7.47/7.61 YES 7.47/7.61 7.47/7.61 Problem 1: 7.47/7.61 7.47/7.61 (VAR v_NonEmpty:S IL:S L:S M:S N:S V:S V1:S V2:S X:S X1:S X2:S X3:S X4:S) 7.47/7.61 (RULES 7.47/7.61 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.61 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.61 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.61 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.61 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.61 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.61 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.61 a__U106(tt) -> tt 7.47/7.61 a__U106(X:S) -> U106(X:S) 7.47/7.61 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.61 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.61 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.61 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.61 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.61 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.61 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.61 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.61 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.61 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.61 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.61 a__U122(tt) -> nil 7.47/7.61 a__U122(X:S) -> U122(X:S) 7.47/7.61 a__U13(tt) -> tt 7.47/7.61 a__U13(X:S) -> U13(X:S) 7.47/7.61 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.61 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.61 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.61 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.61 a__U23(tt) -> tt 7.47/7.61 a__U23(X:S) -> U23(X:S) 7.47/7.61 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.61 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.61 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.61 a__U33(tt) -> tt 7.47/7.61 a__U33(X:S) -> U33(X:S) 7.47/7.61 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.61 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.61 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.61 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.61 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.61 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.61 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.61 a__U46(tt) -> tt 7.47/7.61 a__U46(X:S) -> U46(X:S) 7.47/7.61 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.61 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.61 a__U52(tt) -> tt 7.47/7.61 a__U52(X:S) -> U52(X:S) 7.47/7.61 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.61 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.61 a__U62(tt) -> tt 7.47/7.61 a__U62(X:S) -> U62(X:S) 7.47/7.61 a__U71(tt) -> tt 7.47/7.61 a__U71(X:S) -> U71(X:S) 7.47/7.61 a__U81(tt) -> tt 7.47/7.61 a__U81(X:S) -> U81(X:S) 7.47/7.61 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.61 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.61 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.61 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.61 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.61 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.61 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.61 a__U96(tt) -> tt 7.47/7.61 a__U96(X:S) -> U96(X:S) 7.47/7.61 a__isNat(0) -> tt 7.47/7.61 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__isNat(X:S) -> isNat(X:S) 7.47/7.61 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatIList(zeros) -> tt 7.47/7.61 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.61 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(nil) -> tt 7.47/7.61 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(zeros) -> tt 7.47/7.61 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.61 a__isNatKind(0) -> tt 7.47/7.61 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.61 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.61 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.61 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(nil) -> tt 7.47/7.61 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.61 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 a__length(nil) -> 0 7.47/7.61 a__length(X:S) -> length(X:S) 7.47/7.61 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.61 a__zeros -> cons(0,zeros) 7.47/7.61 a__zeros -> zeros 7.47/7.61 mark(0) -> 0 7.47/7.61 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.61 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.61 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.61 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.61 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.61 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.61 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.61 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.61 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.61 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.61 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.61 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.61 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.61 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.61 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.61 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.61 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.61 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.61 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.61 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.61 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.61 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.61 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.61 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.61 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.61 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.61 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.61 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.61 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.61 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.61 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.61 mark(nil) -> nil 7.47/7.61 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.61 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.61 mark(tt) -> tt 7.47/7.61 mark(zeros) -> a__zeros 7.47/7.61 ) 7.47/7.61 (STRATEGY INNERMOST) 7.47/7.61 7.47/7.61 Problem 1: 7.47/7.61 7.47/7.61 Dependency Pairs Processor: 7.47/7.61 -> Pairs: 7.47/7.61 A__U101(tt,V1:S,V2:S) -> A__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U101(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U102(tt,V1:S,V2:S) -> A__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U102(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U103(tt,V1:S,V2:S) -> A__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U103(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U104(tt,V1:S,V2:S) -> A__U105(a__isNat(V1:S),V2:S) 7.47/7.61 A__U104(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U105(tt,V2:S) -> A__U106(a__isNatIList(V2:S)) 7.47/7.61 A__U105(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.61 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 A__U11(tt,V1:S) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 A__U111(tt,L:S,N:S) -> A__ISNATILISTKIND(L:S) 7.47/7.61 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 A__U112(tt,L:S,N:S) -> A__ISNAT(N:S) 7.47/7.61 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.47/7.61 A__U113(tt,L:S,N:S) -> A__ISNATKIND(N:S) 7.47/7.61 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.47/7.61 A__U114(tt,L:S) -> MARK(L:S) 7.47/7.61 A__U12(tt,V1:S) -> A__U13(a__isNatList(V1:S)) 7.47/7.61 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.47/7.61 A__U121(tt,IL:S) -> A__U122(a__isNatIListKind(IL:S)) 7.47/7.61 A__U121(tt,IL:S) -> A__ISNATILISTKIND(IL:S) 7.47/7.61 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 A__U131(tt,IL:S,M:S,N:S) -> A__ISNATILISTKIND(IL:S) 7.47/7.61 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 A__U132(tt,IL:S,M:S,N:S) -> A__ISNAT(M:S) 7.47/7.61 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 A__U133(tt,IL:S,M:S,N:S) -> A__ISNATKIND(M:S) 7.47/7.61 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 A__U134(tt,IL:S,M:S,N:S) -> A__ISNAT(N:S) 7.47/7.61 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 A__U135(tt,IL:S,M:S,N:S) -> A__ISNATKIND(N:S) 7.47/7.61 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.47/7.61 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 A__U21(tt,V1:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U22(tt,V1:S) -> A__U23(a__isNat(V1:S)) 7.47/7.61 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 A__U31(tt,V:S) -> A__ISNATILISTKIND(V:S) 7.47/7.61 A__U32(tt,V:S) -> A__U33(a__isNatList(V:S)) 7.47/7.61 A__U32(tt,V:S) -> A__ISNATLIST(V:S) 7.47/7.61 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U41(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U42(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U43(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.47/7.61 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U45(tt,V2:S) -> A__U46(a__isNatIList(V2:S)) 7.47/7.61 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.61 A__U51(tt,V2:S) -> A__U52(a__isNatIListKind(V2:S)) 7.47/7.61 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U61(tt,V2:S) -> A__U62(a__isNatIListKind(V2:S)) 7.47/7.61 A__U61(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U91(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U92(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U93(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.47/7.61 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U95(tt,V2:S) -> A__U96(a__isNatList(V2:S)) 7.47/7.61 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.47/7.61 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 A__ISNAT(length(V1:S)) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 A__ISNAT(s(V1:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATILIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 A__ISNATILIST(V:S) -> A__ISNATILISTKIND(V:S) 7.47/7.61 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATKIND(length(V1:S)) -> A__U71(a__isNatIListKind(V1:S)) 7.47/7.61 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__ISNATKIND(s(V1:S)) -> A__U81(a__isNatKind(V1:S)) 7.47/7.61 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATLIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATLIST(take(V1:S,V2:S)) -> A__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATLIST(take(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 A__LENGTH(cons(N:S,L:S)) -> A__ISNATLIST(L:S) 7.47/7.61 A__TAKE(0,IL:S) -> A__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 A__TAKE(0,IL:S) -> A__ISNATILIST(IL:S) 7.47/7.61 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__ISNATILIST(IL:S) 7.47/7.61 MARK(U101(X1:S,X2:S,X3:S)) -> A__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U102(X1:S,X2:S,X3:S)) -> A__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U103(X1:S,X2:S,X3:S)) -> A__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U104(X1:S,X2:S,X3:S)) -> A__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U105(X1:S,X2:S)) -> A__U105(mark(X1:S),X2:S) 7.47/7.61 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U106(X:S)) -> A__U106(mark(X:S)) 7.47/7.61 MARK(U106(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 7.47/7.61 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U111(X1:S,X2:S,X3:S)) -> A__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U112(X1:S,X2:S,X3:S)) -> A__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U113(X1:S,X2:S,X3:S)) -> A__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U114(X1:S,X2:S)) -> A__U114(mark(X1:S),X2:S) 7.47/7.61 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U12(X1:S,X2:S)) -> A__U12(mark(X1:S),X2:S) 7.47/7.61 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U121(X1:S,X2:S)) -> A__U121(mark(X1:S),X2:S) 7.47/7.61 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U122(X:S)) -> A__U122(mark(X:S)) 7.47/7.61 MARK(U122(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U13(X:S)) -> A__U13(mark(X:S)) 7.47/7.61 MARK(U13(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S) 7.47/7.61 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 7.47/7.61 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U23(X:S)) -> A__U23(mark(X:S)) 7.47/7.61 MARK(U23(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S) 7.47/7.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U32(X1:S,X2:S)) -> A__U32(mark(X1:S),X2:S) 7.47/7.61 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U33(X:S)) -> A__U33(mark(X:S)) 7.47/7.61 MARK(U33(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U42(X1:S,X2:S,X3:S)) -> A__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U43(X1:S,X2:S,X3:S)) -> A__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U44(X1:S,X2:S,X3:S)) -> A__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U45(X1:S,X2:S)) -> A__U45(mark(X1:S),X2:S) 7.47/7.61 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U46(X:S)) -> A__U46(mark(X:S)) 7.47/7.61 MARK(U46(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U51(X1:S,X2:S)) -> A__U51(mark(X1:S),X2:S) 7.47/7.61 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U52(X:S)) -> A__U52(mark(X:S)) 7.47/7.61 MARK(U52(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U61(X1:S,X2:S)) -> A__U61(mark(X1:S),X2:S) 7.47/7.61 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U62(X:S)) -> A__U62(mark(X:S)) 7.47/7.61 MARK(U62(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U71(X:S)) -> A__U71(mark(X:S)) 7.47/7.61 MARK(U71(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U81(X:S)) -> A__U81(mark(X:S)) 7.47/7.61 MARK(U81(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U94(X1:S,X2:S,X3:S)) -> A__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U95(X1:S,X2:S)) -> A__U95(mark(X1:S),X2:S) 7.47/7.61 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U96(X:S)) -> A__U96(mark(X:S)) 7.47/7.61 MARK(U96(X:S)) -> MARK(X:S) 7.47/7.61 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(isNat(X:S)) -> A__ISNAT(X:S) 7.47/7.61 MARK(isNatIList(X:S)) -> A__ISNATILIST(X:S) 7.47/7.61 MARK(isNatIListKind(X:S)) -> A__ISNATILISTKIND(X:S) 7.47/7.61 MARK(isNatKind(X:S)) -> A__ISNATKIND(X:S) 7.47/7.61 MARK(isNatList(X:S)) -> A__ISNATLIST(X:S) 7.47/7.61 MARK(length(X:S)) -> A__LENGTH(mark(X:S)) 7.47/7.61 MARK(length(X:S)) -> MARK(X:S) 7.47/7.61 MARK(s(X:S)) -> MARK(X:S) 7.47/7.61 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.47/7.61 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.47/7.61 MARK(zeros) -> A__ZEROS 7.47/7.61 -> Rules: 7.47/7.61 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.61 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.61 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.61 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.61 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.61 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.61 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.61 a__U106(tt) -> tt 7.47/7.61 a__U106(X:S) -> U106(X:S) 7.47/7.61 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.61 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.61 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.61 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.61 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.61 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.61 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.61 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.61 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.61 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.61 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.61 a__U122(tt) -> nil 7.47/7.61 a__U122(X:S) -> U122(X:S) 7.47/7.61 a__U13(tt) -> tt 7.47/7.61 a__U13(X:S) -> U13(X:S) 7.47/7.61 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.61 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.61 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.61 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.61 a__U23(tt) -> tt 7.47/7.61 a__U23(X:S) -> U23(X:S) 7.47/7.61 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.61 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.61 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.61 a__U33(tt) -> tt 7.47/7.61 a__U33(X:S) -> U33(X:S) 7.47/7.61 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.61 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.61 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.61 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.61 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.61 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.61 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.61 a__U46(tt) -> tt 7.47/7.61 a__U46(X:S) -> U46(X:S) 7.47/7.61 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.61 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.61 a__U52(tt) -> tt 7.47/7.61 a__U52(X:S) -> U52(X:S) 7.47/7.61 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.61 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.61 a__U62(tt) -> tt 7.47/7.61 a__U62(X:S) -> U62(X:S) 7.47/7.61 a__U71(tt) -> tt 7.47/7.61 a__U71(X:S) -> U71(X:S) 7.47/7.61 a__U81(tt) -> tt 7.47/7.61 a__U81(X:S) -> U81(X:S) 7.47/7.61 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.61 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.61 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.61 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.61 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.61 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.61 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.61 a__U96(tt) -> tt 7.47/7.61 a__U96(X:S) -> U96(X:S) 7.47/7.61 a__isNat(0) -> tt 7.47/7.61 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__isNat(X:S) -> isNat(X:S) 7.47/7.61 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatIList(zeros) -> tt 7.47/7.61 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.61 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(nil) -> tt 7.47/7.61 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(zeros) -> tt 7.47/7.61 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.61 a__isNatKind(0) -> tt 7.47/7.61 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.61 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.61 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.61 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(nil) -> tt 7.47/7.61 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.61 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 a__length(nil) -> 0 7.47/7.61 a__length(X:S) -> length(X:S) 7.47/7.61 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.61 a__zeros -> cons(0,zeros) 7.47/7.61 a__zeros -> zeros 7.47/7.61 mark(0) -> 0 7.47/7.61 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.61 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.61 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.61 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.61 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.61 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.61 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.61 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.61 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.61 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.61 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.61 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.61 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.61 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.61 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.61 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.61 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.61 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.61 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.61 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.61 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.61 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.61 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.61 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.61 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.61 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.61 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.61 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.61 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.61 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.61 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.61 mark(nil) -> nil 7.47/7.61 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.61 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.61 mark(tt) -> tt 7.47/7.61 mark(zeros) -> a__zeros 7.47/7.61 7.47/7.61 Problem 1: 7.47/7.61 7.47/7.61 SCC Processor: 7.47/7.61 -> Pairs: 7.47/7.61 A__U101(tt,V1:S,V2:S) -> A__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U101(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U102(tt,V1:S,V2:S) -> A__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U102(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U103(tt,V1:S,V2:S) -> A__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U103(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U104(tt,V1:S,V2:S) -> A__U105(a__isNat(V1:S),V2:S) 7.47/7.61 A__U104(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U105(tt,V2:S) -> A__U106(a__isNatIList(V2:S)) 7.47/7.61 A__U105(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.61 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 A__U11(tt,V1:S) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 A__U111(tt,L:S,N:S) -> A__ISNATILISTKIND(L:S) 7.47/7.61 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 A__U112(tt,L:S,N:S) -> A__ISNAT(N:S) 7.47/7.61 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.47/7.61 A__U113(tt,L:S,N:S) -> A__ISNATKIND(N:S) 7.47/7.61 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.47/7.61 A__U114(tt,L:S) -> MARK(L:S) 7.47/7.61 A__U12(tt,V1:S) -> A__U13(a__isNatList(V1:S)) 7.47/7.61 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.47/7.61 A__U121(tt,IL:S) -> A__U122(a__isNatIListKind(IL:S)) 7.47/7.61 A__U121(tt,IL:S) -> A__ISNATILISTKIND(IL:S) 7.47/7.61 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 A__U131(tt,IL:S,M:S,N:S) -> A__ISNATILISTKIND(IL:S) 7.47/7.61 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 A__U132(tt,IL:S,M:S,N:S) -> A__ISNAT(M:S) 7.47/7.61 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 A__U133(tt,IL:S,M:S,N:S) -> A__ISNATKIND(M:S) 7.47/7.61 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 A__U134(tt,IL:S,M:S,N:S) -> A__ISNAT(N:S) 7.47/7.61 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 A__U135(tt,IL:S,M:S,N:S) -> A__ISNATKIND(N:S) 7.47/7.61 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.47/7.61 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 A__U21(tt,V1:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U22(tt,V1:S) -> A__U23(a__isNat(V1:S)) 7.47/7.61 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 A__U31(tt,V:S) -> A__ISNATILISTKIND(V:S) 7.47/7.61 A__U32(tt,V:S) -> A__U33(a__isNatList(V:S)) 7.47/7.61 A__U32(tt,V:S) -> A__ISNATLIST(V:S) 7.47/7.61 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U41(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U42(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U43(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.47/7.61 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U45(tt,V2:S) -> A__U46(a__isNatIList(V2:S)) 7.47/7.61 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.61 A__U51(tt,V2:S) -> A__U52(a__isNatIListKind(V2:S)) 7.47/7.61 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U61(tt,V2:S) -> A__U62(a__isNatIListKind(V2:S)) 7.47/7.61 A__U61(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U91(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S) 7.47/7.61 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U92(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U93(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.47/7.61 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U95(tt,V2:S) -> A__U96(a__isNatList(V2:S)) 7.47/7.61 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.47/7.61 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 A__ISNAT(length(V1:S)) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 A__ISNAT(s(V1:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATILIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 A__ISNATILIST(V:S) -> A__ISNATILISTKIND(V:S) 7.47/7.61 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATKIND(length(V1:S)) -> A__U71(a__isNatIListKind(V1:S)) 7.47/7.61 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__ISNATKIND(s(V1:S)) -> A__U81(a__isNatKind(V1:S)) 7.47/7.61 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATLIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATLIST(take(V1:S,V2:S)) -> A__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATLIST(take(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 A__LENGTH(cons(N:S,L:S)) -> A__ISNATLIST(L:S) 7.47/7.61 A__TAKE(0,IL:S) -> A__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 A__TAKE(0,IL:S) -> A__ISNATILIST(IL:S) 7.47/7.61 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__ISNATILIST(IL:S) 7.47/7.61 MARK(U101(X1:S,X2:S,X3:S)) -> A__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U102(X1:S,X2:S,X3:S)) -> A__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U103(X1:S,X2:S,X3:S)) -> A__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U104(X1:S,X2:S,X3:S)) -> A__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U105(X1:S,X2:S)) -> A__U105(mark(X1:S),X2:S) 7.47/7.61 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U106(X:S)) -> A__U106(mark(X:S)) 7.47/7.61 MARK(U106(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S) 7.47/7.61 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U111(X1:S,X2:S,X3:S)) -> A__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U112(X1:S,X2:S,X3:S)) -> A__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U113(X1:S,X2:S,X3:S)) -> A__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U114(X1:S,X2:S)) -> A__U114(mark(X1:S),X2:S) 7.47/7.61 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U12(X1:S,X2:S)) -> A__U12(mark(X1:S),X2:S) 7.47/7.61 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U121(X1:S,X2:S)) -> A__U121(mark(X1:S),X2:S) 7.47/7.61 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U122(X:S)) -> A__U122(mark(X:S)) 7.47/7.61 MARK(U122(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U13(X:S)) -> A__U13(mark(X:S)) 7.47/7.61 MARK(U13(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S) 7.47/7.61 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S) 7.47/7.61 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U23(X:S)) -> A__U23(mark(X:S)) 7.47/7.61 MARK(U23(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S) 7.47/7.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U32(X1:S,X2:S)) -> A__U32(mark(X1:S),X2:S) 7.47/7.61 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U33(X:S)) -> A__U33(mark(X:S)) 7.47/7.61 MARK(U33(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U42(X1:S,X2:S,X3:S)) -> A__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U43(X1:S,X2:S,X3:S)) -> A__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U44(X1:S,X2:S,X3:S)) -> A__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U45(X1:S,X2:S)) -> A__U45(mark(X1:S),X2:S) 7.47/7.61 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U46(X:S)) -> A__U46(mark(X:S)) 7.47/7.61 MARK(U46(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U51(X1:S,X2:S)) -> A__U51(mark(X1:S),X2:S) 7.47/7.61 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U52(X:S)) -> A__U52(mark(X:S)) 7.47/7.61 MARK(U52(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U61(X1:S,X2:S)) -> A__U61(mark(X1:S),X2:S) 7.47/7.61 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U62(X:S)) -> A__U62(mark(X:S)) 7.47/7.61 MARK(U62(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U71(X:S)) -> A__U71(mark(X:S)) 7.47/7.61 MARK(U71(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U81(X:S)) -> A__U81(mark(X:S)) 7.47/7.61 MARK(U81(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U94(X1:S,X2:S,X3:S)) -> A__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U95(X1:S,X2:S)) -> A__U95(mark(X1:S),X2:S) 7.47/7.61 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U96(X:S)) -> A__U96(mark(X:S)) 7.47/7.61 MARK(U96(X:S)) -> MARK(X:S) 7.47/7.61 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(isNat(X:S)) -> A__ISNAT(X:S) 7.47/7.61 MARK(isNatIList(X:S)) -> A__ISNATILIST(X:S) 7.47/7.61 MARK(isNatIListKind(X:S)) -> A__ISNATILISTKIND(X:S) 7.47/7.61 MARK(isNatKind(X:S)) -> A__ISNATKIND(X:S) 7.47/7.61 MARK(isNatList(X:S)) -> A__ISNATLIST(X:S) 7.47/7.61 MARK(length(X:S)) -> A__LENGTH(mark(X:S)) 7.47/7.61 MARK(length(X:S)) -> MARK(X:S) 7.47/7.61 MARK(s(X:S)) -> MARK(X:S) 7.47/7.61 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.47/7.61 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.47/7.61 MARK(zeros) -> A__ZEROS 7.47/7.61 -> Rules: 7.47/7.61 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.61 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.61 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.61 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.61 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.61 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.61 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.61 a__U106(tt) -> tt 7.47/7.61 a__U106(X:S) -> U106(X:S) 7.47/7.61 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.61 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.61 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.61 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.61 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.61 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.61 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.61 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.61 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.61 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.61 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.61 a__U122(tt) -> nil 7.47/7.61 a__U122(X:S) -> U122(X:S) 7.47/7.61 a__U13(tt) -> tt 7.47/7.61 a__U13(X:S) -> U13(X:S) 7.47/7.61 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.61 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.61 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.61 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.61 a__U23(tt) -> tt 7.47/7.61 a__U23(X:S) -> U23(X:S) 7.47/7.61 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.61 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.61 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.61 a__U33(tt) -> tt 7.47/7.61 a__U33(X:S) -> U33(X:S) 7.47/7.61 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.61 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.61 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.61 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.61 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.61 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.61 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.61 a__U46(tt) -> tt 7.47/7.61 a__U46(X:S) -> U46(X:S) 7.47/7.61 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.61 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.61 a__U52(tt) -> tt 7.47/7.61 a__U52(X:S) -> U52(X:S) 7.47/7.61 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.61 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.61 a__U62(tt) -> tt 7.47/7.61 a__U62(X:S) -> U62(X:S) 7.47/7.61 a__U71(tt) -> tt 7.47/7.61 a__U71(X:S) -> U71(X:S) 7.47/7.61 a__U81(tt) -> tt 7.47/7.61 a__U81(X:S) -> U81(X:S) 7.47/7.61 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.61 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.61 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.61 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.61 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.61 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.61 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.61 a__U96(tt) -> tt 7.47/7.61 a__U96(X:S) -> U96(X:S) 7.47/7.61 a__isNat(0) -> tt 7.47/7.61 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__isNat(X:S) -> isNat(X:S) 7.47/7.61 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatIList(zeros) -> tt 7.47/7.61 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.61 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(nil) -> tt 7.47/7.61 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(zeros) -> tt 7.47/7.61 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.61 a__isNatKind(0) -> tt 7.47/7.61 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.61 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.61 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.61 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(nil) -> tt 7.47/7.61 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.61 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 a__length(nil) -> 0 7.47/7.61 a__length(X:S) -> length(X:S) 7.47/7.61 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.61 a__zeros -> cons(0,zeros) 7.47/7.61 a__zeros -> zeros 7.47/7.61 mark(0) -> 0 7.47/7.61 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.61 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.61 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.61 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.61 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.61 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.61 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.61 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.61 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.61 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.61 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.61 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.61 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.61 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.61 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.61 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.61 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.61 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.61 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.61 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.61 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.61 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.61 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.61 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.61 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.61 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.61 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.61 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.61 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.61 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.61 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.61 mark(nil) -> nil 7.47/7.61 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.61 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.61 mark(tt) -> tt 7.47/7.61 mark(zeros) -> a__zeros 7.47/7.61 ->Strongly Connected Components: 7.47/7.61 ->->Cycle: 7.47/7.61 ->->-> Pairs: 7.47/7.61 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__U61(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.61 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S) 7.47/7.61 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S) 7.47/7.61 ->->-> Rules: 7.47/7.61 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.61 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.61 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.61 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.61 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.61 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.61 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.61 a__U106(tt) -> tt 7.47/7.61 a__U106(X:S) -> U106(X:S) 7.47/7.61 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.61 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.61 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.61 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.61 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.61 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.61 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.61 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.61 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.61 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.61 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.61 a__U122(tt) -> nil 7.47/7.61 a__U122(X:S) -> U122(X:S) 7.47/7.61 a__U13(tt) -> tt 7.47/7.61 a__U13(X:S) -> U13(X:S) 7.47/7.61 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.61 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.61 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.61 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.61 a__U23(tt) -> tt 7.47/7.61 a__U23(X:S) -> U23(X:S) 7.47/7.61 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.61 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.61 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.61 a__U33(tt) -> tt 7.47/7.61 a__U33(X:S) -> U33(X:S) 7.47/7.61 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.61 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.61 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.61 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.61 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.61 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.61 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.61 a__U46(tt) -> tt 7.47/7.61 a__U46(X:S) -> U46(X:S) 7.47/7.61 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.61 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.61 a__U52(tt) -> tt 7.47/7.61 a__U52(X:S) -> U52(X:S) 7.47/7.61 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.61 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.61 a__U62(tt) -> tt 7.47/7.61 a__U62(X:S) -> U62(X:S) 7.47/7.61 a__U71(tt) -> tt 7.47/7.61 a__U71(X:S) -> U71(X:S) 7.47/7.61 a__U81(tt) -> tt 7.47/7.61 a__U81(X:S) -> U81(X:S) 7.47/7.61 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.61 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.61 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.61 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.61 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.61 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.61 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.61 a__U96(tt) -> tt 7.47/7.61 a__U96(X:S) -> U96(X:S) 7.47/7.61 a__isNat(0) -> tt 7.47/7.61 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__isNat(X:S) -> isNat(X:S) 7.47/7.61 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatIList(zeros) -> tt 7.47/7.61 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.61 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(nil) -> tt 7.47/7.61 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(zeros) -> tt 7.47/7.61 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.61 a__isNatKind(0) -> tt 7.47/7.61 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.61 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.61 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.61 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(nil) -> tt 7.47/7.61 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.61 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 a__length(nil) -> 0 7.47/7.61 a__length(X:S) -> length(X:S) 7.47/7.61 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.61 a__zeros -> cons(0,zeros) 7.47/7.61 a__zeros -> zeros 7.47/7.61 mark(0) -> 0 7.47/7.61 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.61 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.61 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.61 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.61 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.61 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.61 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.61 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.61 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.61 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.61 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.61 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.61 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.61 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.61 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.61 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.61 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.61 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.61 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.61 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.61 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.61 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.61 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.61 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.61 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.61 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.61 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.61 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.61 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.61 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.61 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.61 mark(nil) -> nil 7.47/7.61 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.61 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.61 mark(tt) -> tt 7.47/7.61 mark(zeros) -> a__zeros 7.47/7.61 ->->Cycle: 7.47/7.61 ->->-> Pairs: 7.47/7.61 A__U101(tt,V1:S,V2:S) -> A__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U102(tt,V1:S,V2:S) -> A__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U103(tt,V1:S,V2:S) -> A__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U104(tt,V1:S,V2:S) -> A__U105(a__isNat(V1:S),V2:S) 7.47/7.61 A__U104(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U105(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.61 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.47/7.61 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 A__U32(tt,V:S) -> A__ISNATLIST(V:S) 7.47/7.61 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.47/7.61 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.61 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.47/7.61 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.61 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.47/7.61 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 A__ISNATLIST(take(V1:S,V2:S)) -> A__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 ->->-> Rules: 7.47/7.61 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.61 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.61 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.61 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.61 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.61 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.61 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.61 a__U106(tt) -> tt 7.47/7.61 a__U106(X:S) -> U106(X:S) 7.47/7.61 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.61 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.61 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.61 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.61 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.61 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.61 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.61 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.61 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.61 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.61 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.61 a__U122(tt) -> nil 7.47/7.61 a__U122(X:S) -> U122(X:S) 7.47/7.61 a__U13(tt) -> tt 7.47/7.61 a__U13(X:S) -> U13(X:S) 7.47/7.61 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.61 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.61 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.61 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.61 a__U23(tt) -> tt 7.47/7.61 a__U23(X:S) -> U23(X:S) 7.47/7.61 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.61 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.61 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.61 a__U33(tt) -> tt 7.47/7.61 a__U33(X:S) -> U33(X:S) 7.47/7.61 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.61 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.61 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.61 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.61 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.61 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.61 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.61 a__U46(tt) -> tt 7.47/7.61 a__U46(X:S) -> U46(X:S) 7.47/7.61 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.61 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.61 a__U52(tt) -> tt 7.47/7.61 a__U52(X:S) -> U52(X:S) 7.47/7.61 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.61 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.61 a__U62(tt) -> tt 7.47/7.61 a__U62(X:S) -> U62(X:S) 7.47/7.61 a__U71(tt) -> tt 7.47/7.61 a__U71(X:S) -> U71(X:S) 7.47/7.61 a__U81(tt) -> tt 7.47/7.61 a__U81(X:S) -> U81(X:S) 7.47/7.61 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.61 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.61 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.61 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.61 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.61 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.61 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.61 a__U96(tt) -> tt 7.47/7.61 a__U96(X:S) -> U96(X:S) 7.47/7.61 a__isNat(0) -> tt 7.47/7.61 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__isNat(X:S) -> isNat(X:S) 7.47/7.61 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatIList(zeros) -> tt 7.47/7.61 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.61 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(nil) -> tt 7.47/7.61 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.61 a__isNatIListKind(zeros) -> tt 7.47/7.61 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.61 a__isNatKind(0) -> tt 7.47/7.61 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.61 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.61 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.61 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(nil) -> tt 7.47/7.61 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.61 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 a__length(nil) -> 0 7.47/7.61 a__length(X:S) -> length(X:S) 7.47/7.61 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.61 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.61 a__zeros -> cons(0,zeros) 7.47/7.61 a__zeros -> zeros 7.47/7.61 mark(0) -> 0 7.47/7.61 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.61 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.61 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.61 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.61 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.61 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.61 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.61 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.61 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.61 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.61 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.61 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.61 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.61 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.61 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.61 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.61 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.61 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.61 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.61 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.61 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.61 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.61 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.61 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.61 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.61 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.61 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.61 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.61 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.61 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.61 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.61 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.61 mark(nil) -> nil 7.47/7.61 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.61 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.61 mark(tt) -> tt 7.47/7.61 mark(zeros) -> a__zeros 7.47/7.61 ->->Cycle: 7.47/7.61 ->->-> Pairs: 7.47/7.61 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.47/7.61 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.47/7.61 A__U114(tt,L:S) -> MARK(L:S) 7.47/7.61 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.47/7.61 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.61 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.61 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U106(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U111(X1:S,X2:S,X3:S)) -> A__U111(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U112(X1:S,X2:S,X3:S)) -> A__U112(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U113(X1:S,X2:S,X3:S)) -> A__U113(mark(X1:S),X2:S,X3:S) 7.47/7.61 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U114(X1:S,X2:S)) -> A__U114(mark(X1:S),X2:S) 7.47/7.61 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U122(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U13(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.61 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.47/7.61 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U23(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U33(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U46(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U52(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U62(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U71(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U81(X:S)) -> MARK(X:S) 7.47/7.61 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.47/7.61 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(U96(X:S)) -> MARK(X:S) 7.47/7.61 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(length(X:S)) -> A__LENGTH(mark(X:S)) 7.47/7.61 MARK(length(X:S)) -> MARK(X:S) 7.47/7.61 MARK(s(X:S)) -> MARK(X:S) 7.47/7.61 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.47/7.61 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.47/7.61 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.47/7.61 ->->-> Rules: 7.47/7.61 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.61 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.61 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.61 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.61 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.61 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.61 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.61 a__U106(tt) -> tt 7.47/7.61 a__U106(X:S) -> U106(X:S) 7.47/7.61 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.61 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.61 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.61 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.61 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.61 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.61 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.61 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.61 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.61 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.61 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.61 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.61 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.61 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.61 a__U122(tt) -> nil 7.47/7.61 a__U122(X:S) -> U122(X:S) 7.47/7.61 a__U13(tt) -> tt 7.47/7.61 a__U13(X:S) -> U13(X:S) 7.47/7.61 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.61 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.61 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.61 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.61 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.61 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.61 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.61 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.61 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.61 a__U23(tt) -> tt 7.47/7.61 a__U23(X:S) -> U23(X:S) 7.47/7.61 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.61 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.61 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.61 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.61 a__U33(tt) -> tt 7.47/7.61 a__U33(X:S) -> U33(X:S) 7.47/7.61 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.61 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.61 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.61 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.61 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.61 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.61 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.61 a__U46(tt) -> tt 7.47/7.61 a__U46(X:S) -> U46(X:S) 7.47/7.61 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.61 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.61 a__U52(tt) -> tt 7.47/7.61 a__U52(X:S) -> U52(X:S) 7.47/7.61 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.61 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.61 a__U62(tt) -> tt 7.47/7.61 a__U62(X:S) -> U62(X:S) 7.47/7.61 a__U71(tt) -> tt 7.47/7.61 a__U71(X:S) -> U71(X:S) 7.47/7.61 a__U81(tt) -> tt 7.47/7.61 a__U81(X:S) -> U81(X:S) 7.47/7.61 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.61 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.61 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.61 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.61 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.61 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.61 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.61 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.61 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.61 a__U96(tt) -> tt 7.47/7.61 a__U96(X:S) -> U96(X:S) 7.47/7.62 a__isNat(0) -> tt 7.47/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__isNat(X:S) -> isNat(X:S) 7.47/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatIList(zeros) -> tt 7.47/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(nil) -> tt 7.47/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(zeros) -> tt 7.47/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.62 a__isNatKind(0) -> tt 7.47/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(nil) -> tt 7.47/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.62 a__length(nil) -> 0 7.47/7.62 a__length(X:S) -> length(X:S) 7.47/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.62 a__zeros -> cons(0,zeros) 7.47/7.62 a__zeros -> zeros 7.47/7.62 mark(0) -> 0 7.47/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.62 mark(nil) -> nil 7.47/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.62 mark(tt) -> tt 7.47/7.62 mark(zeros) -> a__zeros 7.47/7.62 7.47/7.62 7.47/7.62 The problem is decomposed in 3 subproblems. 7.47/7.62 7.47/7.62 Problem 1.1: 7.47/7.62 7.47/7.62 Subterm Processor: 7.47/7.62 -> Pairs: 7.47/7.62 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.62 A__U61(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.62 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S) 7.47/7.62 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.62 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__U61(a__isNatKind(V1:S),V2:S) 7.47/7.62 A__ISNATILISTKIND(take(V1:S,V2:S)) -> A__ISNATKIND(V1:S) 7.47/7.62 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S) 7.47/7.62 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S) 7.47/7.62 -> Rules: 7.47/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.62 a__U106(tt) -> tt 7.47/7.62 a__U106(X:S) -> U106(X:S) 7.47/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.62 a__U122(tt) -> nil 7.47/7.62 a__U122(X:S) -> U122(X:S) 7.47/7.62 a__U13(tt) -> tt 7.47/7.62 a__U13(X:S) -> U13(X:S) 7.47/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.62 a__U23(tt) -> tt 7.47/7.62 a__U23(X:S) -> U23(X:S) 7.47/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.62 a__U33(tt) -> tt 7.47/7.62 a__U33(X:S) -> U33(X:S) 7.47/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.62 a__U46(tt) -> tt 7.47/7.62 a__U46(X:S) -> U46(X:S) 7.47/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.62 a__U52(tt) -> tt 7.47/7.62 a__U52(X:S) -> U52(X:S) 7.47/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.62 a__U62(tt) -> tt 7.47/7.62 a__U62(X:S) -> U62(X:S) 7.47/7.62 a__U71(tt) -> tt 7.47/7.62 a__U71(X:S) -> U71(X:S) 7.47/7.62 a__U81(tt) -> tt 7.47/7.62 a__U81(X:S) -> U81(X:S) 7.47/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.62 a__U96(tt) -> tt 7.47/7.62 a__U96(X:S) -> U96(X:S) 7.47/7.62 a__isNat(0) -> tt 7.47/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__isNat(X:S) -> isNat(X:S) 7.47/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatIList(zeros) -> tt 7.47/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(nil) -> tt 7.47/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(zeros) -> tt 7.47/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.62 a__isNatKind(0) -> tt 7.47/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(nil) -> tt 7.47/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.62 a__length(nil) -> 0 7.47/7.62 a__length(X:S) -> length(X:S) 7.47/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.62 a__zeros -> cons(0,zeros) 7.47/7.62 a__zeros -> zeros 7.47/7.62 mark(0) -> 0 7.47/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.62 mark(nil) -> nil 7.47/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.62 mark(tt) -> tt 7.47/7.62 mark(zeros) -> a__zeros 7.47/7.62 ->Projection: 7.47/7.62 pi(A__U51) = 2 7.47/7.62 pi(A__U61) = 2 7.47/7.62 pi(A__ISNATILISTKIND) = 1 7.47/7.62 pi(A__ISNATKIND) = 1 7.47/7.62 7.47/7.62 Problem 1.1: 7.47/7.62 7.47/7.62 SCC Processor: 7.47/7.62 -> Pairs: 7.47/7.62 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.62 A__U61(tt,V2:S) -> A__ISNATILISTKIND(V2:S) 7.47/7.62 -> Rules: 7.47/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.62 a__U106(tt) -> tt 7.47/7.62 a__U106(X:S) -> U106(X:S) 7.47/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.62 a__U122(tt) -> nil 7.47/7.62 a__U122(X:S) -> U122(X:S) 7.47/7.62 a__U13(tt) -> tt 7.47/7.62 a__U13(X:S) -> U13(X:S) 7.47/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.62 a__U23(tt) -> tt 7.47/7.62 a__U23(X:S) -> U23(X:S) 7.47/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.62 a__U33(tt) -> tt 7.47/7.62 a__U33(X:S) -> U33(X:S) 7.47/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.62 a__U46(tt) -> tt 7.47/7.62 a__U46(X:S) -> U46(X:S) 7.47/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.62 a__U52(tt) -> tt 7.47/7.62 a__U52(X:S) -> U52(X:S) 7.47/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.62 a__U62(tt) -> tt 7.47/7.62 a__U62(X:S) -> U62(X:S) 7.47/7.62 a__U71(tt) -> tt 7.47/7.62 a__U71(X:S) -> U71(X:S) 7.47/7.62 a__U81(tt) -> tt 7.47/7.62 a__U81(X:S) -> U81(X:S) 7.47/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.62 a__U96(tt) -> tt 7.47/7.62 a__U96(X:S) -> U96(X:S) 7.47/7.62 a__isNat(0) -> tt 7.47/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__isNat(X:S) -> isNat(X:S) 7.47/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatIList(zeros) -> tt 7.47/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(nil) -> tt 7.47/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(zeros) -> tt 7.47/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.62 a__isNatKind(0) -> tt 7.47/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(nil) -> tt 7.47/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.62 a__length(nil) -> 0 7.47/7.62 a__length(X:S) -> length(X:S) 7.47/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.62 a__zeros -> cons(0,zeros) 7.47/7.62 a__zeros -> zeros 7.47/7.62 mark(0) -> 0 7.47/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.62 mark(nil) -> nil 7.47/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.62 mark(tt) -> tt 7.47/7.62 mark(zeros) -> a__zeros 7.47/7.62 ->Strongly Connected Components: 7.47/7.62 There is no strongly connected component 7.47/7.62 7.47/7.62 The problem is finite. 7.47/7.62 7.47/7.62 Problem 1.2: 7.47/7.62 7.47/7.62 Reduction Pairs Processor: 7.47/7.62 -> Pairs: 7.47/7.62 A__U101(tt,V1:S,V2:S) -> A__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 A__U102(tt,V1:S,V2:S) -> A__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 A__U103(tt,V1:S,V2:S) -> A__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 A__U104(tt,V1:S,V2:S) -> A__U105(a__isNat(V1:S),V2:S) 7.47/7.62 A__U104(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.62 A__U105(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.62 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.47/7.62 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.47/7.62 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.47/7.62 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S) 7.47/7.62 A__U32(tt,V:S) -> A__ISNATLIST(V:S) 7.47/7.62 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.47/7.62 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.62 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.47/7.62 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.47/7.62 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.47/7.62 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.47/7.62 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.47/7.62 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S) 7.47/7.62 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 A__ISNATLIST(take(V1:S,V2:S)) -> A__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 -> Rules: 7.47/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.62 a__U106(tt) -> tt 7.47/7.62 a__U106(X:S) -> U106(X:S) 7.47/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.47/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.47/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.47/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.47/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.47/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.47/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.47/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.47/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.47/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.47/7.62 a__U122(tt) -> nil 7.47/7.62 a__U122(X:S) -> U122(X:S) 7.47/7.62 a__U13(tt) -> tt 7.47/7.62 a__U13(X:S) -> U13(X:S) 7.47/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.47/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.47/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.47/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.47/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.47/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.47/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.62 a__U23(tt) -> tt 7.47/7.62 a__U23(X:S) -> U23(X:S) 7.47/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.62 a__U33(tt) -> tt 7.47/7.62 a__U33(X:S) -> U33(X:S) 7.47/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.47/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.47/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.47/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.47/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.47/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.47/7.62 a__U46(tt) -> tt 7.47/7.62 a__U46(X:S) -> U46(X:S) 7.47/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.47/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.47/7.62 a__U52(tt) -> tt 7.47/7.62 a__U52(X:S) -> U52(X:S) 7.47/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.47/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.47/7.62 a__U62(tt) -> tt 7.47/7.62 a__U62(X:S) -> U62(X:S) 7.47/7.62 a__U71(tt) -> tt 7.47/7.62 a__U71(X:S) -> U71(X:S) 7.47/7.62 a__U81(tt) -> tt 7.47/7.62 a__U81(X:S) -> U81(X:S) 7.47/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.47/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.47/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.47/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.47/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.47/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.47/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.47/7.62 a__U96(tt) -> tt 7.47/7.62 a__U96(X:S) -> U96(X:S) 7.47/7.62 a__isNat(0) -> tt 7.47/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__isNat(X:S) -> isNat(X:S) 7.47/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatIList(zeros) -> tt 7.47/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.47/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(nil) -> tt 7.47/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.47/7.62 a__isNatIListKind(zeros) -> tt 7.47/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.47/7.62 a__isNatKind(0) -> tt 7.47/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.47/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.47/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.47/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(nil) -> tt 7.47/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.47/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.47/7.62 a__length(nil) -> 0 7.47/7.62 a__length(X:S) -> length(X:S) 7.47/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.47/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.47/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.47/7.62 a__zeros -> cons(0,zeros) 7.47/7.62 a__zeros -> zeros 7.47/7.62 mark(0) -> 0 7.47/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.47/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.47/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.47/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.47/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.47/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.47/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.47/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.47/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.47/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.47/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.47/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.47/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.47/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.47/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.47/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.47/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.47/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.47/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.47/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.47/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.47/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.47/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.47/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.47/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.47/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.47/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.47/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.47/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.47/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.47/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.47/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.47/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.47/7.62 mark(nil) -> nil 7.47/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.47/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.47/7.62 mark(tt) -> tt 7.47/7.62 mark(zeros) -> a__zeros 7.47/7.62 -> Usable rules: 7.47/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.47/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.47/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.47/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.47/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.47/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.47/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.47/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.47/7.62 a__U106(tt) -> tt 7.47/7.62 a__U106(X:S) -> U106(X:S) 7.47/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.47/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.47/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.47/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.47/7.62 a__U13(tt) -> tt 7.47/7.62 a__U13(X:S) -> U13(X:S) 7.47/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.47/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.47/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.47/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.47/7.62 a__U23(tt) -> tt 7.47/7.62 a__U23(X:S) -> U23(X:S) 7.47/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.47/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.47/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.47/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.47/7.62 a__U33(tt) -> tt 7.47/7.62 a__U33(X:S) -> U33(X:S) 7.47/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.47/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.47/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.62 a__U46(tt) -> tt 7.48/7.62 a__U46(X:S) -> U46(X:S) 7.48/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.62 a__U52(tt) -> tt 7.48/7.62 a__U52(X:S) -> U52(X:S) 7.48/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.62 a__U62(tt) -> tt 7.48/7.62 a__U62(X:S) -> U62(X:S) 7.48/7.62 a__U71(tt) -> tt 7.48/7.62 a__U71(X:S) -> U71(X:S) 7.48/7.62 a__U81(tt) -> tt 7.48/7.62 a__U81(X:S) -> U81(X:S) 7.48/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.62 a__U96(tt) -> tt 7.48/7.62 a__U96(X:S) -> U96(X:S) 7.48/7.62 a__isNat(0) -> tt 7.48/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__isNat(X:S) -> isNat(X:S) 7.48/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatIList(zeros) -> tt 7.48/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(nil) -> tt 7.48/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(zeros) -> tt 7.48/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.62 a__isNatKind(0) -> tt 7.48/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(nil) -> tt 7.48/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.62 ->Interpretation type: 7.48/7.62 Linear 7.48/7.62 ->Coefficients: 7.48/7.62 Natural Numbers 7.48/7.62 ->Dimension: 7.48/7.62 1 7.48/7.62 ->Bound: 7.48/7.62 2 7.48/7.62 ->Interpretation: 7.48/7.62 7.48/7.62 [a__U101](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U102](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U103](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U104](X1,X2,X3) = 2.X1 + 2.X2 + 2 7.48/7.62 [a__U105](X1,X2) = X1 + 2 7.48/7.62 [a__U106](X) = 2 7.48/7.62 [a__U11](X1,X2) = X1 + X2 + 2 7.48/7.62 [a__U111](X1,X2,X3) = 0 7.48/7.62 [a__U112](X1,X2,X3) = 0 7.48/7.62 [a__U113](X1,X2,X3) = 0 7.48/7.62 [a__U114](X1,X2) = 0 7.48/7.62 [a__U12](X1,X2) = X2 + 2 7.48/7.62 [a__U121](X1,X2) = 0 7.48/7.62 [a__U122](X) = 0 7.48/7.62 [a__U13](X) = X + 2 7.48/7.62 [a__U131](X1,X2,X3,X4) = 0 7.48/7.62 [a__U132](X1,X2,X3,X4) = 0 7.48/7.62 [a__U133](X1,X2,X3,X4) = 0 7.48/7.62 [a__U134](X1,X2,X3,X4) = 0 7.48/7.62 [a__U135](X1,X2,X3,X4) = 0 7.48/7.62 [a__U136](X1,X2,X3,X4) = 0 7.48/7.62 [a__U21](X1,X2) = 2.X1 + 2 7.48/7.62 [a__U22](X1,X2) = 2 7.48/7.62 [a__U23](X) = 2 7.48/7.62 [a__U31](X1,X2) = X1 7.48/7.62 [a__U32](X1,X2) = 0 7.48/7.62 [a__U33](X) = 0 7.48/7.62 [a__U41](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [a__U42](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [a__U43](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [a__U44](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [a__U45](X1,X2) = X1 + 2.X2 7.48/7.62 [a__U46](X) = 2.X 7.48/7.62 [a__U51](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U52](X) = 2.X + 2 7.48/7.62 [a__U61](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U62](X) = 2 7.48/7.62 [a__U71](X) = X + 2 7.48/7.62 [a__U81](X) = 2.X + 2 7.48/7.62 [a__U91](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U92](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U93](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U94](X1,X2,X3) = 2.X1 + 2.X2 + 2 7.48/7.62 [a__U95](X1,X2) = 2 7.48/7.62 [a__U96](X) = 2 7.48/7.62 [a__isNat](X) = 2.X 7.48/7.62 [a__isNatIList](X) = X 7.48/7.62 [a__isNatIListKind](X) = X 7.48/7.62 [a__isNatKind](X) = 2.X + 1 7.48/7.62 [a__isNatList](X) = X 7.48/7.62 [a__length](X) = 0 7.48/7.62 [a__take](X1,X2) = 0 7.48/7.62 [a__zeros] = 0 7.48/7.62 [mark](X) = 0 7.48/7.62 [0] = 2 7.48/7.62 [U101](X1,X2,X3) = 2.X2 + 1 7.48/7.62 [U102](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [U103](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [U104](X1,X2,X3) = 2.X1 + 2.X2 + 2 7.48/7.62 [U105](X1,X2) = X1 + 1 7.48/7.62 [U106](X) = 2 7.48/7.62 [U11](X1,X2) = X1 + 2 7.48/7.62 [U111](X1,X2,X3) = 0 7.48/7.62 [U112](X1,X2,X3) = 0 7.48/7.62 [U113](X1,X2,X3) = 0 7.48/7.62 [U114](X1,X2) = 0 7.48/7.62 [U12](X1,X2) = X2 + 2 7.48/7.62 [U121](X1,X2) = 0 7.48/7.62 [U122](X) = 0 7.48/7.62 [U13](X) = X + 2 7.48/7.62 [U131](X1,X2,X3,X4) = 0 7.48/7.62 [U132](X1,X2,X3,X4) = 0 7.48/7.62 [U133](X1,X2,X3,X4) = 0 7.48/7.62 [U134](X1,X2,X3,X4) = 0 7.48/7.62 [U135](X1,X2,X3,X4) = 0 7.48/7.62 [U136](X1,X2,X3,X4) = 0 7.48/7.62 [U21](X1,X2) = 2.X1 + 1 7.48/7.62 [U22](X1,X2) = 2 7.48/7.62 [U23](X) = 1 7.48/7.62 [U31](X1,X2) = X1 7.48/7.62 [U32](X1,X2) = 0 7.48/7.62 [U33](X) = 0 7.48/7.62 [U41](X1,X2,X3) = X3 7.48/7.62 [U42](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [U43](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [U44](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [U45](X1,X2) = X1 + 2.X2 7.48/7.62 [U46](X) = X 7.48/7.62 [U51](X1,X2) = X2 + 2 7.48/7.62 [U52](X) = X + 2 7.48/7.62 [U61](X1,X2) = 1 7.48/7.62 [U62](X) = 0 7.48/7.62 [U71](X) = 2 7.48/7.62 [U81](X) = 2.X + 2 7.48/7.62 [U91](X1,X2,X3) = 2.X2 + X3 7.48/7.62 [U92](X1,X2,X3) = 2.X2 + X3 + 2 7.48/7.62 [U93](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [U94](X1,X2,X3) = 2.X1 + 2.X2 7.48/7.62 [U95](X1,X2) = 2 7.48/7.62 [U96](X) = 2 7.48/7.62 [cons](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.62 [fSNonEmpty] = 0 7.48/7.62 [isNat](X) = 2.X 7.48/7.62 [isNatIList](X) = X 7.48/7.62 [isNatIListKind](X) = X 7.48/7.62 [isNatKind](X) = 2.X + 1 7.48/7.62 [isNatList](X) = 0 7.48/7.62 [length](X) = X + 2 7.48/7.62 [nil] = 2 7.48/7.62 [s](X) = 2.X + 2 7.48/7.62 [take](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.62 [tt] = 0 7.48/7.62 [zeros] = 2 7.48/7.62 [A__U101](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [A__U102](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [A__U103](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [A__U104](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [A__U105](X1,X2) = X1 + 2.X2 + 1 7.48/7.62 [A__U106](X) = 0 7.48/7.62 [A__U11](X1,X2) = 2.X2 + 2 7.48/7.62 [A__U111](X1,X2,X3) = 0 7.48/7.62 [A__U112](X1,X2,X3) = 0 7.48/7.62 [A__U113](X1,X2,X3) = 0 7.48/7.62 [A__U114](X1,X2) = 0 7.48/7.62 [A__U12](X1,X2) = 2.X2 + 2 7.48/7.62 [A__U121](X1,X2) = 0 7.48/7.62 [A__U122](X) = 0 7.48/7.62 [A__U13](X) = 0 7.48/7.62 [A__U131](X1,X2,X3,X4) = 0 7.48/7.62 [A__U132](X1,X2,X3,X4) = 0 7.48/7.62 [A__U133](X1,X2,X3,X4) = 0 7.48/7.62 [A__U134](X1,X2,X3,X4) = 0 7.48/7.62 [A__U135](X1,X2,X3,X4) = 0 7.48/7.62 [A__U136](X1,X2,X3,X4) = 0 7.48/7.62 [A__U21](X1,X2) = X1 + 2.X2 + 2 7.48/7.62 [A__U22](X1,X2) = 2.X2 + 2 7.48/7.62 [A__U23](X) = 0 7.48/7.62 [A__U31](X1,X2) = 2.X2 7.48/7.62 [A__U32](X1,X2) = 2.X2 7.48/7.62 [A__U33](X) = 0 7.48/7.62 [A__U41](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [A__U42](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [A__U43](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [A__U44](X1,X2,X3) = 2.X2 + 2.X3 + 1 7.48/7.62 [A__U45](X1,X2) = X1 + 2.X2 + 1 7.48/7.62 [A__U46](X) = 0 7.48/7.62 [A__U51](X1,X2) = 0 7.48/7.62 [A__U52](X) = 0 7.48/7.62 [A__U61](X1,X2) = 0 7.48/7.62 [A__U62](X) = 0 7.48/7.62 [A__U71](X) = 0 7.48/7.62 [A__U81](X) = 0 7.48/7.62 [A__U91](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [A__U92](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [A__U93](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [A__U94](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [A__U95](X1,X2) = X1 + 2.X2 + 2 7.48/7.62 [A__U96](X) = 0 7.48/7.62 [A__ISNAT](X) = 2.X + 1 7.48/7.62 [A__ISNATILIST](X) = 2.X 7.48/7.62 [A__ISNATILISTKIND](X) = 0 7.48/7.62 [A__ISNATKIND](X) = 0 7.48/7.62 [A__ISNATLIST](X) = 2.X 7.48/7.62 [A__LENGTH](X) = 0 7.48/7.62 [A__TAKE](X1,X2) = 0 7.48/7.62 [A__ZEROS] = 0 7.48/7.62 [MARK](X) = 0 7.48/7.62 7.48/7.62 Problem 1.2: 7.48/7.62 7.48/7.62 SCC Processor: 7.48/7.62 -> Pairs: 7.48/7.62 A__U102(tt,V1:S,V2:S) -> A__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U103(tt,V1:S,V2:S) -> A__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U104(tt,V1:S,V2:S) -> A__U105(a__isNat(V1:S),V2:S) 7.48/7.62 A__U104(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U105(tt,V2:S) -> A__ISNATILIST(V2:S) 7.48/7.62 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.48/7.62 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S) 7.48/7.62 A__U32(tt,V:S) -> A__ISNATLIST(V:S) 7.48/7.62 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.48/7.62 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.48/7.62 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.62 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.62 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__ISNATLIST(take(V1:S,V2:S)) -> A__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 -> Rules: 7.48/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.62 a__U106(tt) -> tt 7.48/7.62 a__U106(X:S) -> U106(X:S) 7.48/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.62 a__U122(tt) -> nil 7.48/7.62 a__U122(X:S) -> U122(X:S) 7.48/7.62 a__U13(tt) -> tt 7.48/7.62 a__U13(X:S) -> U13(X:S) 7.48/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.62 a__U23(tt) -> tt 7.48/7.62 a__U23(X:S) -> U23(X:S) 7.48/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.62 a__U33(tt) -> tt 7.48/7.62 a__U33(X:S) -> U33(X:S) 7.48/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.62 a__U46(tt) -> tt 7.48/7.62 a__U46(X:S) -> U46(X:S) 7.48/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.62 a__U52(tt) -> tt 7.48/7.62 a__U52(X:S) -> U52(X:S) 7.48/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.62 a__U62(tt) -> tt 7.48/7.62 a__U62(X:S) -> U62(X:S) 7.48/7.62 a__U71(tt) -> tt 7.48/7.62 a__U71(X:S) -> U71(X:S) 7.48/7.62 a__U81(tt) -> tt 7.48/7.62 a__U81(X:S) -> U81(X:S) 7.48/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.62 a__U96(tt) -> tt 7.48/7.62 a__U96(X:S) -> U96(X:S) 7.48/7.62 a__isNat(0) -> tt 7.48/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__isNat(X:S) -> isNat(X:S) 7.48/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatIList(zeros) -> tt 7.48/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(nil) -> tt 7.48/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(zeros) -> tt 7.48/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.62 a__isNatKind(0) -> tt 7.48/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(nil) -> tt 7.48/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.62 a__length(nil) -> 0 7.48/7.62 a__length(X:S) -> length(X:S) 7.48/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.62 a__zeros -> cons(0,zeros) 7.48/7.62 a__zeros -> zeros 7.48/7.62 mark(0) -> 0 7.48/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.62 mark(nil) -> nil 7.48/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.62 mark(tt) -> tt 7.48/7.62 mark(zeros) -> a__zeros 7.48/7.62 ->Strongly Connected Components: 7.48/7.62 ->->Cycle: 7.48/7.62 ->->-> Pairs: 7.48/7.62 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.48/7.62 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.62 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.62 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 ->->-> Rules: 7.48/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.62 a__U106(tt) -> tt 7.48/7.62 a__U106(X:S) -> U106(X:S) 7.48/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.62 a__U122(tt) -> nil 7.48/7.62 a__U122(X:S) -> U122(X:S) 7.48/7.62 a__U13(tt) -> tt 7.48/7.62 a__U13(X:S) -> U13(X:S) 7.48/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.62 a__U23(tt) -> tt 7.48/7.62 a__U23(X:S) -> U23(X:S) 7.48/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.62 a__U33(tt) -> tt 7.48/7.62 a__U33(X:S) -> U33(X:S) 7.48/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.62 a__U46(tt) -> tt 7.48/7.62 a__U46(X:S) -> U46(X:S) 7.48/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.62 a__U52(tt) -> tt 7.48/7.62 a__U52(X:S) -> U52(X:S) 7.48/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.62 a__U62(tt) -> tt 7.48/7.62 a__U62(X:S) -> U62(X:S) 7.48/7.62 a__U71(tt) -> tt 7.48/7.62 a__U71(X:S) -> U71(X:S) 7.48/7.62 a__U81(tt) -> tt 7.48/7.62 a__U81(X:S) -> U81(X:S) 7.48/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.62 a__U96(tt) -> tt 7.48/7.62 a__U96(X:S) -> U96(X:S) 7.48/7.62 a__isNat(0) -> tt 7.48/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__isNat(X:S) -> isNat(X:S) 7.48/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatIList(zeros) -> tt 7.48/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(nil) -> tt 7.48/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(zeros) -> tt 7.48/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.62 a__isNatKind(0) -> tt 7.48/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(nil) -> tt 7.48/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.62 a__length(nil) -> 0 7.48/7.62 a__length(X:S) -> length(X:S) 7.48/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.62 a__zeros -> cons(0,zeros) 7.48/7.62 a__zeros -> zeros 7.48/7.62 mark(0) -> 0 7.48/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.62 mark(nil) -> nil 7.48/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.62 mark(tt) -> tt 7.48/7.62 mark(zeros) -> a__zeros 7.48/7.62 ->->Cycle: 7.48/7.62 ->->-> Pairs: 7.48/7.62 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.48/7.62 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.48/7.62 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 ->->-> Rules: 7.48/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.62 a__U106(tt) -> tt 7.48/7.62 a__U106(X:S) -> U106(X:S) 7.48/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.62 a__U122(tt) -> nil 7.48/7.62 a__U122(X:S) -> U122(X:S) 7.48/7.62 a__U13(tt) -> tt 7.48/7.62 a__U13(X:S) -> U13(X:S) 7.48/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.62 a__U23(tt) -> tt 7.48/7.62 a__U23(X:S) -> U23(X:S) 7.48/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.62 a__U33(tt) -> tt 7.48/7.62 a__U33(X:S) -> U33(X:S) 7.48/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.62 a__U46(tt) -> tt 7.48/7.62 a__U46(X:S) -> U46(X:S) 7.48/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.62 a__U52(tt) -> tt 7.48/7.62 a__U52(X:S) -> U52(X:S) 7.48/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.62 a__U62(tt) -> tt 7.48/7.62 a__U62(X:S) -> U62(X:S) 7.48/7.62 a__U71(tt) -> tt 7.48/7.62 a__U71(X:S) -> U71(X:S) 7.48/7.62 a__U81(tt) -> tt 7.48/7.62 a__U81(X:S) -> U81(X:S) 7.48/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.62 a__U96(tt) -> tt 7.48/7.62 a__U96(X:S) -> U96(X:S) 7.48/7.62 a__isNat(0) -> tt 7.48/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__isNat(X:S) -> isNat(X:S) 7.48/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatIList(zeros) -> tt 7.48/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(nil) -> tt 7.48/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(zeros) -> tt 7.48/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.62 a__isNatKind(0) -> tt 7.48/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(nil) -> tt 7.48/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.62 a__length(nil) -> 0 7.48/7.62 a__length(X:S) -> length(X:S) 7.48/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.62 a__zeros -> cons(0,zeros) 7.48/7.62 a__zeros -> zeros 7.48/7.62 mark(0) -> 0 7.48/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.62 mark(nil) -> nil 7.48/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.62 mark(tt) -> tt 7.48/7.62 mark(zeros) -> a__zeros 7.48/7.62 7.48/7.62 7.48/7.62 The problem is decomposed in 2 subproblems. 7.48/7.62 7.48/7.62 Problem 1.2.1: 7.48/7.62 7.48/7.62 Reduction Pairs Processor: 7.48/7.62 -> Pairs: 7.48/7.62 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.48/7.62 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.62 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.48/7.62 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.62 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 -> Rules: 7.48/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.62 a__U106(tt) -> tt 7.48/7.62 a__U106(X:S) -> U106(X:S) 7.48/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.62 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.62 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.62 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.62 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.62 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.62 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.62 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.62 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.62 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.62 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.62 a__U122(tt) -> nil 7.48/7.62 a__U122(X:S) -> U122(X:S) 7.48/7.62 a__U13(tt) -> tt 7.48/7.62 a__U13(X:S) -> U13(X:S) 7.48/7.62 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.62 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.62 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.62 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.62 a__U23(tt) -> tt 7.48/7.62 a__U23(X:S) -> U23(X:S) 7.48/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.62 a__U33(tt) -> tt 7.48/7.62 a__U33(X:S) -> U33(X:S) 7.48/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.62 a__U46(tt) -> tt 7.48/7.62 a__U46(X:S) -> U46(X:S) 7.48/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.62 a__U52(tt) -> tt 7.48/7.62 a__U52(X:S) -> U52(X:S) 7.48/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.62 a__U62(tt) -> tt 7.48/7.62 a__U62(X:S) -> U62(X:S) 7.48/7.62 a__U71(tt) -> tt 7.48/7.62 a__U71(X:S) -> U71(X:S) 7.48/7.62 a__U81(tt) -> tt 7.48/7.62 a__U81(X:S) -> U81(X:S) 7.48/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.62 a__U96(tt) -> tt 7.48/7.62 a__U96(X:S) -> U96(X:S) 7.48/7.62 a__isNat(0) -> tt 7.48/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__isNat(X:S) -> isNat(X:S) 7.48/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatIList(zeros) -> tt 7.48/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(nil) -> tt 7.48/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(zeros) -> tt 7.48/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.62 a__isNatKind(0) -> tt 7.48/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(nil) -> tt 7.48/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.62 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.62 a__length(nil) -> 0 7.48/7.62 a__length(X:S) -> length(X:S) 7.48/7.62 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.62 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.62 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.62 a__zeros -> cons(0,zeros) 7.48/7.62 a__zeros -> zeros 7.48/7.62 mark(0) -> 0 7.48/7.62 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.62 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.62 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.62 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.62 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.62 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.62 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.62 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.62 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.62 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.62 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.62 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.62 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.62 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.62 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.62 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.62 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.62 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.62 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.62 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.62 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.62 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.62 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.62 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.62 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.62 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.62 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.62 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.62 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.62 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.62 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.62 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.62 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.62 mark(nil) -> nil 7.48/7.62 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.62 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.62 mark(tt) -> tt 7.48/7.62 mark(zeros) -> a__zeros 7.48/7.62 -> Usable rules: 7.48/7.62 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.62 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.62 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.62 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.62 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.62 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.62 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.62 a__U106(tt) -> tt 7.48/7.62 a__U106(X:S) -> U106(X:S) 7.48/7.62 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.62 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.62 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.62 a__U13(tt) -> tt 7.48/7.62 a__U13(X:S) -> U13(X:S) 7.48/7.62 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.62 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.62 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.62 a__U23(tt) -> tt 7.48/7.62 a__U23(X:S) -> U23(X:S) 7.48/7.62 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.62 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.62 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.62 a__U33(tt) -> tt 7.48/7.62 a__U33(X:S) -> U33(X:S) 7.48/7.62 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.62 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.62 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.62 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.62 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.62 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.62 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.62 a__U46(tt) -> tt 7.48/7.62 a__U46(X:S) -> U46(X:S) 7.48/7.62 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.62 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.62 a__U52(tt) -> tt 7.48/7.62 a__U52(X:S) -> U52(X:S) 7.48/7.62 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.62 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.62 a__U62(tt) -> tt 7.48/7.62 a__U62(X:S) -> U62(X:S) 7.48/7.62 a__U71(tt) -> tt 7.48/7.62 a__U71(X:S) -> U71(X:S) 7.48/7.62 a__U81(tt) -> tt 7.48/7.62 a__U81(X:S) -> U81(X:S) 7.48/7.62 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.62 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.62 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.62 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.62 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.62 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.62 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.62 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.62 a__U96(tt) -> tt 7.48/7.62 a__U96(X:S) -> U96(X:S) 7.48/7.62 a__isNat(0) -> tt 7.48/7.62 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.62 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.62 a__isNat(X:S) -> isNat(X:S) 7.48/7.62 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatIList(zeros) -> tt 7.48/7.62 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.62 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.62 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(nil) -> tt 7.48/7.62 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.62 a__isNatIListKind(zeros) -> tt 7.48/7.62 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.62 a__isNatKind(0) -> tt 7.48/7.62 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.62 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.62 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.62 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(nil) -> tt 7.48/7.62 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.62 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.62 ->Interpretation type: 7.48/7.62 Linear 7.48/7.62 ->Coefficients: 7.48/7.62 Natural Numbers 7.48/7.62 ->Dimension: 7.48/7.62 1 7.48/7.62 ->Bound: 7.48/7.62 2 7.48/7.62 ->Interpretation: 7.48/7.62 7.48/7.62 [a__U101](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [a__U102](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [a__U103](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U104](X1,X2,X3) = X2 + 2.X3 + 2 7.48/7.62 [a__U105](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U106](X) = 2 7.48/7.62 [a__U11](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.62 [a__U111](X1,X2,X3) = 0 7.48/7.62 [a__U112](X1,X2,X3) = 0 7.48/7.62 [a__U113](X1,X2,X3) = 0 7.48/7.62 [a__U114](X1,X2) = 0 7.48/7.62 [a__U12](X1,X2) = 2.X1 + 2 7.48/7.62 [a__U121](X1,X2) = 0 7.48/7.62 [a__U122](X) = 0 7.48/7.62 [a__U13](X) = 2 7.48/7.62 [a__U131](X1,X2,X3,X4) = 0 7.48/7.62 [a__U132](X1,X2,X3,X4) = 0 7.48/7.62 [a__U133](X1,X2,X3,X4) = 0 7.48/7.62 [a__U134](X1,X2,X3,X4) = 0 7.48/7.62 [a__U135](X1,X2,X3,X4) = 0 7.48/7.62 [a__U136](X1,X2,X3,X4) = 0 7.48/7.62 [a__U21](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.62 [a__U22](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.62 [a__U23](X) = X + 2 7.48/7.62 [a__U31](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U32](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U33](X) = X 7.48/7.62 [a__U41](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [a__U42](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [a__U43](X1,X2,X3) = X1 + 2.X2 + X3 + 2 7.48/7.62 [a__U44](X1,X2,X3) = X1 + 2.X2 + 2 7.48/7.62 [a__U45](X1,X2) = X1 + 2 7.48/7.62 [a__U46](X) = 2 7.48/7.62 [a__U51](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U52](X) = 2 7.48/7.62 [a__U61](X1,X2) = 2.X1 + 2.X2 7.48/7.62 [a__U62](X) = 2.X 7.48/7.62 [a__U71](X) = 2 7.48/7.62 [a__U81](X) = X 7.48/7.62 [a__U91](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 7.48/7.62 [a__U92](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U93](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U94](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [a__U95](X1,X2) = 2.X2 + 2 7.48/7.62 [a__U96](X) = 2 7.48/7.62 [a__isNat](X) = 2.X + 2 7.48/7.62 [a__isNatIList](X) = 2.X + 2 7.48/7.62 [a__isNatIListKind](X) = X + 2 7.48/7.62 [a__isNatKind](X) = 2 7.48/7.62 [a__isNatList](X) = 2.X + 2 7.48/7.62 [a__length](X) = 0 7.48/7.62 [a__take](X1,X2) = 0 7.48/7.62 [a__zeros] = 0 7.48/7.62 [mark](X) = 0 7.48/7.62 [0] = 1 7.48/7.62 [U101](X1,X2,X3) = 2.X1 + 2.X2 + X3 7.48/7.62 [U102](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1 7.48/7.62 [U103](X1,X2,X3) = 2.X2 + 2.X3 7.48/7.62 [U104](X1,X2,X3) = X2 + 2.X3 + 1 7.48/7.62 [U105](X1,X2) = 2.X2 + 2 7.48/7.62 [U106](X) = 2 7.48/7.62 [U11](X1,X2) = 2.X1 + 2 7.48/7.62 [U111](X1,X2,X3) = 0 7.48/7.62 [U112](X1,X2,X3) = 0 7.48/7.62 [U113](X1,X2,X3) = 0 7.48/7.62 [U114](X1,X2) = 0 7.48/7.62 [U12](X1,X2) = X1 + 2 7.48/7.62 [U121](X1,X2) = 0 7.48/7.62 [U122](X) = 0 7.48/7.62 [U13](X) = 1 7.48/7.62 [U131](X1,X2,X3,X4) = 0 7.48/7.62 [U132](X1,X2,X3,X4) = 0 7.48/7.62 [U133](X1,X2,X3,X4) = 0 7.48/7.62 [U134](X1,X2,X3,X4) = 0 7.48/7.62 [U135](X1,X2,X3,X4) = 0 7.48/7.62 [U136](X1,X2,X3,X4) = 0 7.48/7.62 [U21](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.62 [U22](X1,X2) = X2 + 2 7.48/7.62 [U23](X) = 1 7.48/7.62 [U31](X1,X2) = 2.X2 + 2 7.48/7.62 [U32](X1,X2) = X2 + 1 7.48/7.62 [U33](X) = X 7.48/7.62 [U41](X1,X2,X3) = 2.X1 + 2.X2 + 1 7.48/7.62 [U42](X1,X2,X3) = 2.X1 + 2.X2 + 2 7.48/7.62 [U43](X1,X2,X3) = X3 + 2 7.48/7.62 [U44](X1,X2,X3) = 2.X2 7.48/7.62 [U45](X1,X2) = X1 7.48/7.62 [U46](X) = 2 7.48/7.62 [U51](X1,X2) = 2 7.48/7.62 [U52](X) = 0 7.48/7.62 [U61](X1,X2) = 2.X1 + 2.X2 7.48/7.62 [U62](X) = 2.X 7.48/7.62 [U71](X) = 2 7.48/7.62 [U81](X) = 0 7.48/7.62 [U91](X1,X2,X3) = X2 + 2.X3 + 1 7.48/7.62 [U92](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.62 [U93](X1,X2,X3) = 2.X3 7.48/7.62 [U94](X1,X2,X3) = 2.X2 + 1 7.48/7.62 [U95](X1,X2) = 2.X2 + 1 7.48/7.63 [U96](X) = 1 7.48/7.63 [cons](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.63 [fSNonEmpty] = 0 7.48/7.63 [isNat](X) = X + 2 7.48/7.63 [isNatIList](X) = 2.X + 2 7.48/7.63 [isNatIListKind](X) = X + 2 7.48/7.63 [isNatKind](X) = 2 7.48/7.63 [isNatList](X) = X + 2 7.48/7.63 [length](X) = 2.X + 2 7.48/7.63 [nil] = 1 7.48/7.63 [s](X) = X + 2 7.48/7.63 [take](X1,X2) = X1 + 2.X2 + 2 7.48/7.63 [tt] = 2 7.48/7.63 [zeros] = 2 7.48/7.63 [A__U101](X1,X2,X3) = 0 7.48/7.63 [A__U102](X1,X2,X3) = 0 7.48/7.63 [A__U103](X1,X2,X3) = 0 7.48/7.63 [A__U104](X1,X2,X3) = 0 7.48/7.63 [A__U105](X1,X2) = 0 7.48/7.63 [A__U106](X) = 0 7.48/7.63 [A__U11](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.63 [A__U111](X1,X2,X3) = 0 7.48/7.63 [A__U112](X1,X2,X3) = 0 7.48/7.63 [A__U113](X1,X2,X3) = 0 7.48/7.63 [A__U114](X1,X2) = 0 7.48/7.63 [A__U12](X1,X2) = X1 + X2 + 1 7.48/7.63 [A__U121](X1,X2) = 0 7.48/7.63 [A__U122](X) = 0 7.48/7.63 [A__U13](X) = 0 7.48/7.63 [A__U131](X1,X2,X3,X4) = 0 7.48/7.63 [A__U132](X1,X2,X3,X4) = 0 7.48/7.63 [A__U133](X1,X2,X3,X4) = 0 7.48/7.63 [A__U134](X1,X2,X3,X4) = 0 7.48/7.63 [A__U135](X1,X2,X3,X4) = 0 7.48/7.63 [A__U136](X1,X2,X3,X4) = 0 7.48/7.63 [A__U21](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.63 [A__U22](X1,X2) = 2.X2 + 2 7.48/7.63 [A__U23](X) = 0 7.48/7.63 [A__U31](X1,X2) = 0 7.48/7.63 [A__U32](X1,X2) = 0 7.48/7.63 [A__U33](X) = 0 7.48/7.63 [A__U41](X1,X2,X3) = 0 7.48/7.63 [A__U42](X1,X2,X3) = 0 7.48/7.63 [A__U43](X1,X2,X3) = 0 7.48/7.63 [A__U44](X1,X2,X3) = 0 7.48/7.63 [A__U45](X1,X2) = 0 7.48/7.63 [A__U46](X) = 0 7.48/7.63 [A__U51](X1,X2) = 0 7.48/7.63 [A__U52](X) = 0 7.48/7.63 [A__U61](X1,X2) = 0 7.48/7.63 [A__U62](X) = 0 7.48/7.63 [A__U71](X) = 0 7.48/7.63 [A__U81](X) = 0 7.48/7.63 [A__U91](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 7.48/7.63 [A__U92](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 7.48/7.63 [A__U93](X1,X2,X3) = 2.X2 + 2.X3 + 2 7.48/7.63 [A__U94](X1,X2,X3) = X1 + 2.X2 + X3 7.48/7.63 [A__U95](X1,X2) = X2 + 2 7.48/7.63 [A__U96](X) = 0 7.48/7.63 [A__ISNAT](X) = 2.X + 2 7.48/7.63 [A__ISNATILIST](X) = 0 7.48/7.63 [A__ISNATILISTKIND](X) = 0 7.48/7.63 [A__ISNATKIND](X) = 0 7.48/7.63 [A__ISNATLIST](X) = X + 2 7.48/7.63 [A__LENGTH](X) = 0 7.48/7.63 [A__TAKE](X1,X2) = 0 7.48/7.63 [A__ZEROS] = 0 7.48/7.63 [MARK](X) = 0 7.48/7.63 7.48/7.63 Problem 1.2.1: 7.48/7.63 7.48/7.63 SCC Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S) 7.48/7.63 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.63 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.63 A__U94(tt,V1:S,V2:S) -> A__ISNAT(V1:S) 7.48/7.63 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.63 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Strongly Connected Components: 7.48/7.63 ->->Cycle: 7.48/7.63 ->->-> Pairs: 7.48/7.63 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.63 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 ->->-> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->->Cycle: 7.48/7.63 ->->-> Pairs: 7.48/7.63 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.63 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.63 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 ->->-> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 7.48/7.63 7.48/7.63 The problem is decomposed in 2 subproblems. 7.48/7.63 7.48/7.63 Problem 1.2.1.1: 7.48/7.63 7.48/7.63 Subterm Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.63 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Projection: 7.48/7.63 pi(A__U21) = 2 7.48/7.63 pi(A__U22) = 2 7.48/7.63 pi(A__ISNAT) = 1 7.48/7.63 7.48/7.63 Problem 1.2.1.1: 7.48/7.63 7.48/7.63 SCC Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 A__U22(tt,V1:S) -> A__ISNAT(V1:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Strongly Connected Components: 7.48/7.63 There is no strongly connected component 7.48/7.63 7.48/7.63 The problem is finite. 7.48/7.63 7.48/7.63 Problem 1.2.1.2: 7.48/7.63 7.48/7.63 Subterm Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.63 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.63 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Projection: 7.48/7.63 pi(A__U91) = 3 7.48/7.63 pi(A__U92) = 3 7.48/7.63 pi(A__U93) = 3 7.48/7.63 pi(A__U94) = 3 7.48/7.63 pi(A__U95) = 2 7.48/7.63 pi(A__ISNATLIST) = 1 7.48/7.63 7.48/7.63 Problem 1.2.1.2: 7.48/7.63 7.48/7.63 SCC Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U91(tt,V1:S,V2:S) -> A__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 A__U92(tt,V1:S,V2:S) -> A__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U93(tt,V1:S,V2:S) -> A__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U94(tt,V1:S,V2:S) -> A__U95(a__isNat(V1:S),V2:S) 7.48/7.63 A__U95(tt,V2:S) -> A__ISNATLIST(V2:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Strongly Connected Components: 7.48/7.63 There is no strongly connected component 7.48/7.63 7.48/7.63 The problem is finite. 7.48/7.63 7.48/7.63 Problem 1.2.2: 7.48/7.63 7.48/7.63 Subterm Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.48/7.63 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.48/7.63 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Projection: 7.48/7.63 pi(A__U41) = 3 7.48/7.63 pi(A__U42) = 3 7.48/7.63 pi(A__U43) = 3 7.48/7.63 pi(A__U44) = 3 7.48/7.63 pi(A__U45) = 2 7.48/7.63 pi(A__ISNATILIST) = 1 7.48/7.63 7.48/7.63 Problem 1.2.2: 7.48/7.63 7.48/7.63 SCC Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S) 7.48/7.63 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.63 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.63 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.63 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.63 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.63 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.63 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.63 a__U96(tt) -> tt 7.48/7.63 a__U96(X:S) -> U96(X:S) 7.48/7.63 a__isNat(0) -> tt 7.48/7.63 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__isNat(X:S) -> isNat(X:S) 7.48/7.63 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatIList(zeros) -> tt 7.48/7.63 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.63 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(nil) -> tt 7.48/7.63 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.63 a__isNatIListKind(zeros) -> tt 7.48/7.63 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.63 a__isNatKind(0) -> tt 7.48/7.63 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.63 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.63 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.63 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(nil) -> tt 7.48/7.63 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.63 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 a__length(nil) -> 0 7.48/7.63 a__length(X:S) -> length(X:S) 7.48/7.63 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.63 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.63 a__zeros -> cons(0,zeros) 7.48/7.63 a__zeros -> zeros 7.48/7.63 mark(0) -> 0 7.48/7.63 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.63 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.63 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.63 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.63 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.63 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.63 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.63 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.63 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.63 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.63 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.63 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.63 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.63 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.63 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.63 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.63 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.63 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.63 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.63 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.63 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.63 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.63 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.63 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.63 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.63 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.63 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.63 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.63 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.63 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.63 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.63 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.63 mark(nil) -> nil 7.48/7.63 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.63 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.63 mark(tt) -> tt 7.48/7.63 mark(zeros) -> a__zeros 7.48/7.63 ->Strongly Connected Components: 7.48/7.63 There is no strongly connected component 7.48/7.63 7.48/7.63 The problem is finite. 7.48/7.63 7.48/7.63 Problem 1.3: 7.48/7.63 7.48/7.63 Reduction Pairs Processor: 7.48/7.63 -> Pairs: 7.48/7.63 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.48/7.63 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.48/7.63 A__U114(tt,L:S) -> MARK(L:S) 7.48/7.63 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.63 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.63 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.63 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U111(X1:S,X2:S,X3:S)) -> A__U111(mark(X1:S),X2:S,X3:S) 7.48/7.63 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U112(X1:S,X2:S,X3:S)) -> A__U112(mark(X1:S),X2:S,X3:S) 7.48/7.63 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U113(X1:S,X2:S,X3:S)) -> A__U113(mark(X1:S),X2:S,X3:S) 7.48/7.63 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U114(X1:S,X2:S)) -> A__U114(mark(X1:S),X2:S) 7.48/7.63 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.63 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.63 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.63 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.63 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.63 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.63 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.63 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.63 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.63 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.63 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(length(X:S)) -> A__LENGTH(mark(X:S)) 7.48/7.63 MARK(length(X:S)) -> MARK(X:S) 7.48/7.63 MARK(s(X:S)) -> MARK(X:S) 7.48/7.63 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.48/7.63 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.63 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.63 -> Rules: 7.48/7.63 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.63 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.63 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.63 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.63 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.63 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.63 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.63 a__U106(tt) -> tt 7.48/7.63 a__U106(X:S) -> U106(X:S) 7.48/7.63 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.63 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.63 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.63 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.63 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.63 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.63 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.63 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.63 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.63 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.63 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.63 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.63 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.63 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.63 a__U122(tt) -> nil 7.48/7.63 a__U122(X:S) -> U122(X:S) 7.48/7.63 a__U13(tt) -> tt 7.48/7.63 a__U13(X:S) -> U13(X:S) 7.48/7.63 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.63 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.63 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.63 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.63 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.63 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.63 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.63 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.63 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.63 a__U23(tt) -> tt 7.48/7.63 a__U23(X:S) -> U23(X:S) 7.48/7.63 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.63 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.63 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.63 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.63 a__U33(tt) -> tt 7.48/7.63 a__U33(X:S) -> U33(X:S) 7.48/7.63 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.63 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.63 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.63 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.63 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.63 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.63 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.63 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.63 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.63 a__U46(tt) -> tt 7.48/7.63 a__U46(X:S) -> U46(X:S) 7.48/7.63 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.63 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.63 a__U52(tt) -> tt 7.48/7.63 a__U52(X:S) -> U52(X:S) 7.48/7.63 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.63 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.63 a__U62(tt) -> tt 7.48/7.63 a__U62(X:S) -> U62(X:S) 7.48/7.63 a__U71(tt) -> tt 7.48/7.63 a__U71(X:S) -> U71(X:S) 7.48/7.63 a__U81(tt) -> tt 7.48/7.63 a__U81(X:S) -> U81(X:S) 7.48/7.63 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 -> Usable rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 ->Interpretation type: 7.48/7.64 Linear 7.48/7.64 ->Coefficients: 7.48/7.64 Natural Numbers 7.48/7.64 ->Dimension: 7.48/7.64 1 7.48/7.64 ->Bound: 7.48/7.64 2 7.48/7.64 ->Interpretation: 7.48/7.64 7.48/7.64 [a__U101](X1,X2,X3) = X1 7.48/7.64 [a__U102](X1,X2,X3) = X1 7.48/7.64 [a__U103](X1,X2,X3) = X1 7.48/7.64 [a__U104](X1,X2,X3) = X1 7.48/7.64 [a__U105](X1,X2) = X1 7.48/7.64 [a__U106](X) = X 7.48/7.64 [a__U11](X1,X2) = X1 7.48/7.64 [a__U111](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.64 [a__U112](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.64 [a__U113](X1,X2,X3) = X1 + 2.X2 7.48/7.64 [a__U114](X1,X2) = X1 + 2.X2 7.48/7.64 [a__U12](X1,X2) = X1 7.48/7.64 [a__U121](X1,X2) = X1 + 2.X2 7.48/7.64 [a__U122](X) = X 7.48/7.64 [a__U13](X) = X 7.48/7.64 [a__U131](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [a__U132](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [a__U133](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [a__U134](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [a__U135](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [a__U136](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [a__U21](X1,X2) = X1 7.48/7.64 [a__U22](X1,X2) = X1 7.48/7.64 [a__U23](X) = X 7.48/7.64 [a__U31](X1,X2) = X1 7.48/7.64 [a__U32](X1,X2) = X1 7.48/7.64 [a__U33](X) = X 7.48/7.64 [a__U41](X1,X2,X3) = X1 7.48/7.64 [a__U42](X1,X2,X3) = X1 7.48/7.64 [a__U43](X1,X2,X3) = X1 7.48/7.64 [a__U44](X1,X2,X3) = X1 7.48/7.64 [a__U45](X1,X2) = X1 7.48/7.64 [a__U46](X) = X 7.48/7.64 [a__U51](X1,X2) = X1 7.48/7.64 [a__U52](X) = X 7.48/7.64 [a__U61](X1,X2) = X1 7.48/7.64 [a__U62](X) = X 7.48/7.64 [a__U71](X) = X 7.48/7.64 [a__U81](X) = X 7.48/7.64 [a__U91](X1,X2,X3) = X1 7.48/7.64 [a__U92](X1,X2,X3) = X1 7.48/7.64 [a__U93](X1,X2,X3) = X1 7.48/7.64 [a__U94](X1,X2,X3) = X1 7.48/7.64 [a__U95](X1,X2) = X1 7.48/7.64 [a__U96](X) = X 7.48/7.64 [a__isNat](X) = 2 7.48/7.64 [a__isNatIList](X) = 2 7.48/7.64 [a__isNatIListKind](X) = 2 7.48/7.64 [a__isNatKind](X) = 2 7.48/7.64 [a__isNatList](X) = 2 7.48/7.64 [a__length](X) = 2.X + 2 7.48/7.64 [a__take](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.64 [a__zeros] = 1 7.48/7.64 [mark](X) = X 7.48/7.64 [0] = 0 7.48/7.64 [U101](X1,X2,X3) = X1 7.48/7.64 [U102](X1,X2,X3) = X1 7.48/7.64 [U103](X1,X2,X3) = X1 7.48/7.64 [U104](X1,X2,X3) = X1 7.48/7.64 [U105](X1,X2) = X1 7.48/7.64 [U106](X) = X 7.48/7.64 [U11](X1,X2) = X1 7.48/7.64 [U111](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.64 [U112](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.64 [U113](X1,X2,X3) = X1 + 2.X2 7.48/7.64 [U114](X1,X2) = X1 + 2.X2 7.48/7.64 [U12](X1,X2) = X1 7.48/7.64 [U121](X1,X2) = X1 + 2.X2 7.48/7.64 [U122](X) = X 7.48/7.64 [U13](X) = X 7.48/7.64 [U131](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [U132](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [U133](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [U134](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [U135](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [U136](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [U21](X1,X2) = X1 7.48/7.64 [U22](X1,X2) = X1 7.48/7.64 [U23](X) = X 7.48/7.64 [U31](X1,X2) = X1 7.48/7.64 [U32](X1,X2) = X1 7.48/7.64 [U33](X) = X 7.48/7.64 [U41](X1,X2,X3) = X1 7.48/7.64 [U42](X1,X2,X3) = X1 7.48/7.64 [U43](X1,X2,X3) = X1 7.48/7.64 [U44](X1,X2,X3) = X1 7.48/7.64 [U45](X1,X2) = X1 7.48/7.64 [U46](X) = X 7.48/7.64 [U51](X1,X2) = X1 7.48/7.64 [U52](X) = X 7.48/7.64 [U61](X1,X2) = X1 7.48/7.64 [U62](X) = X 7.48/7.64 [U71](X) = X 7.48/7.64 [U81](X) = X 7.48/7.64 [U91](X1,X2,X3) = X1 7.48/7.64 [U92](X1,X2,X3) = X1 7.48/7.64 [U93](X1,X2,X3) = X1 7.48/7.64 [U94](X1,X2,X3) = X1 7.48/7.64 [U95](X1,X2) = X1 7.48/7.64 [U96](X) = X 7.48/7.64 [cons](X1,X2) = 2.X1 + X2 7.48/7.64 [fSNonEmpty] = 0 7.48/7.64 [isNat](X) = 2 7.48/7.64 [isNatIList](X) = 2 7.48/7.64 [isNatIListKind](X) = 2 7.48/7.64 [isNatKind](X) = 2 7.48/7.64 [isNatList](X) = 2 7.48/7.64 [length](X) = 2.X + 2 7.48/7.64 [nil] = 2 7.48/7.64 [s](X) = X 7.48/7.64 [take](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.64 [tt] = 2 7.48/7.64 [zeros] = 1 7.48/7.64 [A__U101](X1,X2,X3) = 0 7.48/7.64 [A__U102](X1,X2,X3) = 0 7.48/7.64 [A__U103](X1,X2,X3) = 0 7.48/7.64 [A__U104](X1,X2,X3) = 0 7.48/7.64 [A__U105](X1,X2) = 0 7.48/7.64 [A__U106](X) = 0 7.48/7.64 [A__U11](X1,X2) = 0 7.48/7.64 [A__U111](X1,X2,X3) = X1 + 2.X2 7.48/7.64 [A__U112](X1,X2,X3) = X1 + 2.X2 7.48/7.64 [A__U113](X1,X2,X3) = X1 + 2.X2 7.48/7.64 [A__U114](X1,X2) = X1 + 2.X2 7.48/7.64 [A__U12](X1,X2) = 0 7.48/7.64 [A__U121](X1,X2) = 0 7.48/7.64 [A__U122](X) = 0 7.48/7.64 [A__U13](X) = 0 7.48/7.64 [A__U131](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.64 [A__U132](X1,X2,X3,X4) = X1 + 2.X2 + 2.X4 7.48/7.64 [A__U133](X1,X2,X3,X4) = X1 + 2.X2 + 2.X4 7.48/7.64 [A__U134](X1,X2,X3,X4) = X1 + 2.X2 + 2.X4 7.48/7.64 [A__U135](X1,X2,X3,X4) = X1 + 2.X2 + 2.X4 7.48/7.64 [A__U136](X1,X2,X3,X4) = 2.X2 + 2.X4 + 1 7.48/7.64 [A__U21](X1,X2) = 0 7.48/7.64 [A__U22](X1,X2) = 0 7.48/7.64 [A__U23](X) = 0 7.48/7.64 [A__U31](X1,X2) = 0 7.48/7.64 [A__U32](X1,X2) = 0 7.48/7.64 [A__U33](X) = 0 7.48/7.64 [A__U41](X1,X2,X3) = 0 7.48/7.64 [A__U42](X1,X2,X3) = 0 7.48/7.64 [A__U43](X1,X2,X3) = 0 7.48/7.64 [A__U44](X1,X2,X3) = 0 7.48/7.64 [A__U45](X1,X2) = 0 7.48/7.64 [A__U46](X) = 0 7.48/7.64 [A__U51](X1,X2) = 0 7.48/7.64 [A__U52](X) = 0 7.48/7.64 [A__U61](X1,X2) = 0 7.48/7.64 [A__U62](X) = 0 7.48/7.64 [A__U71](X) = 0 7.48/7.64 [A__U81](X) = 0 7.48/7.64 [A__U91](X1,X2,X3) = 0 7.48/7.64 [A__U92](X1,X2,X3) = 0 7.48/7.64 [A__U93](X1,X2,X3) = 0 7.48/7.64 [A__U94](X1,X2,X3) = 0 7.48/7.64 [A__U95](X1,X2) = 0 7.48/7.64 [A__U96](X) = 0 7.48/7.64 [A__ISNAT](X) = 0 7.48/7.64 [A__ISNATILIST](X) = 0 7.48/7.64 [A__ISNATILISTKIND](X) = 0 7.48/7.64 [A__ISNATKIND](X) = 0 7.48/7.64 [A__ISNATLIST](X) = 0 7.48/7.64 [A__LENGTH](X) = 2.X + 2 7.48/7.64 [A__TAKE](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.64 [A__ZEROS] = 0 7.48/7.64 [MARK](X) = 2.X + 1 7.48/7.64 7.48/7.64 Problem 1.3: 7.48/7.64 7.48/7.64 SCC Processor: 7.48/7.64 -> Pairs: 7.48/7.64 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.48/7.64 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.48/7.64 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.64 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U111(X1:S,X2:S,X3:S)) -> A__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U112(X1:S,X2:S,X3:S)) -> A__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U113(X1:S,X2:S,X3:S)) -> A__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U114(X1:S,X2:S)) -> A__U114(mark(X1:S),X2:S) 7.48/7.64 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.64 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(length(X:S)) -> A__LENGTH(mark(X:S)) 7.48/7.64 MARK(length(X:S)) -> MARK(X:S) 7.48/7.64 MARK(s(X:S)) -> MARK(X:S) 7.48/7.64 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.48/7.64 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.64 -> Rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 ->Strongly Connected Components: 7.48/7.64 ->->Cycle: 7.48/7.64 ->->-> Pairs: 7.48/7.64 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.48/7.64 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.48/7.64 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 ->->-> Rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 ->->Cycle: 7.48/7.64 ->->-> Pairs: 7.48/7.64 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.64 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.64 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(length(X:S)) -> MARK(X:S) 7.48/7.64 MARK(s(X:S)) -> MARK(X:S) 7.48/7.64 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.48/7.64 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.64 ->->-> Rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 7.48/7.64 7.48/7.64 The problem is decomposed in 2 subproblems. 7.48/7.64 7.48/7.64 Problem 1.3.1: 7.48/7.64 7.48/7.64 Reduction Pairs Processor: 7.48/7.64 -> Pairs: 7.48/7.64 A__U111(tt,L:S,N:S) -> A__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.48/7.64 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.48/7.64 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 -> Rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 -> Usable rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 ->Interpretation type: 7.48/7.64 Linear 7.48/7.64 ->Coefficients: 7.48/7.64 Natural Numbers 7.48/7.64 ->Dimension: 7.48/7.64 1 7.48/7.64 ->Bound: 7.48/7.64 2 7.48/7.64 ->Interpretation: 7.48/7.64 7.48/7.64 [a__U101](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [a__U102](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [a__U103](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [a__U104](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [a__U105](X1,X2) = X1 + X2 7.48/7.64 [a__U106](X) = X 7.48/7.64 [a__U11](X1,X2) = X2 + 1 7.48/7.64 [a__U111](X1,X2,X3) = 2.X2 7.48/7.64 [a__U112](X1,X2,X3) = 2.X2 7.48/7.64 [a__U113](X1,X2,X3) = 2.X2 7.48/7.64 [a__U114](X1,X2) = 2.X2 7.48/7.64 [a__U12](X1,X2) = X2 + 1 7.48/7.64 [a__U121](X1,X2) = X1 7.48/7.64 [a__U122](X) = X 7.48/7.64 [a__U13](X) = X 7.48/7.64 [a__U131](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [a__U132](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [a__U133](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [a__U134](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [a__U135](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [a__U136](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [a__U21](X1,X2) = 2.X2 + 1 7.48/7.64 [a__U22](X1,X2) = 2.X2 + 1 7.48/7.64 [a__U23](X) = X 7.48/7.64 [a__U31](X1,X2) = X1 + X2 7.48/7.64 [a__U32](X1,X2) = X1 + X2 7.48/7.64 [a__U33](X) = 2 7.48/7.64 [a__U41](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [a__U42](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [a__U43](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [a__U44](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [a__U45](X1,X2) = 2.X2 + 2 7.48/7.64 [a__U46](X) = X 7.48/7.64 [a__U51](X1,X2) = 2 7.48/7.64 [a__U52](X) = X 7.48/7.64 [a__U61](X1,X2) = 2 7.48/7.64 [a__U62](X) = X 7.48/7.64 [a__U71](X) = 2 7.48/7.64 [a__U81](X) = 2 7.48/7.64 [a__U91](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [a__U92](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [a__U93](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [a__U94](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [a__U95](X1,X2) = 2.X2 + 1 7.48/7.64 [a__U96](X) = X 7.48/7.64 [a__isNat](X) = X + 1 7.48/7.64 [a__isNatIList](X) = X + 2 7.48/7.64 [a__isNatIListKind](X) = 2 7.48/7.64 [a__isNatKind](X) = 2 7.48/7.64 [a__isNatList](X) = X + 1 7.48/7.64 [a__length](X) = X 7.48/7.64 [a__take](X1,X2) = X1 + X2 7.48/7.64 [a__zeros] = 0 7.48/7.64 [mark](X) = X 7.48/7.64 [0] = 2 7.48/7.64 [U101](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [U102](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [U103](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [U104](X1,X2,X3) = X2 + X3 + 1 7.48/7.64 [U105](X1,X2) = X1 + X2 7.48/7.64 [U106](X) = X 7.48/7.64 [U11](X1,X2) = X2 + 1 7.48/7.64 [U111](X1,X2,X3) = 2.X2 7.48/7.64 [U112](X1,X2,X3) = 2.X2 7.48/7.64 [U113](X1,X2,X3) = 2.X2 7.48/7.64 [U114](X1,X2) = 2.X2 7.48/7.64 [U12](X1,X2) = X2 + 1 7.48/7.64 [U121](X1,X2) = X1 7.48/7.64 [U122](X) = X 7.48/7.64 [U13](X) = X 7.48/7.64 [U131](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [U132](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [U133](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [U134](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [U135](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [U136](X1,X2,X3,X4) = 2.X2 + 2.X3 7.48/7.64 [U21](X1,X2) = 2.X2 + 1 7.48/7.64 [U22](X1,X2) = 2.X2 + 1 7.48/7.64 [U23](X) = X 7.48/7.64 [U31](X1,X2) = X1 + X2 7.48/7.64 [U32](X1,X2) = X1 + X2 7.48/7.64 [U33](X) = 2 7.48/7.64 [U41](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [U42](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [U43](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [U44](X1,X2,X3) = 2.X3 + 2 7.48/7.64 [U45](X1,X2) = 2.X2 + 2 7.48/7.64 [U46](X) = X 7.48/7.64 [U51](X1,X2) = 2 7.48/7.64 [U52](X) = X 7.48/7.64 [U61](X1,X2) = 2 7.48/7.64 [U62](X) = X 7.48/7.64 [U71](X) = 2 7.48/7.64 [U81](X) = 2 7.48/7.64 [U91](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [U92](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [U93](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [U94](X1,X2,X3) = 2.X3 + 1 7.48/7.64 [U95](X1,X2) = 2.X2 + 1 7.48/7.64 [U96](X) = X 7.48/7.64 [cons](X1,X2) = 2.X2 7.48/7.64 [fSNonEmpty] = 0 7.48/7.64 [isNat](X) = X + 1 7.48/7.64 [isNatIList](X) = X + 2 7.48/7.64 [isNatIListKind](X) = 2 7.48/7.64 [isNatKind](X) = 2 7.48/7.64 [isNatList](X) = X + 1 7.48/7.64 [length](X) = X 7.48/7.64 [nil] = 2 7.48/7.64 [s](X) = 2.X 7.48/7.64 [take](X1,X2) = X1 + X2 7.48/7.64 [tt] = 2 7.48/7.64 [zeros] = 0 7.48/7.64 [A__U101](X1,X2,X3) = 0 7.48/7.64 [A__U102](X1,X2,X3) = 0 7.48/7.64 [A__U103](X1,X2,X3) = 0 7.48/7.64 [A__U104](X1,X2,X3) = 0 7.48/7.64 [A__U105](X1,X2) = 0 7.48/7.64 [A__U106](X) = 0 7.48/7.64 [A__U11](X1,X2) = 0 7.48/7.64 [A__U111](X1,X2,X3) = 2.X1 + 2.X2 7.48/7.64 [A__U112](X1,X2,X3) = X1 + 2.X2 + 1 7.48/7.64 [A__U113](X1,X2,X3) = 2.X2 + 2 7.48/7.64 [A__U114](X1,X2) = X1 + 2.X2 7.48/7.64 [A__U12](X1,X2) = 0 7.48/7.64 [A__U121](X1,X2) = 0 7.48/7.64 [A__U122](X) = 0 7.48/7.64 [A__U13](X) = 0 7.48/7.64 [A__U131](X1,X2,X3,X4) = 0 7.48/7.64 [A__U132](X1,X2,X3,X4) = 0 7.48/7.64 [A__U133](X1,X2,X3,X4) = 0 7.48/7.64 [A__U134](X1,X2,X3,X4) = 0 7.48/7.64 [A__U135](X1,X2,X3,X4) = 0 7.48/7.64 [A__U136](X1,X2,X3,X4) = 0 7.48/7.64 [A__U21](X1,X2) = 0 7.48/7.64 [A__U22](X1,X2) = 0 7.48/7.64 [A__U23](X) = 0 7.48/7.64 [A__U31](X1,X2) = 0 7.48/7.64 [A__U32](X1,X2) = 0 7.48/7.64 [A__U33](X) = 0 7.48/7.64 [A__U41](X1,X2,X3) = 0 7.48/7.64 [A__U42](X1,X2,X3) = 0 7.48/7.64 [A__U43](X1,X2,X3) = 0 7.48/7.64 [A__U44](X1,X2,X3) = 0 7.48/7.64 [A__U45](X1,X2) = 0 7.48/7.64 [A__U46](X) = 0 7.48/7.64 [A__U51](X1,X2) = 0 7.48/7.64 [A__U52](X) = 0 7.48/7.64 [A__U61](X1,X2) = 0 7.48/7.64 [A__U62](X) = 0 7.48/7.64 [A__U71](X) = 0 7.48/7.64 [A__U81](X) = 0 7.48/7.64 [A__U91](X1,X2,X3) = 0 7.48/7.64 [A__U92](X1,X2,X3) = 0 7.48/7.64 [A__U93](X1,X2,X3) = 0 7.48/7.64 [A__U94](X1,X2,X3) = 0 7.48/7.64 [A__U95](X1,X2) = 0 7.48/7.64 [A__U96](X) = 0 7.48/7.64 [A__ISNAT](X) = 0 7.48/7.64 [A__ISNATILIST](X) = 0 7.48/7.64 [A__ISNATILISTKIND](X) = 0 7.48/7.64 [A__ISNATKIND](X) = 0 7.48/7.64 [A__ISNATLIST](X) = 0 7.48/7.64 [A__LENGTH](X) = 2.X + 2 7.48/7.64 [A__TAKE](X1,X2) = 0 7.48/7.64 [A__ZEROS] = 0 7.48/7.64 [MARK](X) = 0 7.48/7.64 7.48/7.64 Problem 1.3.1: 7.48/7.64 7.48/7.64 SCC Processor: 7.48/7.64 -> Pairs: 7.48/7.64 A__U112(tt,L:S,N:S) -> A__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 A__U113(tt,L:S,N:S) -> A__U114(a__isNatKind(N:S),L:S) 7.48/7.64 A__U114(tt,L:S) -> A__LENGTH(mark(L:S)) 7.48/7.64 A__LENGTH(cons(N:S,L:S)) -> A__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 -> Rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.64 a__U106(tt) -> tt 7.48/7.64 a__U106(X:S) -> U106(X:S) 7.48/7.64 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.64 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.64 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.64 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.64 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.64 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.64 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.64 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.64 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.64 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.64 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.64 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.64 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.64 a__U122(tt) -> nil 7.48/7.64 a__U122(X:S) -> U122(X:S) 7.48/7.64 a__U13(tt) -> tt 7.48/7.64 a__U13(X:S) -> U13(X:S) 7.48/7.64 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.64 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.64 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.64 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.64 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.64 a__U23(tt) -> tt 7.48/7.64 a__U23(X:S) -> U23(X:S) 7.48/7.64 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.64 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.64 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.64 a__U33(tt) -> tt 7.48/7.64 a__U33(X:S) -> U33(X:S) 7.48/7.64 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.64 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.64 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.64 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.64 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.64 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.64 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.64 a__U46(tt) -> tt 7.48/7.64 a__U46(X:S) -> U46(X:S) 7.48/7.64 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.64 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.64 a__U52(tt) -> tt 7.48/7.64 a__U52(X:S) -> U52(X:S) 7.48/7.64 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.64 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.64 a__U62(tt) -> tt 7.48/7.64 a__U62(X:S) -> U62(X:S) 7.48/7.64 a__U71(tt) -> tt 7.48/7.64 a__U71(X:S) -> U71(X:S) 7.48/7.64 a__U81(tt) -> tt 7.48/7.64 a__U81(X:S) -> U81(X:S) 7.48/7.64 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.64 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.64 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.64 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.64 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.64 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.64 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.64 a__U96(tt) -> tt 7.48/7.64 a__U96(X:S) -> U96(X:S) 7.48/7.64 a__isNat(0) -> tt 7.48/7.64 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.64 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.64 a__isNat(X:S) -> isNat(X:S) 7.48/7.64 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatIList(zeros) -> tt 7.48/7.64 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.64 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.64 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(nil) -> tt 7.48/7.64 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.64 a__isNatIListKind(zeros) -> tt 7.48/7.64 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.64 a__isNatKind(0) -> tt 7.48/7.64 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.64 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.64 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.64 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(nil) -> tt 7.48/7.64 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.64 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.64 a__length(nil) -> 0 7.48/7.64 a__length(X:S) -> length(X:S) 7.48/7.64 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.64 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.64 a__zeros -> cons(0,zeros) 7.48/7.64 a__zeros -> zeros 7.48/7.64 mark(0) -> 0 7.48/7.64 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.64 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.64 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.64 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.64 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.64 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.64 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.64 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.64 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.64 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.64 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.64 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.64 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.64 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.64 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.64 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.64 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.64 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.64 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.64 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.64 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.64 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.64 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.64 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.64 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.64 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.64 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.64 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.64 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.64 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.64 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.64 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.64 mark(nil) -> nil 7.48/7.64 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.64 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.64 mark(tt) -> tt 7.48/7.64 mark(zeros) -> a__zeros 7.48/7.64 ->Strongly Connected Components: 7.48/7.64 There is no strongly connected component 7.48/7.64 7.48/7.64 The problem is finite. 7.48/7.64 7.48/7.64 Problem 1.3.2: 7.48/7.64 7.48/7.64 Reduction Pairs Processor: 7.48/7.64 -> Pairs: 7.48/7.64 A__U131(tt,IL:S,M:S,N:S) -> A__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.64 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.64 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.64 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.64 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.64 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.64 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.64 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.64 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.64 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.64 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.64 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.64 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(length(X:S)) -> MARK(X:S) 7.48/7.64 MARK(s(X:S)) -> MARK(X:S) 7.48/7.64 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.48/7.64 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.64 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.64 -> Rules: 7.48/7.64 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.64 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.64 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.64 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.64 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.64 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.64 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.64 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.64 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.65 a__U106(tt) -> tt 7.48/7.65 a__U106(X:S) -> U106(X:S) 7.48/7.65 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.65 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.65 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.65 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.65 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.65 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.65 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.65 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.65 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.65 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.65 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.65 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.65 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.65 a__U122(tt) -> nil 7.48/7.65 a__U122(X:S) -> U122(X:S) 7.48/7.65 a__U13(tt) -> tt 7.48/7.65 a__U13(X:S) -> U13(X:S) 7.48/7.65 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.65 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.65 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.65 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.65 a__U23(tt) -> tt 7.48/7.65 a__U23(X:S) -> U23(X:S) 7.48/7.65 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.65 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.65 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.65 a__U33(tt) -> tt 7.48/7.65 a__U33(X:S) -> U33(X:S) 7.48/7.65 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.65 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.65 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.65 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.65 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.65 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.65 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.65 a__U46(tt) -> tt 7.48/7.65 a__U46(X:S) -> U46(X:S) 7.48/7.65 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.65 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.65 a__U52(tt) -> tt 7.48/7.65 a__U52(X:S) -> U52(X:S) 7.48/7.65 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.65 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.65 a__U62(tt) -> tt 7.48/7.65 a__U62(X:S) -> U62(X:S) 7.48/7.65 a__U71(tt) -> tt 7.48/7.65 a__U71(X:S) -> U71(X:S) 7.48/7.65 a__U81(tt) -> tt 7.48/7.65 a__U81(X:S) -> U81(X:S) 7.48/7.65 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.65 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.65 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.65 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.65 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.65 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.65 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.65 a__U96(tt) -> tt 7.48/7.65 a__U96(X:S) -> U96(X:S) 7.48/7.65 a__isNat(0) -> tt 7.48/7.65 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__isNat(X:S) -> isNat(X:S) 7.48/7.65 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatIList(zeros) -> tt 7.48/7.65 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.65 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(nil) -> tt 7.48/7.65 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(zeros) -> tt 7.48/7.65 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.65 a__isNatKind(0) -> tt 7.48/7.65 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.65 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.65 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.65 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(nil) -> tt 7.48/7.65 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.65 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.65 a__length(nil) -> 0 7.48/7.65 a__length(X:S) -> length(X:S) 7.48/7.65 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.65 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.65 a__zeros -> cons(0,zeros) 7.48/7.65 a__zeros -> zeros 7.48/7.65 mark(0) -> 0 7.48/7.65 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.65 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.65 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.65 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.65 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.65 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.65 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.65 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.65 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.65 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.65 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.65 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.65 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.65 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.65 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.65 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.65 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.65 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.65 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.65 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.65 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.65 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.65 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.65 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.65 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.65 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.65 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.65 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.65 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.65 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.65 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.65 mark(nil) -> nil 7.48/7.65 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.65 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.65 mark(tt) -> tt 7.48/7.65 mark(zeros) -> a__zeros 7.48/7.65 -> Usable rules: 7.48/7.65 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.65 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.65 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.65 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.65 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.65 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.65 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.65 a__U106(tt) -> tt 7.48/7.65 a__U106(X:S) -> U106(X:S) 7.48/7.65 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.65 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.65 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.65 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.65 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.65 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.65 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.65 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.65 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.65 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.65 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.65 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.65 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.65 a__U122(tt) -> nil 7.48/7.65 a__U122(X:S) -> U122(X:S) 7.48/7.65 a__U13(tt) -> tt 7.48/7.65 a__U13(X:S) -> U13(X:S) 7.48/7.65 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.65 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.65 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.65 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.65 a__U23(tt) -> tt 7.48/7.65 a__U23(X:S) -> U23(X:S) 7.48/7.65 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.65 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.65 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.65 a__U33(tt) -> tt 7.48/7.65 a__U33(X:S) -> U33(X:S) 7.48/7.65 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.65 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.65 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.65 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.65 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.65 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.65 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.65 a__U46(tt) -> tt 7.48/7.65 a__U46(X:S) -> U46(X:S) 7.48/7.65 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.65 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.65 a__U52(tt) -> tt 7.48/7.65 a__U52(X:S) -> U52(X:S) 7.48/7.65 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.65 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.65 a__U62(tt) -> tt 7.48/7.65 a__U62(X:S) -> U62(X:S) 7.48/7.65 a__U71(tt) -> tt 7.48/7.65 a__U71(X:S) -> U71(X:S) 7.48/7.65 a__U81(tt) -> tt 7.48/7.65 a__U81(X:S) -> U81(X:S) 7.48/7.65 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.65 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.65 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.65 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.65 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.65 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.65 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.65 a__U96(tt) -> tt 7.48/7.65 a__U96(X:S) -> U96(X:S) 7.48/7.65 a__isNat(0) -> tt 7.48/7.65 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__isNat(X:S) -> isNat(X:S) 7.48/7.65 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatIList(zeros) -> tt 7.48/7.65 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.65 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(nil) -> tt 7.48/7.65 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(zeros) -> tt 7.48/7.65 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.65 a__isNatKind(0) -> tt 7.48/7.65 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.65 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.65 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.65 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(nil) -> tt 7.48/7.65 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.65 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.65 a__length(nil) -> 0 7.48/7.65 a__length(X:S) -> length(X:S) 7.48/7.65 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.65 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.65 a__zeros -> cons(0,zeros) 7.48/7.65 a__zeros -> zeros 7.48/7.65 mark(0) -> 0 7.48/7.65 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.65 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.65 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.65 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.65 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.65 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.65 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.65 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.65 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.65 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.65 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.65 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.65 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.65 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.65 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.65 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.65 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.65 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.65 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.65 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.65 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.65 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.65 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.65 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.65 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.65 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.65 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.65 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.65 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.65 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.65 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.65 mark(nil) -> nil 7.48/7.65 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.65 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.65 mark(tt) -> tt 7.48/7.65 mark(zeros) -> a__zeros 7.48/7.65 ->Interpretation type: 7.48/7.65 Linear 7.48/7.65 ->Coefficients: 7.48/7.65 Natural Numbers 7.48/7.65 ->Dimension: 7.48/7.65 1 7.48/7.65 ->Bound: 7.48/7.65 2 7.48/7.65 ->Interpretation: 7.48/7.65 7.48/7.65 [a__U101](X1,X2,X3) = X1 7.48/7.65 [a__U102](X1,X2,X3) = X1 7.48/7.65 [a__U103](X1,X2,X3) = X1 7.48/7.65 [a__U104](X1,X2,X3) = X1 7.48/7.65 [a__U105](X1,X2) = X1 7.48/7.65 [a__U106](X) = X 7.48/7.65 [a__U11](X1,X2) = X1 7.48/7.65 [a__U111](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.65 [a__U112](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.65 [a__U113](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.65 [a__U114](X1,X2) = X1 + 2.X2 7.48/7.65 [a__U12](X1,X2) = X1 7.48/7.65 [a__U121](X1,X2) = X1 + 2.X2 7.48/7.65 [a__U122](X) = X 7.48/7.65 [a__U13](X) = X 7.48/7.65 [a__U131](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [a__U132](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [a__U133](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [a__U134](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + X4 7.48/7.65 [a__U135](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + X4 7.48/7.65 [a__U136](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + X4 7.48/7.65 [a__U21](X1,X2) = X1 7.48/7.65 [a__U22](X1,X2) = X1 7.48/7.65 [a__U23](X) = X 7.48/7.65 [a__U31](X1,X2) = X1 7.48/7.65 [a__U32](X1,X2) = X1 7.48/7.65 [a__U33](X) = X 7.48/7.65 [a__U41](X1,X2,X3) = X1 7.48/7.65 [a__U42](X1,X2,X3) = X1 7.48/7.65 [a__U43](X1,X2,X3) = X1 7.48/7.65 [a__U44](X1,X2,X3) = X1 7.48/7.65 [a__U45](X1,X2) = X1 7.48/7.65 [a__U46](X) = X 7.48/7.65 [a__U51](X1,X2) = X1 7.48/7.65 [a__U52](X) = X 7.48/7.65 [a__U61](X1,X2) = X1 7.48/7.65 [a__U62](X) = X 7.48/7.65 [a__U71](X) = X 7.48/7.65 [a__U81](X) = X 7.48/7.65 [a__U91](X1,X2,X3) = X1 7.48/7.65 [a__U92](X1,X2,X3) = X1 7.48/7.65 [a__U93](X1,X2,X3) = X1 7.48/7.65 [a__U94](X1,X2,X3) = X1 7.48/7.65 [a__U95](X1,X2) = X1 7.48/7.65 [a__U96](X) = X 7.48/7.65 [a__isNat](X) = 2 7.48/7.65 [a__isNatIList](X) = 2 7.48/7.65 [a__isNatIListKind](X) = 2 7.48/7.65 [a__isNatKind](X) = 2 7.48/7.65 [a__isNatList](X) = 2 7.48/7.65 [a__length](X) = 2.X + 2 7.48/7.65 [a__take](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.65 [a__zeros] = 0 7.48/7.65 [mark](X) = X 7.48/7.65 [0] = 0 7.48/7.65 [U101](X1,X2,X3) = X1 7.48/7.65 [U102](X1,X2,X3) = X1 7.48/7.65 [U103](X1,X2,X3) = X1 7.48/7.65 [U104](X1,X2,X3) = X1 7.48/7.65 [U105](X1,X2) = X1 7.48/7.65 [U106](X) = X 7.48/7.65 [U11](X1,X2) = X1 7.48/7.65 [U111](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.65 [U112](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.65 [U113](X1,X2,X3) = X1 + 2.X2 + 2.X3 7.48/7.65 [U114](X1,X2) = X1 + 2.X2 7.48/7.65 [U12](X1,X2) = X1 7.48/7.65 [U121](X1,X2) = X1 + 2.X2 7.48/7.65 [U122](X) = X 7.48/7.65 [U13](X) = X 7.48/7.65 [U131](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [U132](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [U133](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [U134](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + X4 7.48/7.65 [U135](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + X4 7.48/7.65 [U136](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + X4 7.48/7.65 [U21](X1,X2) = X1 7.48/7.65 [U22](X1,X2) = X1 7.48/7.65 [U23](X) = X 7.48/7.65 [U31](X1,X2) = X1 7.48/7.65 [U32](X1,X2) = X1 7.48/7.65 [U33](X) = X 7.48/7.65 [U41](X1,X2,X3) = X1 7.48/7.65 [U42](X1,X2,X3) = X1 7.48/7.65 [U43](X1,X2,X3) = X1 7.48/7.65 [U44](X1,X2,X3) = X1 7.48/7.65 [U45](X1,X2) = X1 7.48/7.65 [U46](X) = X 7.48/7.65 [U51](X1,X2) = X1 7.48/7.65 [U52](X) = X 7.48/7.65 [U61](X1,X2) = X1 7.48/7.65 [U62](X) = X 7.48/7.65 [U71](X) = X 7.48/7.65 [U81](X) = X 7.48/7.65 [U91](X1,X2,X3) = X1 7.48/7.65 [U92](X1,X2,X3) = X1 7.48/7.65 [U93](X1,X2,X3) = X1 7.48/7.65 [U94](X1,X2,X3) = X1 7.48/7.65 [U95](X1,X2) = X1 7.48/7.65 [U96](X) = X 7.48/7.65 [cons](X1,X2) = X1 + X2 7.48/7.65 [fSNonEmpty] = 0 7.48/7.65 [isNat](X) = 2 7.48/7.65 [isNatIList](X) = 2 7.48/7.65 [isNatIListKind](X) = 2 7.48/7.65 [isNatKind](X) = 2 7.48/7.65 [isNatList](X) = 2 7.48/7.65 [length](X) = 2.X + 2 7.48/7.65 [nil] = 2 7.48/7.65 [s](X) = X 7.48/7.65 [take](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.65 [tt] = 2 7.48/7.65 [zeros] = 0 7.48/7.65 [A__U101](X1,X2,X3) = 0 7.48/7.65 [A__U102](X1,X2,X3) = 0 7.48/7.65 [A__U103](X1,X2,X3) = 0 7.48/7.65 [A__U104](X1,X2,X3) = 0 7.48/7.65 [A__U105](X1,X2) = 0 7.48/7.65 [A__U106](X) = 0 7.48/7.65 [A__U11](X1,X2) = 0 7.48/7.65 [A__U111](X1,X2,X3) = 0 7.48/7.65 [A__U112](X1,X2,X3) = 0 7.48/7.65 [A__U113](X1,X2,X3) = 0 7.48/7.65 [A__U114](X1,X2) = 0 7.48/7.65 [A__U12](X1,X2) = 0 7.48/7.65 [A__U121](X1,X2) = 0 7.48/7.65 [A__U122](X) = 0 7.48/7.65 [A__U13](X) = 0 7.48/7.65 [A__U131](X1,X2,X3,X4) = X1 + 2.X2 + 2.X3 + 2.X4 7.48/7.65 [A__U132](X1,X2,X3,X4) = 2.X2 + 2.X3 + 2.X4 + 1 7.48/7.65 [A__U133](X1,X2,X3,X4) = 2.X2 + 2.X3 + 2.X4 + 1 7.48/7.65 [A__U134](X1,X2,X3,X4) = X2 + 2.X3 + 2.X4 + 1 7.48/7.65 [A__U135](X1,X2,X3,X4) = X2 + 2.X3 + 2.X4 + 1 7.48/7.65 [A__U136](X1,X2,X3,X4) = X2 + 2.X3 + 2.X4 + 1 7.48/7.65 [A__U21](X1,X2) = 0 7.48/7.65 [A__U22](X1,X2) = 0 7.48/7.65 [A__U23](X) = 0 7.48/7.65 [A__U31](X1,X2) = 0 7.48/7.65 [A__U32](X1,X2) = 0 7.48/7.65 [A__U33](X) = 0 7.48/7.65 [A__U41](X1,X2,X3) = 0 7.48/7.65 [A__U42](X1,X2,X3) = 0 7.48/7.65 [A__U43](X1,X2,X3) = 0 7.48/7.65 [A__U44](X1,X2,X3) = 0 7.48/7.65 [A__U45](X1,X2) = 0 7.48/7.65 [A__U46](X) = 0 7.48/7.65 [A__U51](X1,X2) = 0 7.48/7.65 [A__U52](X) = 0 7.48/7.65 [A__U61](X1,X2) = 0 7.48/7.65 [A__U62](X) = 0 7.48/7.65 [A__U71](X) = 0 7.48/7.65 [A__U81](X) = 0 7.48/7.65 [A__U91](X1,X2,X3) = 0 7.48/7.65 [A__U92](X1,X2,X3) = 0 7.48/7.65 [A__U93](X1,X2,X3) = 0 7.48/7.65 [A__U94](X1,X2,X3) = 0 7.48/7.65 [A__U95](X1,X2) = 0 7.48/7.65 [A__U96](X) = 0 7.48/7.65 [A__ISNAT](X) = 0 7.48/7.65 [A__ISNATILIST](X) = 0 7.48/7.65 [A__ISNATILISTKIND](X) = 0 7.48/7.65 [A__ISNATKIND](X) = 0 7.48/7.65 [A__ISNATLIST](X) = 0 7.48/7.65 [A__LENGTH](X) = 0 7.48/7.65 [A__TAKE](X1,X2) = 2.X1 + 2.X2 + 2 7.48/7.65 [A__ZEROS] = 0 7.48/7.65 [MARK](X) = 2.X + 1 7.48/7.65 7.48/7.65 Problem 1.3.2: 7.48/7.65 7.48/7.65 SCC Processor: 7.48/7.65 -> Pairs: 7.48/7.65 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.65 A__TAKE(s(M:S),cons(N:S,IL:S)) -> A__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> A__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.65 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(length(X:S)) -> MARK(X:S) 7.48/7.65 MARK(s(X:S)) -> MARK(X:S) 7.48/7.65 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S)) 7.48/7.65 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.65 -> Rules: 7.48/7.65 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.65 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.65 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.65 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.65 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.65 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.65 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.65 a__U106(tt) -> tt 7.48/7.65 a__U106(X:S) -> U106(X:S) 7.48/7.65 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.65 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.65 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.65 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.65 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.65 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.65 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.65 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.65 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.65 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.65 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.65 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.65 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.65 a__U122(tt) -> nil 7.48/7.65 a__U122(X:S) -> U122(X:S) 7.48/7.65 a__U13(tt) -> tt 7.48/7.65 a__U13(X:S) -> U13(X:S) 7.48/7.65 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.65 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.65 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.65 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.65 a__U23(tt) -> tt 7.48/7.65 a__U23(X:S) -> U23(X:S) 7.48/7.65 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.65 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.65 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.65 a__U33(tt) -> tt 7.48/7.65 a__U33(X:S) -> U33(X:S) 7.48/7.65 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.65 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.65 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.65 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.65 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.65 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.65 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.65 a__U46(tt) -> tt 7.48/7.65 a__U46(X:S) -> U46(X:S) 7.48/7.65 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.65 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.65 a__U52(tt) -> tt 7.48/7.65 a__U52(X:S) -> U52(X:S) 7.48/7.65 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.65 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.65 a__U62(tt) -> tt 7.48/7.65 a__U62(X:S) -> U62(X:S) 7.48/7.65 a__U71(tt) -> tt 7.48/7.65 a__U71(X:S) -> U71(X:S) 7.48/7.65 a__U81(tt) -> tt 7.48/7.65 a__U81(X:S) -> U81(X:S) 7.48/7.65 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.65 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.65 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.65 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.65 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.65 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.65 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.65 a__U96(tt) -> tt 7.48/7.65 a__U96(X:S) -> U96(X:S) 7.48/7.65 a__isNat(0) -> tt 7.48/7.65 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__isNat(X:S) -> isNat(X:S) 7.48/7.65 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatIList(zeros) -> tt 7.48/7.65 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.65 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(nil) -> tt 7.48/7.65 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(zeros) -> tt 7.48/7.65 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.65 a__isNatKind(0) -> tt 7.48/7.65 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.65 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.65 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.65 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(nil) -> tt 7.48/7.65 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.65 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.65 a__length(nil) -> 0 7.48/7.65 a__length(X:S) -> length(X:S) 7.48/7.65 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.65 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.65 a__zeros -> cons(0,zeros) 7.48/7.65 a__zeros -> zeros 7.48/7.65 mark(0) -> 0 7.48/7.65 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.65 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.65 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.65 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.65 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.65 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.65 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.65 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.65 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.65 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.65 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.65 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.65 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.65 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.65 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.65 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.65 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.65 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.65 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.65 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.65 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.65 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.65 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.65 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.65 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.65 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.65 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.65 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.65 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.65 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.65 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.65 mark(nil) -> nil 7.48/7.65 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.65 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.65 mark(tt) -> tt 7.48/7.65 mark(zeros) -> a__zeros 7.48/7.65 ->Strongly Connected Components: 7.48/7.65 ->->Cycle: 7.48/7.65 ->->-> Pairs: 7.48/7.65 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.65 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.65 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(length(X:S)) -> MARK(X:S) 7.48/7.65 MARK(s(X:S)) -> MARK(X:S) 7.48/7.65 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.65 ->->-> Rules: 7.48/7.65 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.65 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.65 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.65 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.65 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.65 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.65 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.65 a__U106(tt) -> tt 7.48/7.65 a__U106(X:S) -> U106(X:S) 7.48/7.65 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.65 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.65 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.65 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.65 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.65 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.65 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.65 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.65 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.65 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.65 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.65 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.65 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.65 a__U122(tt) -> nil 7.48/7.65 a__U122(X:S) -> U122(X:S) 7.48/7.65 a__U13(tt) -> tt 7.48/7.65 a__U13(X:S) -> U13(X:S) 7.48/7.65 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.65 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.65 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.65 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.65 a__U23(tt) -> tt 7.48/7.65 a__U23(X:S) -> U23(X:S) 7.48/7.65 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.65 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.65 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.65 a__U33(tt) -> tt 7.48/7.65 a__U33(X:S) -> U33(X:S) 7.48/7.65 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.65 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.65 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.65 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.65 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.65 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.65 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.65 a__U46(tt) -> tt 7.48/7.65 a__U46(X:S) -> U46(X:S) 7.48/7.65 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.65 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.65 a__U52(tt) -> tt 7.48/7.65 a__U52(X:S) -> U52(X:S) 7.48/7.65 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.65 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.65 a__U62(tt) -> tt 7.48/7.65 a__U62(X:S) -> U62(X:S) 7.48/7.65 a__U71(tt) -> tt 7.48/7.65 a__U71(X:S) -> U71(X:S) 7.48/7.65 a__U81(tt) -> tt 7.48/7.65 a__U81(X:S) -> U81(X:S) 7.48/7.65 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.65 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.65 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.65 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.65 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.65 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.65 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.65 a__U96(tt) -> tt 7.48/7.65 a__U96(X:S) -> U96(X:S) 7.48/7.65 a__isNat(0) -> tt 7.48/7.65 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__isNat(X:S) -> isNat(X:S) 7.48/7.65 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatIList(zeros) -> tt 7.48/7.65 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.65 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(nil) -> tt 7.48/7.65 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(zeros) -> tt 7.48/7.65 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.65 a__isNatKind(0) -> tt 7.48/7.65 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.65 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.65 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.65 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(nil) -> tt 7.48/7.65 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.65 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.65 a__length(nil) -> 0 7.48/7.65 a__length(X:S) -> length(X:S) 7.48/7.65 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.65 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.65 a__zeros -> cons(0,zeros) 7.48/7.65 a__zeros -> zeros 7.48/7.65 mark(0) -> 0 7.48/7.65 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.65 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.65 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.65 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.65 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.65 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.65 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.65 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.65 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.65 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.65 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.65 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.65 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.65 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.65 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.65 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.65 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.65 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.65 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.65 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.65 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.65 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.65 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.65 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.65 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.65 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.65 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.65 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.65 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.65 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.65 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.65 mark(nil) -> nil 7.48/7.65 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.65 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.65 mark(tt) -> tt 7.48/7.65 mark(zeros) -> a__zeros 7.48/7.65 7.48/7.65 Problem 1.3.2: 7.48/7.65 7.48/7.65 Subterm Processor: 7.48/7.65 -> Pairs: 7.48/7.65 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.65 MARK(U101(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U102(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U103(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U104(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U105(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U106(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U11(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U111(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U112(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U113(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U114(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U12(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U121(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U122(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U13(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U131(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> A__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U132(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> A__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U133(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> A__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U134(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> A__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U135(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> A__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 MARK(U136(X1:S,X2:S,X3:S,X4:S)) -> MARK(X1:S) 7.48/7.65 MARK(U21(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U22(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U23(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U31(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U32(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U33(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U45(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U46(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U51(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U52(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U61(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U62(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U71(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U81(X:S)) -> MARK(X:S) 7.48/7.65 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U94(X1:S,X2:S,X3:S)) -> MARK(X1:S) 7.48/7.65 MARK(U95(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(U96(X:S)) -> MARK(X:S) 7.48/7.65 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(length(X:S)) -> MARK(X:S) 7.48/7.65 MARK(s(X:S)) -> MARK(X:S) 7.48/7.65 MARK(take(X1:S,X2:S)) -> MARK(X1:S) 7.48/7.65 MARK(take(X1:S,X2:S)) -> MARK(X2:S) 7.48/7.65 -> Rules: 7.48/7.65 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.65 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.65 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.65 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.65 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.65 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.65 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.65 a__U106(tt) -> tt 7.48/7.65 a__U106(X:S) -> U106(X:S) 7.48/7.65 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.65 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.65 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.65 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.65 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.65 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.65 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.65 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.65 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.65 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.65 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.65 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.65 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.65 a__U122(tt) -> nil 7.48/7.65 a__U122(X:S) -> U122(X:S) 7.48/7.65 a__U13(tt) -> tt 7.48/7.65 a__U13(X:S) -> U13(X:S) 7.48/7.65 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.65 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.65 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.65 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.65 a__U23(tt) -> tt 7.48/7.65 a__U23(X:S) -> U23(X:S) 7.48/7.65 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.65 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.65 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.65 a__U33(tt) -> tt 7.48/7.65 a__U33(X:S) -> U33(X:S) 7.48/7.65 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.65 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.65 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.65 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.65 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.65 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.65 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.65 a__U46(tt) -> tt 7.48/7.65 a__U46(X:S) -> U46(X:S) 7.48/7.65 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.65 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.65 a__U52(tt) -> tt 7.48/7.65 a__U52(X:S) -> U52(X:S) 7.48/7.65 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.65 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.65 a__U62(tt) -> tt 7.48/7.65 a__U62(X:S) -> U62(X:S) 7.48/7.65 a__U71(tt) -> tt 7.48/7.65 a__U71(X:S) -> U71(X:S) 7.48/7.65 a__U81(tt) -> tt 7.48/7.65 a__U81(X:S) -> U81(X:S) 7.48/7.65 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.65 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.65 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.65 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.65 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.65 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.65 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.65 a__U96(tt) -> tt 7.48/7.65 a__U96(X:S) -> U96(X:S) 7.48/7.65 a__isNat(0) -> tt 7.48/7.65 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__isNat(X:S) -> isNat(X:S) 7.48/7.65 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatIList(zeros) -> tt 7.48/7.65 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.65 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(nil) -> tt 7.48/7.65 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(zeros) -> tt 7.48/7.65 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.65 a__isNatKind(0) -> tt 7.48/7.65 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.65 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.65 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.65 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(nil) -> tt 7.48/7.65 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.65 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.65 a__length(nil) -> 0 7.48/7.65 a__length(X:S) -> length(X:S) 7.48/7.65 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.65 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.65 a__zeros -> cons(0,zeros) 7.48/7.65 a__zeros -> zeros 7.48/7.65 mark(0) -> 0 7.48/7.65 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.65 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.65 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.65 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.65 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.65 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.65 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.65 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.65 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.65 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.65 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.65 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.65 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.65 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.65 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.65 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.65 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.65 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.65 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.65 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.65 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.65 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.65 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.65 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.65 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.65 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.65 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.65 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.65 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.65 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.65 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.65 mark(nil) -> nil 7.48/7.65 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.65 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.65 mark(tt) -> tt 7.48/7.65 mark(zeros) -> a__zeros 7.48/7.65 ->Projection: 7.48/7.65 pi(A__U132) = 4 7.48/7.65 pi(A__U133) = 4 7.48/7.65 pi(A__U134) = 4 7.48/7.65 pi(A__U135) = 4 7.48/7.65 pi(A__U136) = 4 7.48/7.65 pi(MARK) = 1 7.48/7.65 7.48/7.65 Problem 1.3.2: 7.48/7.65 7.48/7.65 SCC Processor: 7.48/7.65 -> Pairs: 7.48/7.65 A__U132(tt,IL:S,M:S,N:S) -> A__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U133(tt,IL:S,M:S,N:S) -> A__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 A__U134(tt,IL:S,M:S,N:S) -> A__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U135(tt,IL:S,M:S,N:S) -> A__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 A__U136(tt,IL:S,M:S,N:S) -> MARK(N:S) 7.48/7.65 -> Rules: 7.48/7.65 a__U101(tt,V1:S,V2:S) -> a__U102(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U101(X1:S,X2:S,X3:S) -> U101(X1:S,X2:S,X3:S) 7.48/7.65 a__U102(tt,V1:S,V2:S) -> a__U103(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U102(X1:S,X2:S,X3:S) -> U102(X1:S,X2:S,X3:S) 7.48/7.65 a__U103(tt,V1:S,V2:S) -> a__U104(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U103(X1:S,X2:S,X3:S) -> U103(X1:S,X2:S,X3:S) 7.48/7.65 a__U104(tt,V1:S,V2:S) -> a__U105(a__isNat(V1:S),V2:S) 7.48/7.65 a__U104(X1:S,X2:S,X3:S) -> U104(X1:S,X2:S,X3:S) 7.48/7.65 a__U105(tt,V2:S) -> a__U106(a__isNatIList(V2:S)) 7.48/7.65 a__U105(X1:S,X2:S) -> U105(X1:S,X2:S) 7.48/7.65 a__U106(tt) -> tt 7.48/7.65 a__U106(X:S) -> U106(X:S) 7.48/7.65 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S) 7.48/7.65 a__U111(tt,L:S,N:S) -> a__U112(a__isNatIListKind(L:S),L:S,N:S) 7.48/7.65 a__U111(X1:S,X2:S,X3:S) -> U111(X1:S,X2:S,X3:S) 7.48/7.65 a__U112(tt,L:S,N:S) -> a__U113(a__isNat(N:S),L:S,N:S) 7.48/7.65 a__U112(X1:S,X2:S,X3:S) -> U112(X1:S,X2:S,X3:S) 7.48/7.65 a__U113(tt,L:S,N:S) -> a__U114(a__isNatKind(N:S),L:S) 7.48/7.65 a__U113(X1:S,X2:S,X3:S) -> U113(X1:S,X2:S,X3:S) 7.48/7.65 a__U114(tt,L:S) -> s(a__length(mark(L:S))) 7.48/7.65 a__U114(X1:S,X2:S) -> U114(X1:S,X2:S) 7.48/7.65 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S)) 7.48/7.65 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S) 7.48/7.65 a__U121(tt,IL:S) -> a__U122(a__isNatIListKind(IL:S)) 7.48/7.65 a__U121(X1:S,X2:S) -> U121(X1:S,X2:S) 7.48/7.65 a__U122(tt) -> nil 7.48/7.65 a__U122(X:S) -> U122(X:S) 7.48/7.65 a__U13(tt) -> tt 7.48/7.65 a__U13(X:S) -> U13(X:S) 7.48/7.65 a__U131(tt,IL:S,M:S,N:S) -> a__U132(a__isNatIListKind(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__U131(X1:S,X2:S,X3:S,X4:S) -> U131(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U132(tt,IL:S,M:S,N:S) -> a__U133(a__isNat(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U132(X1:S,X2:S,X3:S,X4:S) -> U132(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U133(tt,IL:S,M:S,N:S) -> a__U134(a__isNatKind(M:S),IL:S,M:S,N:S) 7.48/7.65 a__U133(X1:S,X2:S,X3:S,X4:S) -> U133(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U134(tt,IL:S,M:S,N:S) -> a__U135(a__isNat(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U134(X1:S,X2:S,X3:S,X4:S) -> U134(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U135(tt,IL:S,M:S,N:S) -> a__U136(a__isNatKind(N:S),IL:S,M:S,N:S) 7.48/7.65 a__U135(X1:S,X2:S,X3:S,X4:S) -> U135(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U136(tt,IL:S,M:S,N:S) -> cons(mark(N:S),take(M:S,IL:S)) 7.48/7.65 a__U136(X1:S,X2:S,X3:S,X4:S) -> U136(X1:S,X2:S,X3:S,X4:S) 7.48/7.65 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S) 7.48/7.65 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S)) 7.48/7.65 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S) 7.48/7.65 a__U23(tt) -> tt 7.48/7.65 a__U23(X:S) -> U23(X:S) 7.48/7.65 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S) 7.48/7.65 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S)) 7.48/7.65 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S) 7.48/7.65 a__U33(tt) -> tt 7.48/7.65 a__U33(X:S) -> U33(X:S) 7.48/7.65 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S) 7.48/7.65 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S) 7.48/7.65 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S) 7.48/7.65 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S) 7.48/7.65 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S) 7.48/7.65 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S)) 7.48/7.65 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S) 7.48/7.65 a__U46(tt) -> tt 7.48/7.65 a__U46(X:S) -> U46(X:S) 7.48/7.65 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S)) 7.48/7.65 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S) 7.48/7.65 a__U52(tt) -> tt 7.48/7.65 a__U52(X:S) -> U52(X:S) 7.48/7.65 a__U61(tt,V2:S) -> a__U62(a__isNatIListKind(V2:S)) 7.48/7.65 a__U61(X1:S,X2:S) -> U61(X1:S,X2:S) 7.48/7.65 a__U62(tt) -> tt 7.48/7.65 a__U62(X:S) -> U62(X:S) 7.48/7.65 a__U71(tt) -> tt 7.48/7.65 a__U71(X:S) -> U71(X:S) 7.48/7.65 a__U81(tt) -> tt 7.48/7.65 a__U81(X:S) -> U81(X:S) 7.48/7.65 a__U91(tt,V1:S,V2:S) -> a__U92(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S) 7.48/7.65 a__U92(tt,V1:S,V2:S) -> a__U93(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S) 7.48/7.65 a__U93(tt,V1:S,V2:S) -> a__U94(a__isNatIListKind(V2:S),V1:S,V2:S) 7.48/7.65 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S) 7.48/7.65 a__U94(tt,V1:S,V2:S) -> a__U95(a__isNat(V1:S),V2:S) 7.48/7.65 a__U94(X1:S,X2:S,X3:S) -> U94(X1:S,X2:S,X3:S) 7.48/7.65 a__U95(tt,V2:S) -> a__U96(a__isNatList(V2:S)) 7.48/7.65 a__U95(X1:S,X2:S) -> U95(X1:S,X2:S) 7.48/7.65 a__U96(tt) -> tt 7.48/7.65 a__U96(X:S) -> U96(X:S) 7.48/7.65 a__isNat(0) -> tt 7.48/7.65 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S) 7.48/7.65 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S) 7.48/7.65 a__isNat(X:S) -> isNat(X:S) 7.48/7.65 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatIList(zeros) -> tt 7.48/7.65 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S) 7.48/7.65 a__isNatIList(X:S) -> isNatIList(X:S) 7.48/7.65 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(nil) -> tt 7.48/7.65 a__isNatIListKind(take(V1:S,V2:S)) -> a__U61(a__isNatKind(V1:S),V2:S) 7.48/7.65 a__isNatIListKind(zeros) -> tt 7.48/7.65 a__isNatIListKind(X:S) -> isNatIListKind(X:S) 7.48/7.65 a__isNatKind(0) -> tt 7.48/7.65 a__isNatKind(length(V1:S)) -> a__U71(a__isNatIListKind(V1:S)) 7.48/7.65 a__isNatKind(s(V1:S)) -> a__U81(a__isNatKind(V1:S)) 7.48/7.65 a__isNatKind(X:S) -> isNatKind(X:S) 7.48/7.65 a__isNatList(cons(V1:S,V2:S)) -> a__U91(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(nil) -> tt 7.48/7.65 a__isNatList(take(V1:S,V2:S)) -> a__U101(a__isNatKind(V1:S),V1:S,V2:S) 7.48/7.65 a__isNatList(X:S) -> isNatList(X:S) 7.48/7.65 a__length(cons(N:S,L:S)) -> a__U111(a__isNatList(L:S),L:S,N:S) 7.48/7.65 a__length(nil) -> 0 7.48/7.65 a__length(X:S) -> length(X:S) 7.48/7.65 a__take(0,IL:S) -> a__U121(a__isNatIList(IL:S),IL:S) 7.48/7.65 a__take(s(M:S),cons(N:S,IL:S)) -> a__U131(a__isNatIList(IL:S),IL:S,M:S,N:S) 7.48/7.65 a__take(X1:S,X2:S) -> take(X1:S,X2:S) 7.48/7.65 a__zeros -> cons(0,zeros) 7.48/7.65 a__zeros -> zeros 7.48/7.65 mark(0) -> 0 7.48/7.65 mark(U101(X1:S,X2:S,X3:S)) -> a__U101(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U102(X1:S,X2:S,X3:S)) -> a__U102(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U103(X1:S,X2:S,X3:S)) -> a__U103(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U104(X1:S,X2:S,X3:S)) -> a__U104(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U105(X1:S,X2:S)) -> a__U105(mark(X1:S),X2:S) 7.48/7.65 mark(U106(X:S)) -> a__U106(mark(X:S)) 7.48/7.65 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S) 7.48/7.65 mark(U111(X1:S,X2:S,X3:S)) -> a__U111(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U112(X1:S,X2:S,X3:S)) -> a__U112(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U113(X1:S,X2:S,X3:S)) -> a__U113(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U114(X1:S,X2:S)) -> a__U114(mark(X1:S),X2:S) 7.48/7.65 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S) 7.48/7.65 mark(U121(X1:S,X2:S)) -> a__U121(mark(X1:S),X2:S) 7.48/7.65 mark(U122(X:S)) -> a__U122(mark(X:S)) 7.48/7.65 mark(U13(X:S)) -> a__U13(mark(X:S)) 7.48/7.65 mark(U131(X1:S,X2:S,X3:S,X4:S)) -> a__U131(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U132(X1:S,X2:S,X3:S,X4:S)) -> a__U132(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U133(X1:S,X2:S,X3:S,X4:S)) -> a__U133(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U134(X1:S,X2:S,X3:S,X4:S)) -> a__U134(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U135(X1:S,X2:S,X3:S,X4:S)) -> a__U135(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U136(X1:S,X2:S,X3:S,X4:S)) -> a__U136(mark(X1:S),X2:S,X3:S,X4:S) 7.48/7.65 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S) 7.48/7.65 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S) 7.48/7.65 mark(U23(X:S)) -> a__U23(mark(X:S)) 7.48/7.65 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S) 7.48/7.65 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S) 7.48/7.65 mark(U33(X:S)) -> a__U33(mark(X:S)) 7.48/7.65 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S) 7.48/7.65 mark(U46(X:S)) -> a__U46(mark(X:S)) 7.48/7.65 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S) 7.48/7.65 mark(U52(X:S)) -> a__U52(mark(X:S)) 7.48/7.65 mark(U61(X1:S,X2:S)) -> a__U61(mark(X1:S),X2:S) 7.48/7.65 mark(U62(X:S)) -> a__U62(mark(X:S)) 7.48/7.65 mark(U71(X:S)) -> a__U71(mark(X:S)) 7.48/7.65 mark(U81(X:S)) -> a__U81(mark(X:S)) 7.48/7.65 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U94(X1:S,X2:S,X3:S)) -> a__U94(mark(X1:S),X2:S,X3:S) 7.48/7.65 mark(U95(X1:S,X2:S)) -> a__U95(mark(X1:S),X2:S) 7.48/7.65 mark(U96(X:S)) -> a__U96(mark(X:S)) 7.48/7.65 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 7.48/7.65 mark(isNat(X:S)) -> a__isNat(X:S) 7.48/7.65 mark(isNatIList(X:S)) -> a__isNatIList(X:S) 7.48/7.65 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S) 7.48/7.65 mark(isNatKind(X:S)) -> a__isNatKind(X:S) 7.48/7.65 mark(isNatList(X:S)) -> a__isNatList(X:S) 7.48/7.65 mark(length(X:S)) -> a__length(mark(X:S)) 7.48/7.65 mark(nil) -> nil 7.48/7.65 mark(s(X:S)) -> s(mark(X:S)) 7.48/7.65 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S)) 7.48/7.65 mark(tt) -> tt 7.48/7.65 mark(zeros) -> a__zeros 7.48/7.65 ->Strongly Connected Components: 7.48/7.65 There is no strongly connected component 7.48/7.65 7.48/7.65 The problem is finite. 7.48/7.65 EOF