MAYBE MAYBE TRS: { mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(tt()) -> active(tt()), mark(s(X)) -> active(s(mark(X))), mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))), mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)), mark(and(X1, X2)) -> active(and(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(0()) -> active(0()), active(U11(tt(), N)) -> mark(N), active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)), active(plus(N, 0())) -> mark(U11(isNat(N), N)), active(U21(tt(), M, N)) -> mark(s(plus(N, M))), active(and(tt(), X)) -> mark(X), active(isNat(s(V1))) -> mark(isNat(V1)), active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))), active(isNat(0())) -> mark(tt()), U11(X1, mark(X2)) -> U11(X1, X2), U11(X1, active(X2)) -> U11(X1, X2), U11(mark(X1), X2) -> U11(X1, X2), U11(active(X1), X2) -> U11(X1, X2), s(mark(X)) -> s(X), s(active(X)) -> s(X), plus(X1, mark(X2)) -> plus(X1, X2), plus(X1, active(X2)) -> plus(X1, X2), plus(mark(X1), X2) -> plus(X1, X2), plus(active(X1), X2) -> plus(X1, X2), U21(X1, X2, mark(X3)) -> U21(X1, X2, X3), U21(X1, X2, active(X3)) -> U21(X1, X2, X3), U21(X1, mark(X2), X3) -> U21(X1, X2, X3), U21(X1, active(X2), X3) -> U21(X1, X2, X3), U21(mark(X1), X2, X3) -> U21(X1, X2, X3), U21(active(X1), X2, X3) -> U21(X1, X2, X3), and(X1, mark(X2)) -> and(X1, X2), and(X1, active(X2)) -> and(X1, X2), and(mark(X1), X2) -> and(X1, X2), and(active(X1), X2) -> and(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X) } DUP: We consider a duplicating system. Trs: { mark(U11(X1, X2)) -> active(U11(mark(X1), X2)), mark(tt()) -> active(tt()), mark(s(X)) -> active(s(mark(X))), mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))), mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)), mark(and(X1, X2)) -> active(and(mark(X1), X2)), mark(isNat(X)) -> active(isNat(X)), mark(0()) -> active(0()), active(U11(tt(), N)) -> mark(N), active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)), active(plus(N, 0())) -> mark(U11(isNat(N), N)), active(U21(tt(), M, N)) -> mark(s(plus(N, M))), active(and(tt(), X)) -> mark(X), active(isNat(s(V1))) -> mark(isNat(V1)), active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))), active(isNat(0())) -> mark(tt()), U11(X1, mark(X2)) -> U11(X1, X2), U11(X1, active(X2)) -> U11(X1, X2), U11(mark(X1), X2) -> U11(X1, X2), U11(active(X1), X2) -> U11(X1, X2), s(mark(X)) -> s(X), s(active(X)) -> s(X), plus(X1, mark(X2)) -> plus(X1, X2), plus(X1, active(X2)) -> plus(X1, X2), plus(mark(X1), X2) -> plus(X1, X2), plus(active(X1), X2) -> plus(X1, X2), U21(X1, X2, mark(X3)) -> U21(X1, X2, X3), U21(X1, X2, active(X3)) -> U21(X1, X2, X3), U21(X1, mark(X2), X3) -> U21(X1, X2, X3), U21(X1, active(X2), X3) -> U21(X1, X2, X3), U21(mark(X1), X2, X3) -> U21(X1, X2, X3), U21(active(X1), X2, X3) -> U21(X1, X2, X3), and(X1, mark(X2)) -> and(X1, X2), and(X1, active(X2)) -> and(X1, X2), and(mark(X1), X2) -> and(X1, X2), and(active(X1), X2) -> and(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X) } Fail