1.18/1.73	YES
1.18/1.73	
1.18/1.73	Problem 1: 
1.18/1.73	
1.18/1.73	(VAR v_NonEmpty:S L:S N:S V:S V1:S V2:S X:S X1:S X2:S X3:S)
1.18/1.73	(RULES
1.18/1.73	a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	a__U13(tt) -> tt
1.18/1.73	a__U13(X:S) -> U13(X:S)
1.18/1.73	a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	a__U23(tt) -> tt
1.18/1.73	a__U23(X:S) -> U23(X:S)
1.18/1.73	a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	a__U33(tt) -> tt
1.18/1.73	a__U33(X:S) -> U33(X:S)
1.18/1.73	a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	a__U46(tt) -> tt
1.18/1.73	a__U46(X:S) -> U46(X:S)
1.18/1.73	a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	a__U52(tt) -> tt
1.18/1.73	a__U52(X:S) -> U52(X:S)
1.18/1.73	a__U61(tt) -> tt
1.18/1.73	a__U61(X:S) -> U61(X:S)
1.18/1.73	a__U71(tt) -> tt
1.18/1.73	a__U71(X:S) -> U71(X:S)
1.18/1.73	a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	a__U86(tt) -> tt
1.18/1.73	a__U86(X:S) -> U86(X:S)
1.18/1.73	a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	a__isNat(0) -> tt
1.18/1.73	a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	a__isNat(X:S) -> isNat(X:S)
1.18/1.73	a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	a__isNatIList(zeros) -> tt
1.18/1.73	a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	a__isNatIListKind(nil) -> tt
1.18/1.73	a__isNatIListKind(zeros) -> tt
1.18/1.73	a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	a__isNatKind(0) -> tt
1.18/1.73	a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	a__isNatList(nil) -> tt
1.18/1.73	a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	a__length(nil) -> 0
1.18/1.73	a__length(X:S) -> length(X:S)
1.18/1.73	a__zeros -> cons(0,zeros)
1.18/1.73	a__zeros -> zeros
1.18/1.73	mark(0) -> 0
1.18/1.73	mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	mark(nil) -> nil
1.18/1.73	mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	mark(tt) -> tt
1.18/1.73	mark(zeros) -> a__zeros
1.18/1.73	) 
1.18/1.73	(STRATEGY INNERMOST)
1.18/1.73	
1.18/1.73	Problem 1: 
1.18/1.73	
1.18/1.73	Dependency Pairs Processor:
1.18/1.73	-> Pairs:
1.18/1.73	 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 A__U11(tt,V1:S) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__U12(tt,V1:S) -> A__U13(a__isNatList(V1:S))
1.18/1.73	 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S)
1.18/1.73	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 A__U21(tt,V1:S) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__U22(tt,V1:S) -> A__U23(a__isNat(V1:S))
1.18/1.73	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 A__U31(tt,V:S) -> A__ISNATILISTKIND(V:S)
1.18/1.73	 A__U32(tt,V:S) -> A__U33(a__isNatList(V:S))
1.18/1.73	 A__U32(tt,V:S) -> A__ISNATLIST(V:S)
1.18/1.73	 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__U41(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U42(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U43(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U45(tt,V2:S) -> A__U46(a__isNatIList(V2:S))
1.18/1.73	 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S)
1.18/1.73	 A__U51(tt,V2:S) -> A__U52(a__isNatIListKind(V2:S))
1.18/1.73	 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__U81(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U82(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U83(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 A__U84(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U85(tt,V2:S) -> A__U86(a__isNatList(V2:S))
1.18/1.73	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.73	 A__U91(tt,L:S,N:S) -> A__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 A__U91(tt,L:S,N:S) -> A__ISNATILISTKIND(L:S)
1.18/1.73	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 A__U92(tt,L:S,N:S) -> A__ISNAT(N:S)
1.18/1.73	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 A__U93(tt,L:S,N:S) -> A__ISNATKIND(N:S)
1.18/1.73	 A__U94(tt,L:S) -> A__LENGTH(mark(L:S))
1.18/1.73	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.73	 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 A__ISNAT(length(V1:S)) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 A__ISNAT(s(V1:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__ISNATILIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 A__ISNATILIST(V:S) -> A__ISNATILISTKIND(V:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATKIND(length(V1:S)) -> A__U61(a__isNatIListKind(V1:S))
1.18/1.73	 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__ISNATKIND(s(V1:S)) -> A__U71(a__isNatKind(V1:S))
1.18/1.73	 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__LENGTH(cons(N:S,L:S)) -> A__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 A__LENGTH(cons(N:S,L:S)) -> A__ISNATLIST(L:S)
1.18/1.73	 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S)
1.18/1.73	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U12(X1:S,X2:S)) -> A__U12(mark(X1:S),X2:S)
1.18/1.73	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U13(X:S)) -> A__U13(mark(X:S))
1.18/1.73	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S)
1.18/1.73	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S)
1.18/1.73	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U23(X:S)) -> A__U23(mark(X:S))
1.18/1.73	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S)
1.18/1.73	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U32(X1:S,X2:S)) -> A__U32(mark(X1:S),X2:S)
1.18/1.73	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U33(X:S)) -> A__U33(mark(X:S))
1.18/1.73	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U42(X1:S,X2:S,X3:S)) -> A__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U43(X1:S,X2:S,X3:S)) -> A__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U44(X1:S,X2:S,X3:S)) -> A__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U45(X1:S,X2:S)) -> A__U45(mark(X1:S),X2:S)
1.18/1.73	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U46(X:S)) -> A__U46(mark(X:S))
1.18/1.73	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U51(X1:S,X2:S)) -> A__U51(mark(X1:S),X2:S)
1.18/1.73	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U52(X:S)) -> A__U52(mark(X:S))
1.18/1.73	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U61(X:S)) -> A__U61(mark(X:S))
1.18/1.73	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U71(X:S)) -> A__U71(mark(X:S))
1.18/1.73	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U81(X1:S,X2:S,X3:S)) -> A__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U82(X1:S,X2:S,X3:S)) -> A__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U83(X1:S,X2:S,X3:S)) -> A__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U84(X1:S,X2:S,X3:S)) -> A__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U85(X1:S,X2:S)) -> A__U85(mark(X1:S),X2:S)
1.18/1.73	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U86(X:S)) -> A__U86(mark(X:S))
1.18/1.73	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.73	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(isNat(X:S)) -> A__ISNAT(X:S)
1.18/1.73	 MARK(isNatIList(X:S)) -> A__ISNATILIST(X:S)
1.18/1.73	 MARK(isNatIListKind(X:S)) -> A__ISNATILISTKIND(X:S)
1.18/1.73	 MARK(isNatKind(X:S)) -> A__ISNATKIND(X:S)
1.18/1.73	 MARK(isNatList(X:S)) -> A__ISNATLIST(X:S)
1.18/1.73	 MARK(length(X:S)) -> A__LENGTH(mark(X:S))
1.18/1.73	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(zeros) -> A__ZEROS
1.18/1.73	-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	 a__isNat(0) -> tt
1.18/1.73	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__isNat(X:S) -> isNat(X:S)
1.18/1.73	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatIList(zeros) -> tt
1.18/1.73	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 a__isNatIListKind(nil) -> tt
1.18/1.73	 a__isNatIListKind(zeros) -> tt
1.18/1.73	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	 a__isNatKind(0) -> tt
1.18/1.73	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatList(nil) -> tt
1.18/1.73	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 a__length(nil) -> 0
1.18/1.73	 a__length(X:S) -> length(X:S)
1.18/1.73	 a__zeros -> cons(0,zeros)
1.18/1.73	 a__zeros -> zeros
1.18/1.73	 mark(0) -> 0
1.18/1.73	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	 mark(nil) -> nil
1.18/1.73	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	 mark(tt) -> tt
1.18/1.73	 mark(zeros) -> a__zeros
1.18/1.73	
1.18/1.73	Problem 1: 
1.18/1.73	
1.18/1.73	SCC Processor:
1.18/1.73	-> Pairs:
1.18/1.73	 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 A__U11(tt,V1:S) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__U12(tt,V1:S) -> A__U13(a__isNatList(V1:S))
1.18/1.73	 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S)
1.18/1.73	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 A__U21(tt,V1:S) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__U22(tt,V1:S) -> A__U23(a__isNat(V1:S))
1.18/1.73	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U31(tt,V:S) -> A__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 A__U31(tt,V:S) -> A__ISNATILISTKIND(V:S)
1.18/1.73	 A__U32(tt,V:S) -> A__U33(a__isNatList(V:S))
1.18/1.73	 A__U32(tt,V:S) -> A__ISNATLIST(V:S)
1.18/1.73	 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__U41(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U42(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U43(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 A__U44(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U45(tt,V2:S) -> A__U46(a__isNatIList(V2:S))
1.18/1.73	 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S)
1.18/1.73	 A__U51(tt,V2:S) -> A__U52(a__isNatIListKind(V2:S))
1.18/1.73	 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__U81(tt,V1:S,V2:S) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U82(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U83(tt,V1:S,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 A__U84(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U85(tt,V2:S) -> A__U86(a__isNatList(V2:S))
1.18/1.73	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.73	 A__U91(tt,L:S,N:S) -> A__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 A__U91(tt,L:S,N:S) -> A__ISNATILISTKIND(L:S)
1.18/1.73	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 A__U92(tt,L:S,N:S) -> A__ISNAT(N:S)
1.18/1.73	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 A__U93(tt,L:S,N:S) -> A__ISNATKIND(N:S)
1.18/1.73	 A__U94(tt,L:S) -> A__LENGTH(mark(L:S))
1.18/1.73	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.73	 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 A__ISNAT(length(V1:S)) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 A__ISNAT(s(V1:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__ISNATILIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATILIST(V:S) -> A__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 A__ISNATILIST(V:S) -> A__ISNATILISTKIND(V:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATKIND(length(V1:S)) -> A__U61(a__isNatIListKind(V1:S))
1.18/1.73	 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__ISNATKIND(s(V1:S)) -> A__U71(a__isNatKind(V1:S))
1.18/1.73	 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__LENGTH(cons(N:S,L:S)) -> A__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 A__LENGTH(cons(N:S,L:S)) -> A__ISNATLIST(L:S)
1.18/1.73	 MARK(U11(X1:S,X2:S)) -> A__U11(mark(X1:S),X2:S)
1.18/1.73	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U12(X1:S,X2:S)) -> A__U12(mark(X1:S),X2:S)
1.18/1.73	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U13(X:S)) -> A__U13(mark(X:S))
1.18/1.73	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U21(X1:S,X2:S)) -> A__U21(mark(X1:S),X2:S)
1.18/1.73	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U22(X1:S,X2:S)) -> A__U22(mark(X1:S),X2:S)
1.18/1.73	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U23(X:S)) -> A__U23(mark(X:S))
1.18/1.73	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U31(X1:S,X2:S)) -> A__U31(mark(X1:S),X2:S)
1.18/1.73	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U32(X1:S,X2:S)) -> A__U32(mark(X1:S),X2:S)
1.18/1.73	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U33(X:S)) -> A__U33(mark(X:S))
1.18/1.73	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U41(X1:S,X2:S,X3:S)) -> A__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U42(X1:S,X2:S,X3:S)) -> A__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U43(X1:S,X2:S,X3:S)) -> A__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U44(X1:S,X2:S,X3:S)) -> A__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U45(X1:S,X2:S)) -> A__U45(mark(X1:S),X2:S)
1.18/1.73	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U46(X:S)) -> A__U46(mark(X:S))
1.18/1.73	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U51(X1:S,X2:S)) -> A__U51(mark(X1:S),X2:S)
1.18/1.73	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U52(X:S)) -> A__U52(mark(X:S))
1.18/1.73	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U61(X:S)) -> A__U61(mark(X:S))
1.18/1.73	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U71(X:S)) -> A__U71(mark(X:S))
1.18/1.73	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U81(X1:S,X2:S,X3:S)) -> A__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U82(X1:S,X2:S,X3:S)) -> A__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U83(X1:S,X2:S,X3:S)) -> A__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U84(X1:S,X2:S,X3:S)) -> A__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U85(X1:S,X2:S)) -> A__U85(mark(X1:S),X2:S)
1.18/1.73	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U86(X:S)) -> A__U86(mark(X:S))
1.18/1.73	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.73	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(isNat(X:S)) -> A__ISNAT(X:S)
1.18/1.73	 MARK(isNatIList(X:S)) -> A__ISNATILIST(X:S)
1.18/1.73	 MARK(isNatIListKind(X:S)) -> A__ISNATILISTKIND(X:S)
1.18/1.73	 MARK(isNatKind(X:S)) -> A__ISNATKIND(X:S)
1.18/1.73	 MARK(isNatList(X:S)) -> A__ISNATLIST(X:S)
1.18/1.73	 MARK(length(X:S)) -> A__LENGTH(mark(X:S))
1.18/1.73	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(zeros) -> A__ZEROS
1.18/1.73	-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	 a__isNat(0) -> tt
1.18/1.73	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__isNat(X:S) -> isNat(X:S)
1.18/1.73	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatIList(zeros) -> tt
1.18/1.73	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 a__isNatIListKind(nil) -> tt
1.18/1.73	 a__isNatIListKind(zeros) -> tt
1.18/1.73	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	 a__isNatKind(0) -> tt
1.18/1.73	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatList(nil) -> tt
1.18/1.73	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 a__length(nil) -> 0
1.18/1.73	 a__length(X:S) -> length(X:S)
1.18/1.73	 a__zeros -> cons(0,zeros)
1.18/1.73	 a__zeros -> zeros
1.18/1.73	 mark(0) -> 0
1.18/1.73	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	 mark(nil) -> nil
1.18/1.73	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	 mark(tt) -> tt
1.18/1.73	 mark(zeros) -> a__zeros
1.18/1.73	->Strongly Connected Components:
1.18/1.73	->->Cycle:
1.18/1.73	->->-> Pairs:
1.18/1.73	 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	->->-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	 a__isNat(0) -> tt
1.18/1.73	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__isNat(X:S) -> isNat(X:S)
1.18/1.73	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatIList(zeros) -> tt
1.18/1.73	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 a__isNatIListKind(nil) -> tt
1.18/1.73	 a__isNatIListKind(zeros) -> tt
1.18/1.73	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	 a__isNatKind(0) -> tt
1.18/1.73	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatList(nil) -> tt
1.18/1.73	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 a__length(nil) -> 0
1.18/1.73	 a__length(X:S) -> length(X:S)
1.18/1.73	 a__zeros -> cons(0,zeros)
1.18/1.73	 a__zeros -> zeros
1.18/1.73	 mark(0) -> 0
1.18/1.73	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	 mark(nil) -> nil
1.18/1.73	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	 mark(tt) -> tt
1.18/1.73	 mark(zeros) -> a__zeros
1.18/1.73	->->Cycle:
1.18/1.73	->->-> Pairs:
1.18/1.73	 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S)
1.18/1.73	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 A__U84(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.73	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.73	 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	->->-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	 a__isNat(0) -> tt
1.18/1.73	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__isNat(X:S) -> isNat(X:S)
1.18/1.73	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatIList(zeros) -> tt
1.18/1.73	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 a__isNatIListKind(nil) -> tt
1.18/1.73	 a__isNatIListKind(zeros) -> tt
1.18/1.73	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	 a__isNatKind(0) -> tt
1.18/1.73	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatList(nil) -> tt
1.18/1.73	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 a__length(nil) -> 0
1.18/1.73	 a__length(X:S) -> length(X:S)
1.18/1.73	 a__zeros -> cons(0,zeros)
1.18/1.73	 a__zeros -> zeros
1.18/1.73	 mark(0) -> 0
1.18/1.73	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	 mark(nil) -> nil
1.18/1.73	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	 mark(tt) -> tt
1.18/1.73	 mark(zeros) -> a__zeros
1.18/1.73	->->Cycle:
1.18/1.73	->->-> Pairs:
1.18/1.73	 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S)
1.18/1.73	 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	->->-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	 a__isNat(0) -> tt
1.18/1.73	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__isNat(X:S) -> isNat(X:S)
1.18/1.73	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatIList(zeros) -> tt
1.18/1.73	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 a__isNatIListKind(nil) -> tt
1.18/1.73	 a__isNatIListKind(zeros) -> tt
1.18/1.73	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	 a__isNatKind(0) -> tt
1.18/1.73	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatList(nil) -> tt
1.18/1.73	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 a__length(nil) -> 0
1.18/1.73	 a__length(X:S) -> length(X:S)
1.18/1.73	 a__zeros -> cons(0,zeros)
1.18/1.73	 a__zeros -> zeros
1.18/1.73	 mark(0) -> 0
1.18/1.73	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	 mark(nil) -> nil
1.18/1.73	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	 mark(tt) -> tt
1.18/1.73	 mark(zeros) -> a__zeros
1.18/1.73	->->Cycle:
1.18/1.73	->->-> Pairs:
1.18/1.73	 A__U91(tt,L:S,N:S) -> A__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 A__U94(tt,L:S) -> A__LENGTH(mark(L:S))
1.18/1.73	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.73	 A__LENGTH(cons(N:S,L:S)) -> A__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.73	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.73	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.73	 MARK(length(X:S)) -> A__LENGTH(mark(X:S))
1.18/1.73	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.73	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.73	->->-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.73	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.73	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.73	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.73	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.73	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.73	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.73	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.73	 a__isNat(0) -> tt
1.18/1.73	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__isNat(X:S) -> isNat(X:S)
1.18/1.73	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatIList(zeros) -> tt
1.18/1.73	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.73	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 a__isNatIListKind(nil) -> tt
1.18/1.73	 a__isNatIListKind(zeros) -> tt
1.18/1.73	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.73	 a__isNatKind(0) -> tt
1.18/1.73	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.73	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.73	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.73	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__isNatList(nil) -> tt
1.18/1.73	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.73	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.73	 a__length(nil) -> 0
1.18/1.73	 a__length(X:S) -> length(X:S)
1.18/1.73	 a__zeros -> cons(0,zeros)
1.18/1.73	 a__zeros -> zeros
1.18/1.73	 mark(0) -> 0
1.18/1.73	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.73	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.73	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.73	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.73	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.73	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.73	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.73	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.73	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.73	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.73	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.73	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.73	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.73	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.73	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.73	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.73	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.73	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.73	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.73	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.73	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.73	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.73	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.73	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.73	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.73	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.73	 mark(nil) -> nil
1.18/1.73	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.73	 mark(tt) -> tt
1.18/1.73	 mark(zeros) -> a__zeros
1.18/1.73	
1.18/1.73	
1.18/1.73	The problem is decomposed in 4 subproblems.
1.18/1.73	
1.18/1.73	Problem 1.1: 
1.18/1.73	
1.18/1.73	Subterm Processor:
1.18/1.73	-> Pairs:
1.18/1.73	 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__U51(a__isNatKind(V1:S),V2:S)
1.18/1.73	 A__ISNATILISTKIND(cons(V1:S,V2:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	 A__ISNATKIND(length(V1:S)) -> A__ISNATILISTKIND(V1:S)
1.18/1.73	 A__ISNATKIND(s(V1:S)) -> A__ISNATKIND(V1:S)
1.18/1.73	-> Rules:
1.18/1.73	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.73	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.73	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.73	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.73	 a__U13(tt) -> tt
1.18/1.73	 a__U13(X:S) -> U13(X:S)
1.18/1.73	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.73	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.73	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.73	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.73	 a__U23(tt) -> tt
1.18/1.73	 a__U23(X:S) -> U23(X:S)
1.18/1.73	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.73	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.73	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.73	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.73	 a__U33(tt) -> tt
1.18/1.73	 a__U33(X:S) -> U33(X:S)
1.18/1.73	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.73	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.73	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.73	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.73	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.73	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.73	 a__U46(tt) -> tt
1.18/1.73	 a__U46(X:S) -> U46(X:S)
1.18/1.73	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.73	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.73	 a__U52(tt) -> tt
1.18/1.73	 a__U52(X:S) -> U52(X:S)
1.18/1.73	 a__U61(tt) -> tt
1.18/1.73	 a__U61(X:S) -> U61(X:S)
1.18/1.73	 a__U71(tt) -> tt
1.18/1.73	 a__U71(X:S) -> U71(X:S)
1.18/1.73	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.73	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.73	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.73	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.73	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.73	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.73	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.73	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.73	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.73	 a__U86(tt) -> tt
1.18/1.73	 a__U86(X:S) -> U86(X:S)
1.18/1.73	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Projection:
1.18/1.74	 pi(A__U51) = 2
1.18/1.74	 pi(A__ISNATILISTKIND) = 1
1.18/1.74	 pi(A__ISNATKIND) = 1
1.18/1.74	
1.18/1.74	Problem 1.1: 
1.18/1.74	
1.18/1.74	SCC Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U51(tt,V2:S) -> A__ISNATILISTKIND(V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Strongly Connected Components:
1.18/1.74	 There is no strongly connected component
1.18/1.74	
1.18/1.74	The problem is finite.
1.18/1.74	
1.18/1.74	Problem 1.2: 
1.18/1.74	
1.18/1.74	Reduction Pairs Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U11(tt,V1:S) -> A__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S)
1.18/1.74	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.74	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.74	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.74	 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	-> Usable rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	->Interpretation type:
1.18/1.74	 Linear
1.18/1.74	->Coefficients:
1.18/1.74	 Natural Numbers
1.18/1.74	->Dimension:
1.18/1.74	 1
1.18/1.74	->Bound:
1.18/1.74	 2
1.18/1.74	->Interpretation:
1.18/1.74	 
1.18/1.74	[a__U11](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.74	[a__U12](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.74	[a__U13](X) = X + 2
1.18/1.74	[a__U21](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.74	[a__U22](X1,X2) = 2.X2 + 2
1.18/1.74	[a__U23](X) = 2
1.18/1.74	[a__U31](X1,X2) = 0
1.18/1.74	[a__U32](X1,X2) = 0
1.18/1.74	[a__U33](X) = 0
1.18/1.74	[a__U41](X1,X2,X3) = 0
1.18/1.74	[a__U42](X1,X2,X3) = 0
1.18/1.74	[a__U43](X1,X2,X3) = 0
1.18/1.74	[a__U44](X1,X2,X3) = 0
1.18/1.74	[a__U45](X1,X2) = 0
1.18/1.74	[a__U46](X) = 0
1.18/1.74	[a__U51](X1,X2) = X1
1.18/1.74	[a__U52](X) = 2
1.18/1.74	[a__U61](X) = 2
1.18/1.74	[a__U71](X) = 2
1.18/1.74	[a__U81](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[a__U82](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
1.18/1.74	[a__U83](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[a__U84](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[a__U85](X1,X2) = X1 + 2.X2
1.18/1.74	[a__U86](X) = X
1.18/1.74	[a__U91](X1,X2,X3) = 0
1.18/1.74	[a__U92](X1,X2,X3) = 0
1.18/1.74	[a__U93](X1,X2,X3) = 0
1.18/1.74	[a__U94](X1,X2) = 0
1.18/1.74	[a__isNat](X) = 2.X + 2
1.18/1.74	[a__isNatIList](X) = 0
1.18/1.74	[a__isNatIListKind](X) = 2
1.18/1.74	[a__isNatKind](X) = 2
1.18/1.74	[a__isNatList](X) = 2.X + 2
1.18/1.74	[a__length](X) = 0
1.18/1.74	[a__zeros] = 0
1.18/1.74	[mark](X) = 0
1.18/1.74	[0] = 2
1.18/1.74	[U11](X1,X2) = X1 + 2.X2 + 2
1.18/1.74	[U12](X1,X2) = 2.X1 + 2
1.18/1.74	[U13](X) = 2
1.18/1.74	[U21](X1,X2) = X1 + 2
1.18/1.74	[U22](X1,X2) = 2.X2 + 2
1.18/1.74	[U23](X) = 2
1.18/1.74	[U31](X1,X2) = 0
1.18/1.74	[U32](X1,X2) = 0
1.18/1.74	[U33](X) = 0
1.18/1.74	[U41](X1,X2,X3) = 0
1.18/1.74	[U42](X1,X2,X3) = 0
1.18/1.74	[U43](X1,X2,X3) = 0
1.18/1.74	[U44](X1,X2,X3) = 0
1.18/1.74	[U45](X1,X2) = 0
1.18/1.74	[U46](X) = 0
1.18/1.74	[U51](X1,X2) = X1
1.18/1.74	[U52](X) = 2
1.18/1.74	[U61](X) = 1
1.18/1.74	[U71](X) = 1
1.18/1.74	[U81](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[U82](X1,X2,X3) = 2.X1 + X2 + X3 + 1
1.18/1.74	[U83](X1,X2,X3) = X1 + X2 + X3 + 1
1.18/1.74	[U84](X1,X2,X3) = X1 + 2.X2 + X3 + 1
1.18/1.74	[U85](X1,X2) = X1 + X2
1.18/1.74	[U86](X) = 0
1.18/1.74	[U91](X1,X2,X3) = 0
1.18/1.74	[U92](X1,X2,X3) = 0
1.18/1.74	[U93](X1,X2,X3) = 0
1.18/1.74	[U94](X1,X2) = 0
1.18/1.74	[cons](X1,X2) = X1 + X2 + 2
1.18/1.74	[fSNonEmpty] = 0
1.18/1.74	[isNat](X) = 2.X
1.18/1.74	[isNatIList](X) = 0
1.18/1.74	[isNatIListKind](X) = 2
1.18/1.74	[isNatKind](X) = 1
1.18/1.74	[isNatList](X) = 2.X + 2
1.18/1.74	[length](X) = 2.X + 2
1.18/1.74	[nil] = 2
1.18/1.74	[s](X) = 2.X + 2
1.18/1.74	[tt] = 2
1.18/1.74	[zeros] = 2
1.18/1.74	[A__U11](X1,X2) = 2.X1 + 2.X2 + 2
1.18/1.74	[A__U12](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.74	[A__U13](X) = 0
1.18/1.74	[A__U21](X1,X2) = X1 + 2.X2 + 2
1.18/1.74	[A__U22](X1,X2) = X1 + 2.X2 + 2
1.18/1.74	[A__U23](X) = 0
1.18/1.74	[A__U31](X1,X2) = 0
1.18/1.74	[A__U32](X1,X2) = 0
1.18/1.74	[A__U33](X) = 0
1.18/1.74	[A__U41](X1,X2,X3) = 0
1.18/1.74	[A__U42](X1,X2,X3) = 0
1.18/1.74	[A__U43](X1,X2,X3) = 0
1.18/1.74	[A__U44](X1,X2,X3) = 0
1.18/1.74	[A__U45](X1,X2) = 0
1.18/1.74	[A__U46](X) = 0
1.18/1.74	[A__U51](X1,X2) = 0
1.18/1.74	[A__U52](X) = 0
1.18/1.74	[A__U61](X) = 0
1.18/1.74	[A__U71](X) = 0
1.18/1.74	[A__U81](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[A__U82](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[A__U83](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[A__U84](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.74	[A__U85](X1,X2) = X1 + 2.X2 + 2
1.18/1.74	[A__U86](X) = 0
1.18/1.74	[A__U91](X1,X2,X3) = 0
1.18/1.74	[A__U92](X1,X2,X3) = 0
1.18/1.74	[A__U93](X1,X2,X3) = 0
1.18/1.74	[A__U94](X1,X2) = 0
1.18/1.74	[A__ISNAT](X) = 2.X + 2
1.18/1.74	[A__ISNATILIST](X) = 0
1.18/1.74	[A__ISNATILISTKIND](X) = 0
1.18/1.74	[A__ISNATKIND](X) = 0
1.18/1.74	[A__ISNATLIST](X) = 2.X + 2
1.18/1.74	[A__LENGTH](X) = 0
1.18/1.74	[A__ZEROS] = 0
1.18/1.74	[MARK](X) = 0
1.18/1.74	
1.18/1.74	Problem 1.2: 
1.18/1.74	
1.18/1.74	SCC Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U12(tt,V1:S) -> A__ISNATLIST(V1:S)
1.18/1.74	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.74	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__ISNAT(V1:S)
1.18/1.74	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.74	 A__ISNAT(length(V1:S)) -> A__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Strongly Connected Components:
1.18/1.74	->->Cycle:
1.18/1.74	->->-> Pairs:
1.18/1.74	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.74	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	->->-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->->Cycle:
1.18/1.74	->->-> Pairs:
1.18/1.74	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.74	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	->->-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	
1.18/1.74	
1.18/1.74	The problem is decomposed in 2 subproblems.
1.18/1.74	
1.18/1.74	Problem 1.2.1: 
1.18/1.74	
1.18/1.74	Subterm Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.74	 A__ISNAT(s(V1:S)) -> A__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Projection:
1.18/1.74	 pi(A__U21) = 2
1.18/1.74	 pi(A__U22) = 2
1.18/1.74	 pi(A__ISNAT) = 1
1.18/1.74	
1.18/1.74	Problem 1.2.1: 
1.18/1.74	
1.18/1.74	SCC Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U21(tt,V1:S) -> A__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 A__U22(tt,V1:S) -> A__ISNAT(V1:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Strongly Connected Components:
1.18/1.74	 There is no strongly connected component
1.18/1.74	
1.18/1.74	The problem is finite.
1.18/1.74	
1.18/1.74	Problem 1.2.2: 
1.18/1.74	
1.18/1.74	Subterm Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.74	 A__ISNATLIST(cons(V1:S,V2:S)) -> A__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Projection:
1.18/1.74	 pi(A__U81) = 3
1.18/1.74	 pi(A__U82) = 3
1.18/1.74	 pi(A__U83) = 3
1.18/1.74	 pi(A__U84) = 3
1.18/1.74	 pi(A__U85) = 2
1.18/1.74	 pi(A__ISNATLIST) = 1
1.18/1.74	
1.18/1.74	Problem 1.2.2: 
1.18/1.74	
1.18/1.74	SCC Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U81(tt,V1:S,V2:S) -> A__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U82(tt,V1:S,V2:S) -> A__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U83(tt,V1:S,V2:S) -> A__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U84(tt,V1:S,V2:S) -> A__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U85(tt,V2:S) -> A__ISNATLIST(V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Strongly Connected Components:
1.18/1.74	 There is no strongly connected component
1.18/1.74	
1.18/1.74	The problem is finite.
1.18/1.74	
1.18/1.74	Problem 1.3: 
1.18/1.74	
1.18/1.74	Subterm Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S)
1.18/1.74	 A__ISNATILIST(cons(V1:S,V2:S)) -> A__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Projection:
1.18/1.74	 pi(A__U41) = 3
1.18/1.74	 pi(A__U42) = 3
1.18/1.74	 pi(A__U43) = 3
1.18/1.74	 pi(A__U44) = 3
1.18/1.74	 pi(A__U45) = 2
1.18/1.74	 pi(A__ISNATILIST) = 1
1.18/1.74	
1.18/1.74	Problem 1.3: 
1.18/1.74	
1.18/1.74	SCC Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U41(tt,V1:S,V2:S) -> A__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 A__U42(tt,V1:S,V2:S) -> A__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U43(tt,V1:S,V2:S) -> A__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 A__U44(tt,V1:S,V2:S) -> A__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 A__U45(tt,V2:S) -> A__ISNATILIST(V2:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	->Strongly Connected Components:
1.18/1.74	 There is no strongly connected component
1.18/1.74	
1.18/1.74	The problem is finite.
1.18/1.74	
1.18/1.74	Problem 1.4: 
1.18/1.74	
1.18/1.74	Reduction Pairs Processor:
1.18/1.74	-> Pairs:
1.18/1.74	 A__U91(tt,L:S,N:S) -> A__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 A__U94(tt,L:S) -> A__LENGTH(mark(L:S))
1.18/1.74	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.74	 A__LENGTH(cons(N:S,L:S)) -> A__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.74	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.74	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.74	 MARK(length(X:S)) -> A__LENGTH(mark(X:S))
1.18/1.74	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.74	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.74	-> Rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.74	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.74	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.74	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.74	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.74	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.74	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.74	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.74	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.74	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.74	 mark(nil) -> nil
1.18/1.74	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.74	 mark(tt) -> tt
1.18/1.74	 mark(zeros) -> a__zeros
1.18/1.74	-> Usable rules:
1.18/1.74	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.74	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.74	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.74	 a__U13(tt) -> tt
1.18/1.74	 a__U13(X:S) -> U13(X:S)
1.18/1.74	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.74	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.74	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.74	 a__U23(tt) -> tt
1.18/1.74	 a__U23(X:S) -> U23(X:S)
1.18/1.74	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.74	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.74	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.74	 a__U33(tt) -> tt
1.18/1.74	 a__U33(X:S) -> U33(X:S)
1.18/1.74	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.74	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.74	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.74	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.74	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.74	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.74	 a__U46(tt) -> tt
1.18/1.74	 a__U46(X:S) -> U46(X:S)
1.18/1.74	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.74	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.74	 a__U52(tt) -> tt
1.18/1.74	 a__U52(X:S) -> U52(X:S)
1.18/1.74	 a__U61(tt) -> tt
1.18/1.74	 a__U61(X:S) -> U61(X:S)
1.18/1.74	 a__U71(tt) -> tt
1.18/1.74	 a__U71(X:S) -> U71(X:S)
1.18/1.74	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.74	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.74	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.74	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.74	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.74	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.74	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.74	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.74	 a__U86(tt) -> tt
1.18/1.74	 a__U86(X:S) -> U86(X:S)
1.18/1.74	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.74	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.74	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.74	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.74	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.74	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.74	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.74	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.74	 a__isNat(0) -> tt
1.18/1.74	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.74	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.74	 a__isNat(X:S) -> isNat(X:S)
1.18/1.74	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatIList(zeros) -> tt
1.18/1.74	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.74	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.74	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.74	 a__isNatIListKind(nil) -> tt
1.18/1.74	 a__isNatIListKind(zeros) -> tt
1.18/1.74	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.74	 a__isNatKind(0) -> tt
1.18/1.74	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.74	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.74	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.74	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.74	 a__isNatList(nil) -> tt
1.18/1.74	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.74	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.74	 a__length(nil) -> 0
1.18/1.74	 a__length(X:S) -> length(X:S)
1.18/1.74	 a__zeros -> cons(0,zeros)
1.18/1.74	 a__zeros -> zeros
1.18/1.74	 mark(0) -> 0
1.18/1.74	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.74	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.74	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.74	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.74	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.74	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.74	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.74	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.74	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.74	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.74	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.74	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.74	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.74	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.74	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.74	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.74	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.75	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.75	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.75	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.75	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.75	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.75	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.75	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.75	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.75	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.75	 mark(nil) -> nil
1.18/1.75	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.75	 mark(tt) -> tt
1.18/1.75	 mark(zeros) -> a__zeros
1.18/1.75	->Interpretation type:
1.18/1.75	 Linear
1.18/1.75	->Coefficients:
1.18/1.75	 Natural Numbers
1.18/1.75	->Dimension:
1.18/1.75	 1
1.18/1.75	->Bound:
1.18/1.75	 2
1.18/1.75	->Interpretation:
1.18/1.75	 
1.18/1.75	[a__U11](X1,X2) = X1 + X2 + 2
1.18/1.75	[a__U12](X1,X2) = X1 + X2 + 2
1.18/1.75	[a__U13](X) = X + 2
1.18/1.75	[a__U21](X1,X2) = X1 + X2
1.18/1.75	[a__U22](X1,X2) = X1 + X2
1.18/1.75	[a__U23](X) = X
1.18/1.75	[a__U31](X1,X2) = X1 + 2.X2
1.18/1.75	[a__U32](X1,X2) = X1 + 2.X2
1.18/1.75	[a__U33](X) = X + 2
1.18/1.75	[a__U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[a__U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[a__U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[a__U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[a__U45](X1,X2) = X1 + 2.X2 + 2
1.18/1.75	[a__U46](X) = X + 2
1.18/1.75	[a__U51](X1,X2) = X1
1.18/1.75	[a__U52](X) = X
1.18/1.75	[a__U61](X) = X
1.18/1.75	[a__U71](X) = X
1.18/1.75	[a__U81](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[a__U82](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[a__U83](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[a__U84](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[a__U85](X1,X2) = X1 + 2.X2
1.18/1.75	[a__U86](X) = X
1.18/1.75	[a__U91](X1,X2,X3) = X1 + X2 + X3 + 2
1.18/1.75	[a__U92](X1,X2,X3) = X1 + X2 + X3 + 2
1.18/1.75	[a__U93](X1,X2,X3) = X1 + X2 + 2
1.18/1.75	[a__U94](X1,X2) = X1 + X2 + 2
1.18/1.75	[a__isNat](X) = X + 2
1.18/1.75	[a__isNatIList](X) = 2.X + 2
1.18/1.75	[a__isNatIListKind](X) = 2
1.18/1.75	[a__isNatKind](X) = 2
1.18/1.75	[a__isNatList](X) = X
1.18/1.75	[a__length](X) = X + 2
1.18/1.75	[a__zeros] = 2
1.18/1.75	[mark](X) = X + 2
1.18/1.75	[0] = 0
1.18/1.75	[U11](X1,X2) = X1 + X2 + 2
1.18/1.75	[U12](X1,X2) = X1 + X2 + 2
1.18/1.75	[U13](X) = X + 2
1.18/1.75	[U21](X1,X2) = X1 + X2
1.18/1.75	[U22](X1,X2) = X1 + X2
1.18/1.75	[U23](X) = X
1.18/1.75	[U31](X1,X2) = X1 + 2.X2
1.18/1.75	[U32](X1,X2) = X1 + 2.X2
1.18/1.75	[U33](X) = X + 2
1.18/1.75	[U41](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[U42](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[U43](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[U44](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[U45](X1,X2) = X1 + 2.X2 + 2
1.18/1.75	[U46](X) = X + 2
1.18/1.75	[U51](X1,X2) = X1
1.18/1.75	[U52](X) = X
1.18/1.75	[U61](X) = X
1.18/1.75	[U71](X) = X
1.18/1.75	[U81](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[U82](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[U83](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[U84](X1,X2,X3) = X1 + X2 + 2.X3
1.18/1.75	[U85](X1,X2) = X1 + 2.X2
1.18/1.75	[U86](X) = X
1.18/1.75	[U91](X1,X2,X3) = X1 + X2 + X3 + 2
1.18/1.75	[U92](X1,X2,X3) = X1 + X2 + X3 + 2
1.18/1.75	[U93](X1,X2,X3) = X1 + X2 + 2
1.18/1.75	[U94](X1,X2) = X1 + X2 + 2
1.18/1.75	[cons](X1,X2) = X1 + 2.X2 + 2
1.18/1.75	[fSNonEmpty] = 0
1.18/1.75	[isNat](X) = X + 1
1.18/1.75	[isNatIList](X) = 2.X + 2
1.18/1.75	[isNatIListKind](X) = 2
1.18/1.75	[isNatKind](X) = 2
1.18/1.75	[isNatList](X) = X
1.18/1.75	[length](X) = X + 2
1.18/1.75	[nil] = 2
1.18/1.75	[s](X) = X
1.18/1.75	[tt] = 2
1.18/1.75	[zeros] = 0
1.18/1.75	[A__U11](X1,X2) = 0
1.18/1.75	[A__U12](X1,X2) = 0
1.18/1.75	[A__U13](X) = 0
1.18/1.75	[A__U21](X1,X2) = 0
1.18/1.75	[A__U22](X1,X2) = 0
1.18/1.75	[A__U23](X) = 0
1.18/1.75	[A__U31](X1,X2) = 0
1.18/1.75	[A__U32](X1,X2) = 0
1.18/1.75	[A__U33](X) = 0
1.18/1.75	[A__U41](X1,X2,X3) = 0
1.18/1.75	[A__U42](X1,X2,X3) = 0
1.18/1.75	[A__U43](X1,X2,X3) = 0
1.18/1.75	[A__U44](X1,X2,X3) = 0
1.18/1.75	[A__U45](X1,X2) = 0
1.18/1.75	[A__U46](X) = 0
1.18/1.75	[A__U51](X1,X2) = 0
1.18/1.75	[A__U52](X) = 0
1.18/1.75	[A__U61](X) = 0
1.18/1.75	[A__U71](X) = 0
1.18/1.75	[A__U81](X1,X2,X3) = 0
1.18/1.75	[A__U82](X1,X2,X3) = 0
1.18/1.75	[A__U83](X1,X2,X3) = 0
1.18/1.75	[A__U84](X1,X2,X3) = 0
1.18/1.75	[A__U85](X1,X2) = 0
1.18/1.75	[A__U86](X) = 0
1.18/1.75	[A__U91](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
1.18/1.75	[A__U92](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
1.18/1.75	[A__U93](X1,X2,X3) = 2.X1 + 2.X2 + 1
1.18/1.75	[A__U94](X1,X2) = 2.X1 + 2.X2 + 1
1.18/1.75	[A__ISNAT](X) = 0
1.18/1.75	[A__ISNATILIST](X) = 0
1.18/1.75	[A__ISNATILISTKIND](X) = 0
1.18/1.75	[A__ISNATKIND](X) = 0
1.18/1.75	[A__ISNATLIST](X) = 0
1.18/1.75	[A__LENGTH](X) = 2.X + 1
1.18/1.75	[A__ZEROS] = 0
1.18/1.75	[MARK](X) = 2.X + 2
1.18/1.75	
1.18/1.75	Problem 1.4: 
1.18/1.75	
1.18/1.75	SCC Processor:
1.18/1.75	-> Pairs:
1.18/1.75	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 A__U94(tt,L:S) -> A__LENGTH(mark(L:S))
1.18/1.75	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.75	 A__LENGTH(cons(N:S,L:S)) -> A__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.75	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U91(X1:S,X2:S,X3:S)) -> A__U91(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.75	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(length(X:S)) -> A__LENGTH(mark(X:S))
1.18/1.75	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.75	-> Rules:
1.18/1.75	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.75	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.75	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.75	 a__U13(tt) -> tt
1.18/1.75	 a__U13(X:S) -> U13(X:S)
1.18/1.75	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.75	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.75	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.75	 a__U23(tt) -> tt
1.18/1.75	 a__U23(X:S) -> U23(X:S)
1.18/1.75	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.75	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.75	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.75	 a__U33(tt) -> tt
1.18/1.75	 a__U33(X:S) -> U33(X:S)
1.18/1.75	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.75	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.75	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.75	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.75	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.75	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.75	 a__U46(tt) -> tt
1.18/1.75	 a__U46(X:S) -> U46(X:S)
1.18/1.75	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.75	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.75	 a__U52(tt) -> tt
1.18/1.75	 a__U52(X:S) -> U52(X:S)
1.18/1.75	 a__U61(tt) -> tt
1.18/1.75	 a__U61(X:S) -> U61(X:S)
1.18/1.75	 a__U71(tt) -> tt
1.18/1.75	 a__U71(X:S) -> U71(X:S)
1.18/1.75	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.75	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.75	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.75	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.75	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.75	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.75	 a__U86(tt) -> tt
1.18/1.75	 a__U86(X:S) -> U86(X:S)
1.18/1.75	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.75	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.75	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.75	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.75	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.75	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.75	 a__isNat(0) -> tt
1.18/1.75	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__isNat(X:S) -> isNat(X:S)
1.18/1.75	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatIList(zeros) -> tt
1.18/1.75	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.75	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.75	 a__isNatIListKind(nil) -> tt
1.18/1.75	 a__isNatIListKind(zeros) -> tt
1.18/1.75	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.75	 a__isNatKind(0) -> tt
1.18/1.75	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.75	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.75	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.75	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatList(nil) -> tt
1.18/1.75	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.75	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.75	 a__length(nil) -> 0
1.18/1.75	 a__length(X:S) -> length(X:S)
1.18/1.75	 a__zeros -> cons(0,zeros)
1.18/1.75	 a__zeros -> zeros
1.18/1.75	 mark(0) -> 0
1.18/1.75	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.75	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.75	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.75	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.75	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.75	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.75	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.75	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.75	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.75	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.75	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.75	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.75	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.75	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.75	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.75	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.75	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.75	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.75	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.75	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.75	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.75	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.75	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.75	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.75	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.75	 mark(nil) -> nil
1.18/1.75	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.75	 mark(tt) -> tt
1.18/1.75	 mark(zeros) -> a__zeros
1.18/1.75	->Strongly Connected Components:
1.18/1.75	->->Cycle:
1.18/1.75	->->-> Pairs:
1.18/1.75	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.75	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.75	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.75	->->-> Rules:
1.18/1.75	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.75	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.75	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.75	 a__U13(tt) -> tt
1.18/1.75	 a__U13(X:S) -> U13(X:S)
1.18/1.75	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.75	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.75	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.75	 a__U23(tt) -> tt
1.18/1.75	 a__U23(X:S) -> U23(X:S)
1.18/1.75	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.75	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.75	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.75	 a__U33(tt) -> tt
1.18/1.75	 a__U33(X:S) -> U33(X:S)
1.18/1.75	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.75	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.75	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.75	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.75	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.75	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.75	 a__U46(tt) -> tt
1.18/1.75	 a__U46(X:S) -> U46(X:S)
1.18/1.75	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.75	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.75	 a__U52(tt) -> tt
1.18/1.75	 a__U52(X:S) -> U52(X:S)
1.18/1.75	 a__U61(tt) -> tt
1.18/1.75	 a__U61(X:S) -> U61(X:S)
1.18/1.75	 a__U71(tt) -> tt
1.18/1.75	 a__U71(X:S) -> U71(X:S)
1.18/1.75	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.75	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.75	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.75	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.75	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.75	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.75	 a__U86(tt) -> tt
1.18/1.75	 a__U86(X:S) -> U86(X:S)
1.18/1.75	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.75	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.75	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.75	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.75	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.75	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.75	 a__isNat(0) -> tt
1.18/1.75	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__isNat(X:S) -> isNat(X:S)
1.18/1.75	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatIList(zeros) -> tt
1.18/1.75	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.75	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.75	 a__isNatIListKind(nil) -> tt
1.18/1.75	 a__isNatIListKind(zeros) -> tt
1.18/1.75	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.75	 a__isNatKind(0) -> tt
1.18/1.75	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.75	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.75	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.75	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatList(nil) -> tt
1.18/1.75	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.75	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.75	 a__length(nil) -> 0
1.18/1.75	 a__length(X:S) -> length(X:S)
1.18/1.75	 a__zeros -> cons(0,zeros)
1.18/1.75	 a__zeros -> zeros
1.18/1.75	 mark(0) -> 0
1.18/1.75	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.75	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.75	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.75	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.75	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.75	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.75	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.75	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.75	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.75	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.75	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.75	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.75	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.75	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.75	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.75	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.75	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.75	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.75	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.75	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.75	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.75	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.75	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.75	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.75	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.75	 mark(nil) -> nil
1.18/1.75	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.75	 mark(tt) -> tt
1.18/1.75	 mark(zeros) -> a__zeros
1.18/1.75	
1.18/1.75	Problem 1.4: 
1.18/1.75	
1.18/1.75	Subterm Processor:
1.18/1.75	-> Pairs:
1.18/1.75	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.75	 MARK(U11(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U12(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U13(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U21(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U22(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U23(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U31(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U32(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U33(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U41(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U42(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U43(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U44(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U45(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U46(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U51(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U52(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U61(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U71(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U81(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U82(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U83(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U84(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U85(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U86(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(U91(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U92(X1:S,X2:S,X3:S)) -> A__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U92(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U93(X1:S,X2:S,X3:S)) -> A__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 MARK(U93(X1:S,X2:S,X3:S)) -> MARK(X1:S)
1.18/1.75	 MARK(U94(X1:S,X2:S)) -> A__U94(mark(X1:S),X2:S)
1.18/1.75	 MARK(U94(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
1.18/1.75	 MARK(length(X:S)) -> MARK(X:S)
1.18/1.75	 MARK(s(X:S)) -> MARK(X:S)
1.18/1.75	-> Rules:
1.18/1.75	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.75	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.75	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.75	 a__U13(tt) -> tt
1.18/1.75	 a__U13(X:S) -> U13(X:S)
1.18/1.75	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.75	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.75	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.75	 a__U23(tt) -> tt
1.18/1.75	 a__U23(X:S) -> U23(X:S)
1.18/1.75	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.75	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.75	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.75	 a__U33(tt) -> tt
1.18/1.75	 a__U33(X:S) -> U33(X:S)
1.18/1.75	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.75	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.75	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.75	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.75	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.75	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.75	 a__U46(tt) -> tt
1.18/1.75	 a__U46(X:S) -> U46(X:S)
1.18/1.75	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.75	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.75	 a__U52(tt) -> tt
1.18/1.75	 a__U52(X:S) -> U52(X:S)
1.18/1.75	 a__U61(tt) -> tt
1.18/1.75	 a__U61(X:S) -> U61(X:S)
1.18/1.75	 a__U71(tt) -> tt
1.18/1.75	 a__U71(X:S) -> U71(X:S)
1.18/1.75	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.75	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.75	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.75	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.75	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.75	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.75	 a__U86(tt) -> tt
1.18/1.75	 a__U86(X:S) -> U86(X:S)
1.18/1.75	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.75	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.75	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.75	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.75	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.75	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.75	 a__isNat(0) -> tt
1.18/1.75	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__isNat(X:S) -> isNat(X:S)
1.18/1.75	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatIList(zeros) -> tt
1.18/1.75	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.75	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.75	 a__isNatIListKind(nil) -> tt
1.18/1.75	 a__isNatIListKind(zeros) -> tt
1.18/1.75	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.75	 a__isNatKind(0) -> tt
1.18/1.75	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.75	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.75	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.75	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatList(nil) -> tt
1.18/1.75	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.75	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.75	 a__length(nil) -> 0
1.18/1.75	 a__length(X:S) -> length(X:S)
1.18/1.75	 a__zeros -> cons(0,zeros)
1.18/1.75	 a__zeros -> zeros
1.18/1.75	 mark(0) -> 0
1.18/1.75	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.75	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.75	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.75	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.75	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.75	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.75	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.75	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.75	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.75	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.75	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.75	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.75	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.75	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.75	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.75	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.75	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.75	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.75	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.75	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.75	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.75	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.75	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.75	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.75	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.75	 mark(nil) -> nil
1.18/1.75	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.75	 mark(tt) -> tt
1.18/1.75	 mark(zeros) -> a__zeros
1.18/1.75	->Projection:
1.18/1.75	 pi(A__U92) = 2
1.18/1.75	 pi(A__U93) = 2
1.18/1.75	 pi(A__U94) = 2
1.18/1.75	 pi(MARK) = 1
1.18/1.75	
1.18/1.75	Problem 1.4: 
1.18/1.75	
1.18/1.75	SCC Processor:
1.18/1.75	-> Pairs:
1.18/1.75	 A__U92(tt,L:S,N:S) -> A__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 A__U93(tt,L:S,N:S) -> A__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 A__U94(tt,L:S) -> MARK(L:S)
1.18/1.75	-> Rules:
1.18/1.75	 a__U11(tt,V1:S) -> a__U12(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__U11(X1:S,X2:S) -> U11(X1:S,X2:S)
1.18/1.75	 a__U12(tt,V1:S) -> a__U13(a__isNatList(V1:S))
1.18/1.75	 a__U12(X1:S,X2:S) -> U12(X1:S,X2:S)
1.18/1.75	 a__U13(tt) -> tt
1.18/1.75	 a__U13(X:S) -> U13(X:S)
1.18/1.75	 a__U21(tt,V1:S) -> a__U22(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__U21(X1:S,X2:S) -> U21(X1:S,X2:S)
1.18/1.75	 a__U22(tt,V1:S) -> a__U23(a__isNat(V1:S))
1.18/1.75	 a__U22(X1:S,X2:S) -> U22(X1:S,X2:S)
1.18/1.75	 a__U23(tt) -> tt
1.18/1.75	 a__U23(X:S) -> U23(X:S)
1.18/1.75	 a__U31(tt,V:S) -> a__U32(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__U31(X1:S,X2:S) -> U31(X1:S,X2:S)
1.18/1.75	 a__U32(tt,V:S) -> a__U33(a__isNatList(V:S))
1.18/1.75	 a__U32(X1:S,X2:S) -> U32(X1:S,X2:S)
1.18/1.75	 a__U33(tt) -> tt
1.18/1.75	 a__U33(X:S) -> U33(X:S)
1.18/1.75	 a__U41(tt,V1:S,V2:S) -> a__U42(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U41(X1:S,X2:S,X3:S) -> U41(X1:S,X2:S,X3:S)
1.18/1.75	 a__U42(tt,V1:S,V2:S) -> a__U43(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U42(X1:S,X2:S,X3:S) -> U42(X1:S,X2:S,X3:S)
1.18/1.75	 a__U43(tt,V1:S,V2:S) -> a__U44(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U43(X1:S,X2:S,X3:S) -> U43(X1:S,X2:S,X3:S)
1.18/1.75	 a__U44(tt,V1:S,V2:S) -> a__U45(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U44(X1:S,X2:S,X3:S) -> U44(X1:S,X2:S,X3:S)
1.18/1.75	 a__U45(tt,V2:S) -> a__U46(a__isNatIList(V2:S))
1.18/1.75	 a__U45(X1:S,X2:S) -> U45(X1:S,X2:S)
1.18/1.75	 a__U46(tt) -> tt
1.18/1.75	 a__U46(X:S) -> U46(X:S)
1.18/1.75	 a__U51(tt,V2:S) -> a__U52(a__isNatIListKind(V2:S))
1.18/1.75	 a__U51(X1:S,X2:S) -> U51(X1:S,X2:S)
1.18/1.75	 a__U52(tt) -> tt
1.18/1.75	 a__U52(X:S) -> U52(X:S)
1.18/1.75	 a__U61(tt) -> tt
1.18/1.75	 a__U61(X:S) -> U61(X:S)
1.18/1.75	 a__U71(tt) -> tt
1.18/1.75	 a__U71(X:S) -> U71(X:S)
1.18/1.75	 a__U81(tt,V1:S,V2:S) -> a__U82(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__U81(X1:S,X2:S,X3:S) -> U81(X1:S,X2:S,X3:S)
1.18/1.75	 a__U82(tt,V1:S,V2:S) -> a__U83(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U82(X1:S,X2:S,X3:S) -> U82(X1:S,X2:S,X3:S)
1.18/1.75	 a__U83(tt,V1:S,V2:S) -> a__U84(a__isNatIListKind(V2:S),V1:S,V2:S)
1.18/1.75	 a__U83(X1:S,X2:S,X3:S) -> U83(X1:S,X2:S,X3:S)
1.18/1.75	 a__U84(tt,V1:S,V2:S) -> a__U85(a__isNat(V1:S),V2:S)
1.18/1.75	 a__U84(X1:S,X2:S,X3:S) -> U84(X1:S,X2:S,X3:S)
1.18/1.75	 a__U85(tt,V2:S) -> a__U86(a__isNatList(V2:S))
1.18/1.75	 a__U85(X1:S,X2:S) -> U85(X1:S,X2:S)
1.18/1.75	 a__U86(tt) -> tt
1.18/1.75	 a__U86(X:S) -> U86(X:S)
1.18/1.75	 a__U91(tt,L:S,N:S) -> a__U92(a__isNatIListKind(L:S),L:S,N:S)
1.18/1.75	 a__U91(X1:S,X2:S,X3:S) -> U91(X1:S,X2:S,X3:S)
1.18/1.75	 a__U92(tt,L:S,N:S) -> a__U93(a__isNat(N:S),L:S,N:S)
1.18/1.75	 a__U92(X1:S,X2:S,X3:S) -> U92(X1:S,X2:S,X3:S)
1.18/1.75	 a__U93(tt,L:S,N:S) -> a__U94(a__isNatKind(N:S),L:S)
1.18/1.75	 a__U93(X1:S,X2:S,X3:S) -> U93(X1:S,X2:S,X3:S)
1.18/1.75	 a__U94(tt,L:S) -> s(a__length(mark(L:S)))
1.18/1.75	 a__U94(X1:S,X2:S) -> U94(X1:S,X2:S)
1.18/1.75	 a__isNat(0) -> tt
1.18/1.75	 a__isNat(length(V1:S)) -> a__U11(a__isNatIListKind(V1:S),V1:S)
1.18/1.75	 a__isNat(s(V1:S)) -> a__U21(a__isNatKind(V1:S),V1:S)
1.18/1.75	 a__isNat(X:S) -> isNat(X:S)
1.18/1.75	 a__isNatIList(cons(V1:S,V2:S)) -> a__U41(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatIList(zeros) -> tt
1.18/1.75	 a__isNatIList(V:S) -> a__U31(a__isNatIListKind(V:S),V:S)
1.18/1.75	 a__isNatIList(X:S) -> isNatIList(X:S)
1.18/1.75	 a__isNatIListKind(cons(V1:S,V2:S)) -> a__U51(a__isNatKind(V1:S),V2:S)
1.18/1.75	 a__isNatIListKind(nil) -> tt
1.18/1.75	 a__isNatIListKind(zeros) -> tt
1.18/1.75	 a__isNatIListKind(X:S) -> isNatIListKind(X:S)
1.18/1.75	 a__isNatKind(0) -> tt
1.18/1.75	 a__isNatKind(length(V1:S)) -> a__U61(a__isNatIListKind(V1:S))
1.18/1.75	 a__isNatKind(s(V1:S)) -> a__U71(a__isNatKind(V1:S))
1.18/1.75	 a__isNatKind(X:S) -> isNatKind(X:S)
1.18/1.75	 a__isNatList(cons(V1:S,V2:S)) -> a__U81(a__isNatKind(V1:S),V1:S,V2:S)
1.18/1.75	 a__isNatList(nil) -> tt
1.18/1.75	 a__isNatList(X:S) -> isNatList(X:S)
1.18/1.75	 a__length(cons(N:S,L:S)) -> a__U91(a__isNatList(L:S),L:S,N:S)
1.18/1.75	 a__length(nil) -> 0
1.18/1.75	 a__length(X:S) -> length(X:S)
1.18/1.75	 a__zeros -> cons(0,zeros)
1.18/1.75	 a__zeros -> zeros
1.18/1.75	 mark(0) -> 0
1.18/1.75	 mark(U11(X1:S,X2:S)) -> a__U11(mark(X1:S),X2:S)
1.18/1.75	 mark(U12(X1:S,X2:S)) -> a__U12(mark(X1:S),X2:S)
1.18/1.75	 mark(U13(X:S)) -> a__U13(mark(X:S))
1.18/1.75	 mark(U21(X1:S,X2:S)) -> a__U21(mark(X1:S),X2:S)
1.18/1.75	 mark(U22(X1:S,X2:S)) -> a__U22(mark(X1:S),X2:S)
1.18/1.75	 mark(U23(X:S)) -> a__U23(mark(X:S))
1.18/1.75	 mark(U31(X1:S,X2:S)) -> a__U31(mark(X1:S),X2:S)
1.18/1.75	 mark(U32(X1:S,X2:S)) -> a__U32(mark(X1:S),X2:S)
1.18/1.75	 mark(U33(X:S)) -> a__U33(mark(X:S))
1.18/1.75	 mark(U41(X1:S,X2:S,X3:S)) -> a__U41(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U42(X1:S,X2:S,X3:S)) -> a__U42(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U43(X1:S,X2:S,X3:S)) -> a__U43(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U44(X1:S,X2:S,X3:S)) -> a__U44(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U45(X1:S,X2:S)) -> a__U45(mark(X1:S),X2:S)
1.18/1.75	 mark(U46(X:S)) -> a__U46(mark(X:S))
1.18/1.75	 mark(U51(X1:S,X2:S)) -> a__U51(mark(X1:S),X2:S)
1.18/1.75	 mark(U52(X:S)) -> a__U52(mark(X:S))
1.18/1.75	 mark(U61(X:S)) -> a__U61(mark(X:S))
1.18/1.75	 mark(U71(X:S)) -> a__U71(mark(X:S))
1.18/1.75	 mark(U81(X1:S,X2:S,X3:S)) -> a__U81(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U82(X1:S,X2:S,X3:S)) -> a__U82(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U83(X1:S,X2:S,X3:S)) -> a__U83(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U84(X1:S,X2:S,X3:S)) -> a__U84(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U85(X1:S,X2:S)) -> a__U85(mark(X1:S),X2:S)
1.18/1.75	 mark(U86(X:S)) -> a__U86(mark(X:S))
1.18/1.75	 mark(U91(X1:S,X2:S,X3:S)) -> a__U91(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U92(X1:S,X2:S,X3:S)) -> a__U92(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U93(X1:S,X2:S,X3:S)) -> a__U93(mark(X1:S),X2:S,X3:S)
1.18/1.75	 mark(U94(X1:S,X2:S)) -> a__U94(mark(X1:S),X2:S)
1.18/1.75	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
1.18/1.75	 mark(isNat(X:S)) -> a__isNat(X:S)
1.18/1.75	 mark(isNatIList(X:S)) -> a__isNatIList(X:S)
1.18/1.75	 mark(isNatIListKind(X:S)) -> a__isNatIListKind(X:S)
1.18/1.75	 mark(isNatKind(X:S)) -> a__isNatKind(X:S)
1.18/1.75	 mark(isNatList(X:S)) -> a__isNatList(X:S)
1.18/1.75	 mark(length(X:S)) -> a__length(mark(X:S))
1.18/1.75	 mark(nil) -> nil
1.18/1.75	 mark(s(X:S)) -> s(mark(X:S))
1.18/1.75	 mark(tt) -> tt
1.18/1.75	 mark(zeros) -> a__zeros
1.18/1.75	->Strongly Connected Components:
1.18/1.75	 There is no strongly connected component
1.18/1.75	
1.18/1.75	The problem is finite.
1.18/1.75	EOF