possubterms: U32(tt,x48:S)->[], tt->[1]) 0.002/0.002 (rule: U33(tt) -> tt, id: 27, possubterms: U33(tt)->[], tt->[1]) 0.002/0.002 (rule: U41(tt,x49:S,x50:S) -> U42(isNatKind(x49:S),x49:S,x50:S), id: 28, possubterms: U41(tt,x49:S,x50:S)->[], tt->[1]) 0.002/0.002 (rule: U42(tt,x51:S,x52:S) -> U43(isNatIListKind(x52:S),x51:S,x52:S), id: 29, possubterms: U42(tt,x51:S,x52:S)->[], tt->[1]) 0.002/0.002 (rule: U43(tt,x53:S,x54:S) -> U44(isNatIListKind(x54:S),x53:S,x54:S), id: 30, possubterms: U43(tt,x53:S,x54:S)->[], tt->[1]) 0.002/0.002 (rule: U44(tt,x55:S,x56:S) -> U45(isNat(x55:S),x56:S), id: 31, possubterms: U44(tt,x55:S,x56:S)->[], tt->[1]) 0.002/0.002 (rule: U45(tt,x57:S) -> U46(isNatIList(x57:S)), id: 32, possubterms: U45(tt,x57:S)->[], tt->[1]) 0.002/0.002 (rule: U46(tt) -> tt, id: 33, possubterms: U46(tt)->[], tt->[1]) 0.002/0.002 (rule: U51(tt,x58:S) -> U52(isNatIListKind(x58:S)), id: 34, possubterms: U51(tt,x58:S)->[], tt->[1]) 0.002/0.002 (rule: U52(tt) -> tt, id: 35, possubterms: U52(tt)->[], tt->[1]) 0.002/0.002 (rule: U61(tt,x59:S) -> U62(isNatIListKind(x59:S)), id: 36, possubterms: U61(tt,x59:S)->[], tt->[1]) 0.002/0.002 (rule: U62(tt) -> tt, id: 37, possubterms: U62(tt)->[], tt->[1]) 0.002/0.002 (rule: U71(tt) -> tt, id: 38, possubterms: U71(tt)->[], tt->[1]) 0.002/0.002 (rule: U81(tt) -> tt, id: 39, possubterms: U81(tt)->[], tt->[1]) 0.002/0.002 (rule: U91(tt,x60:S,x61:S) -> U92(isNatKind(x60:S),x60:S,x61:S), id: 40, possubterms: U91(tt,x60:S,x61:S)->[], tt->[1]) 0.002/0.002 (rule: U92(tt,x62:S,x63:S) -> U93(isNatIListKind(x63:S),x62:S,x63:S), id: 41, possubterms: U92(tt,x62:S,x63:S)->[], tt->[1]) 0.002/0.002 (rule: U93(tt,x64:S,x65:S) -> U94(isNatIListKind(x65:S),x64:S,x65:S), id: 42, possubterms: U93(tt,x64:S,x65:S)->[], tt->[1]) 0.002/0.002 (rule: U94(tt,x66:S,x67:S) -> U95(isNat(x66:S),x67:S), id: 43, possubterms: U94(tt,x66:S,x67:S)->[], tt->[1]) 0.002/0.002 (rule: U95(tt,x68:S) -> U96(isNatList(x68:S)), id: 44, possubterms: U95(tt,x68:S)->[], tt->[1]) 0.002/0.002 (rule: U96(tt) -> tt, id: 45, possubterms: U96(tt)->[], tt->[1]) 0.002/0.002 (rule: isNat(length(x69:S)) -> U11(isNatIListKind(x69:S),x69:S), id: 46, possubterms: isNat(length(x69:S))->[]) 0.002/0.002 (rule: isNat(0) -> tt, id: 47, possubterms: isNat(0)->[]) 0.002/0.002 (rule: isNat(s(x70:S)) -> U21(isNatKind(x70:S),x70:S), id: 48, possubterms: isNat(s(x70:S))->[]) 0.002/0.002 (rule: isNatIList(zeros) -> tt, id: 49, possubterms: isNatIList(zeros)->[]) 0.002/0.002 (rule: isNatIList(cons(x71:S,x72:S)) -> U41(isNatKind(x71:S),x71:S,x72:S), id: 50, possubterms: isNatIList(cons(x71:S,x72:S))->[]) 0.002/0.002 (rule: isNatIList(x73:S) -> U31(isNatIListKind(x73:S),x73:S), id: 51, possubterms: isNatIList(x73:S)->[]) 0.002/0.002 (rule: isNatIListKind(take(x74:S,x75:S)) -> U61(isNatKind(x74:S),x75:S), id: 52, possubterms: isNatIListKind(take(x74:S,x75:S))->[]) 0.002/0.002 (rule: isNatIListKind(zeros) -> tt, id: 53, possubterms: isNatIListKind(zeros)->[]) 0.002/0.002 (rule: isNatIListKind(cons(x76:S,x77:S)) -> U51(isNatKind(x76:S),x77:S), id: 54, possubterms: isNatIListKind(cons(x76:S,x77:S))->[]) 0.002/0.002 (rule: isNatIListKind(nil) -> tt, id: 55, possubterms: isNatIListKind(nil)->[]) 0.002/0.002 (rule: isNatKind(length(x78:S)) -> U71(isNatIListKind(x78:S)), id: 56, possubterms: isNatKind(length(x78:S))->[]) 0.002/0.002 (rule: isNatKind(0) -> tt, id: 57, possubterms: isNatKind(0)->[]) 0.002/0.002 (rule: isNatKind(s(x79:S)) -> U81(isNatKind(x79:S)), id: 58, possubterms: isNatKind(s(x79:S))->[]) 0.002/0.002 (rule: isNatList(take(x80:S,x81:S)) -> U101(isNatKind(x80:S),x80:S,x81:S), id: 59, possubterms: isNatList(take(x80:S,x81:S))->[]) 0.002/0.002 (rule: isNatList(cons(x82:S,x83:S)) -> U91(isNatKind(x82:S),x82:S,x83:S), id: 60, possubterms: isNatList(cons(x82:S,x83:S))->[]) 0.002/0.002 (rule: isNatList(nil) -> tt, id: 61, possubterms: isNatList(nil)->[]) 0.002/0.002 (rule: length(cons(x85:S,x84:S)) -> U111(isNatList(x84:S),x84:S,x85:S), id: 62, possubterms: length(cons(x85:S,x84:S))->[], cons(x85:S,x84:S)->[1]) 0.002/0.002 (rule: length(nil) -> 0, id: 63, possubterms: length(nil)->[], nil->[1]) 0.002/0.002 (rule: take(0,x86:S) -> U121(isNatIList(x86:S),x86:S), id: 64, possubterms: take(0,x86:S)->[], 0->[1]) 0.002/0.002 (rule: take(s(x88:S),cons(x89:S,x87:S)) -> U131(isNatIList(x87:S),x87:S,x88:S,x89:S), id: 65, possubterms: take(s(x88:S),cons(x89:S,x87:S))->[], s(x88:S)->[1], cons(x89:S,x87:S)->[2]) 0.002/0.002 (rule: zeros -> cons(0,zeros), id: 66, possubterms: zeros->[]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 (R51 unifies with R49 at p: [], l: isNatIList(x73:S), lp: isNatIList(x73:S), sig: {x73:S -> zeros}, l': isNatIList(zeros), r: U31(isNatIListKind(x73:S),x73:S), r': tt) 0.002/0.002 (R51 unifies with R50 at p: [], l: isNatIList(x73:S), lp: isNatIList(x73:S), sig: {x73:S -> cons(V1:S,V2:S)}, l': isNatIList(cons(V1:S,V2:S)), r: U31(isNatIListKind(x73:S),x73:S), r': U41(isNatKind(V1:S),V1:S,V2:S)) 0.002/0.002 0.002/0.002 -> Critical pairs info: 0.002/0.002 => Not trivial, Overlay, NW0, N1 0.002/0.002 => Not trivial, Overlay, NW0, N2 0.002/0.002 0.002/0.002 -> Problem conclusions: 0.002/0.002 Left linear, Not right linear, Not linear 0.002/0.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.002/0.002 Not Huet-Levy confluent, Not Newman confluent 0.002/0.002 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 No Convergence Brute Force Processor: 0.002/0.002 -> Rewritings: 0.002/0.002 s: U41(isNatKind(V1:S),V1:S,V2:S) 0.002/0.002 Nodes: [0] 0.002/0.002 Edges: [] 0.002/0.002 ID: 0 => ('U41(isNatKind(V1:S),V1:S,V2:S)', D0) 0.002/0.002 t: U31(isNatIListKind(cons(V1:S,V2:S)),cons(V1:S,V2:S)) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('U31(isNatIListKind(cons(V1:S,V2:S)),cons(V1:S,V2:S))', D0) 0.002/0.002 ID: 1 => ('U31(U51(isNatKind(V1:S),V2:S),cons(V1:S,V2:S))', D1, R54, P[1], S{x76:S -> V1:S, x77:S -> V2:S}), NR: 'U51(isNatKind(V1:S),V2:S)' 0.002/0.002 U41(isNatKind(V1:S),V1:S,V2:S) ->* no union *<- U31(isNatIListKind(cons(V1:S,V2:S)),cons(V1:S,V2:S)) 0.002/0.002 "Not joinable" 0.002/0.002 0.002/0.002 The problem is not joinable. 0.002/0.002 0.01user 0.00system 0:00.02elapsed 72%CPU (0avgtext+0avgdata 11848maxresident)k 0.002/0.002 0inputs+0outputs (0major+1205minor)pagefaults 0swaps