MAYBE MAYBE TRS: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(tt()) -> active(tt()), mark(U11(X)) -> active(U11(mark(X))), mark(U21(X)) -> active(U21(mark(X))), mark(U31(X)) -> active(U31(mark(X))), mark(U42(X)) -> active(U42(mark(X))), mark(isNatIList(X)) -> active(isNatIList(X)), mark(U41(X1, X2)) -> active(U41(mark(X1), X2)), mark(U52(X)) -> active(U52(mark(X))), mark(isNatList(X)) -> active(isNatList(X)), mark(U51(X1, X2)) -> active(U51(mark(X1), X2)), mark(U62(X1, X2)) -> active(U62(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(U61(X1, X2, X3)) -> active(U61(mark(X1), X2, X3)), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(nil()) -> active(nil()), cons(X1, mark(X2)) -> cons(X1, X2), cons(X1, active(X2)) -> cons(X1, X2), cons(mark(X1), X2) -> cons(X1, X2), cons(active(X1), X2) -> cons(X1, X2), active(zeros()) -> mark(cons(0(), zeros())), active(U11(tt())) -> mark(tt()), active(U21(tt())) -> mark(tt()), active(U31(tt())) -> mark(tt()), active(U42(tt())) -> mark(tt()), active(isNatIList(V)) -> mark(U31(isNatList(V))), active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2)), active(isNatIList(zeros())) -> mark(tt()), active(U41(tt(), V2)) -> mark(U42(isNatIList(V2))), active(U52(tt())) -> mark(tt()), active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2)), active(isNatList(nil())) -> mark(tt()), active(U51(tt(), V2)) -> mark(U52(isNatList(V2))), active(U62(tt(), L)) -> mark(s(length(L))), active(isNat(0())) -> mark(tt()), active(isNat(s(V1))) -> mark(U21(isNat(V1))), active(isNat(length(V1))) -> mark(U11(isNatList(V1))), active(U61(tt(), L, N)) -> mark(U62(isNat(N), L)), active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N)), active(length(nil())) -> mark(0()), U11(mark(X)) -> U11(X), U11(active(X)) -> U11(X), U21(mark(X)) -> U21(X), U21(active(X)) -> U21(X), U31(mark(X)) -> U31(X), U31(active(X)) -> U31(X), U42(mark(X)) -> U42(X), U42(active(X)) -> U42(X), isNatIList(mark(X)) -> isNatIList(X), isNatIList(active(X)) -> isNatIList(X), U41(X1, mark(X2)) -> U41(X1, X2), U41(X1, active(X2)) -> U41(X1, X2), U41(mark(X1), X2) -> U41(X1, X2), U41(active(X1), X2) -> U41(X1, X2), U52(mark(X)) -> U52(X), U52(active(X)) -> U52(X), isNatList(mark(X)) -> isNatList(X), isNatList(active(X)) -> isNatList(X), U51(X1, mark(X2)) -> U51(X1, X2), U51(X1, active(X2)) -> U51(X1, X2), U51(mark(X1), X2) -> U51(X1, X2), U51(active(X1), X2) -> U51(X1, X2), U62(X1, mark(X2)) -> U62(X1, X2), U62(X1, active(X2)) -> U62(X1, X2), U62(mark(X1), X2) -> U62(X1, X2), U62(active(X1), X2) -> U62(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), U61(X1, X2, mark(X3)) -> U61(X1, X2, X3), U61(X1, X2, active(X3)) -> U61(X1, X2, X3), U61(X1, mark(X2), X3) -> U61(X1, X2, X3), U61(X1, active(X2), X3) -> U61(X1, X2, X3), U61(mark(X1), X2, X3) -> U61(X1, X2, X3), U61(active(X1), X2, X3) -> U61(X1, X2, X3), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X) } DUP: We consider a duplicating system. Trs: { mark(cons(X1, X2)) -> active(cons(mark(X1), X2)), mark(0()) -> active(0()), mark(zeros()) -> active(zeros()), mark(tt()) -> active(tt()), mark(U11(X)) -> active(U11(mark(X))), mark(U21(X)) -> active(U21(mark(X))), mark(U31(X)) -> active(U31(mark(X))), mark(U42(X)) -> active(U42(mark(X))), mark(isNatIList(X)) -> active(isNatIList(X)), mark(U41(X1, X2)) -> active(U41(mark(X1), X2)), mark(U52(X)) -> active(U52(mark(X))), mark(isNatList(X)) -> active(isNatList(X)), mark(U51(X1, X2)) -> active(U51(mark(X1), X2)), mark(U62(X1, X2)) -> active(U62(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(U61(X1, X2, X3)) -> active(U61(mark(X1), X2, X3)), mark(s(X)) -> active(s(mark(X))), mark(length(X)) -> active(length(mark(X))), mark(nil()) -> active(nil()), cons(X1, mark(X2)) -> cons(X1, X2), cons(X1, active(X2)) -> cons(X1, X2), cons(mark(X1), X2) -> cons(X1, X2), cons(active(X1), X2) -> cons(X1, X2), active(zeros()) -> mark(cons(0(), zeros())), active(U11(tt())) -> mark(tt()), active(U21(tt())) -> mark(tt()), active(U31(tt())) -> mark(tt()), active(U42(tt())) -> mark(tt()), active(isNatIList(V)) -> mark(U31(isNatList(V))), active(isNatIList(cons(V1, V2))) -> mark(U41(isNat(V1), V2)), active(isNatIList(zeros())) -> mark(tt()), active(U41(tt(), V2)) -> mark(U42(isNatIList(V2))), active(U52(tt())) -> mark(tt()), active(isNatList(cons(V1, V2))) -> mark(U51(isNat(V1), V2)), active(isNatList(nil())) -> mark(tt()), active(U51(tt(), V2)) -> mark(U52(isNatList(V2))), active(U62(tt(), L)) -> mark(s(length(L))), active(isNat(0())) -> mark(tt()), active(isNat(s(V1))) -> mark(U21(isNat(V1))), active(isNat(length(V1))) -> mark(U11(isNatList(V1))), active(U61(tt(), L, N)) -> mark(U62(isNat(N), L)), active(length(cons(N, L))) -> mark(U61(isNatList(L), L, N)), active(length(nil())) -> mark(0()), U11(mark(X)) -> U11(X), U11(active(X)) -> U11(X), U21(mark(X)) -> U21(X), U21(active(X)) -> U21(X), U31(mark(X)) -> U31(X), U31(active(X)) -> U31(X), U42(mark(X)) -> U42(X), U42(active(X)) -> U42(X), isNatIList(mark(X)) -> isNatIList(X), isNatIList(active(X)) -> isNatIList(X), U41(X1, mark(X2)) -> U41(X1, X2), U41(X1, active(X2)) -> U41(X1, X2), U41(mark(X1), X2) -> U41(X1, X2), U41(active(X1), X2) -> U41(X1, X2), U52(mark(X)) -> U52(X), U52(active(X)) -> U52(X), isNatList(mark(X)) -> isNatList(X), isNatList(active(X)) -> isNatList(X), U51(X1, mark(X2)) -> U51(X1, X2), U51(X1, active(X2)) -> U51(X1, X2), U51(mark(X1), X2) -> U51(X1, X2), U51(active(X1), X2) -> U51(X1, X2), U62(X1, mark(X2)) -> U62(X1, X2), U62(X1, active(X2)) -> U62(X1, X2), U62(mark(X1), X2) -> U62(X1, X2), U62(active(X1), X2) -> U62(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), U61(X1, X2, mark(X3)) -> U61(X1, X2, X3), U61(X1, X2, active(X3)) -> U61(X1, X2, X3), U61(X1, mark(X2), X3) -> U61(X1, X2, X3), U61(X1, active(X2), X3) -> U61(X1, X2, X3), U61(mark(X1), X2, X3) -> U61(X1, X2, X3), U61(active(X1), X2, X3) -> U61(X1, X2, X3), s(mark(X)) -> s(X), s(active(X)) -> s(X), length(mark(X)) -> length(X), length(active(X)) -> length(X) } Fail