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