(VAR V2 L N V1 V X1 X2 X3 X) (RULES active(zeros) -> mark(cons(0,zeros)) active(U11(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt)) -> mark(tt) active(U41(tt,V2)) -> mark(U42(isNatIList(V2))) active(U42(tt)) -> mark(tt) active(U51(tt,V2)) -> mark(U52(isNatList(V2))) active(U52(tt)) -> mark(tt) active(U61(tt,L,N)) -> mark(U62(isNat(N),L)) active(U62(tt,L)) -> mark(s(length(L))) active(isNat(0)) -> mark(tt) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros)) -> mark(tt) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil)) -> mark(tt) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(nil)) -> mark(0) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) active(cons(X1,X2)) -> cons(active(X1),X2) active(U11(X)) -> U11(active(X)) active(U21(X)) -> U21(active(X)) active(U31(X)) -> U31(active(X)) active(U41(X1,X2)) -> U41(active(X1),X2) active(U42(X)) -> U42(active(X)) active(U51(X1,X2)) -> U51(active(X1),X2) active(U52(X)) -> U52(active(X)) active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3) active(U62(X1,X2)) -> U62(active(X1),X2) active(s(X)) -> s(active(X)) active(length(X)) -> length(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) U11(mark(X)) -> mark(U11(X)) U21(mark(X)) -> mark(U21(X)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1),X2) -> mark(U41(X1,X2)) U42(mark(X)) -> mark(U42(X)) U51(mark(X1),X2) -> mark(U51(X1,X2)) U52(mark(X)) -> mark(U52(X)) U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3)) U62(mark(X1),X2) -> mark(U62(X1,X2)) s(mark(X)) -> mark(s(X)) length(mark(X)) -> mark(length(X)) proper(zeros) -> ok(zeros) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(0) -> ok(0) proper(U11(X)) -> U11(proper(X)) proper(tt) -> ok(tt) proper(U21(X)) -> U21(proper(X)) proper(U31(X)) -> U31(proper(X)) proper(U41(X1,X2)) -> U41(proper(X1),proper(X2)) proper(U42(X)) -> U42(proper(X)) proper(isNatIList(X)) -> isNatIList(proper(X)) proper(U51(X1,X2)) -> U51(proper(X1),proper(X2)) proper(U52(X)) -> U52(proper(X)) proper(isNatList(X)) -> isNatList(proper(X)) proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3)) proper(U62(X1,X2)) -> U62(proper(X1),proper(X2)) proper(isNat(X)) -> isNat(proper(X)) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil) -> ok(nil) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) U11(ok(X)) -> ok(U11(X)) U21(ok(X)) -> ok(U21(X)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1),ok(X2)) -> ok(U41(X1,X2)) U42(ok(X)) -> ok(U42(X)) isNatIList(ok(X)) -> ok(isNatIList(X)) U51(ok(X1),ok(X2)) -> ok(U51(X1,X2)) U52(ok(X)) -> ok(U52(X)) isNatList(ok(X)) -> ok(isNatList(X)) U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3)) U62(ok(X1),ok(X2)) -> ok(U62(X1,X2)) isNat(ok(X)) -> ok(isNat(X)) s(ok(X)) -> ok(s(X)) length(ok(X)) -> ok(length(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) )