MAYBE MAYBE TRS: { msubst(a, id()) -> a, msubst(msubst(a, s), t) -> msubst(a, circ(s, t)), circ(s, id()) -> s, circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t)), circ(cons(lift(), s), cons(a, t)) -> cons(a, circ(s, t)), circ(cons(lift(), s), cons(lift(), t)) -> cons(lift(), circ(s, t)), circ(cons(lift(), s), circ(cons(lift(), t), u)) -> circ(cons(lift(), circ(s, t)), u), circ(circ(s, t), u) -> circ(s, circ(t, u)), circ(id(), s) -> s, subst(a, id()) -> a } DUP: We consider a duplicating system. Trs: { msubst(a, id()) -> a, msubst(msubst(a, s), t) -> msubst(a, circ(s, t)), circ(s, id()) -> s, circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t)), circ(cons(lift(), s), cons(a, t)) -> cons(a, circ(s, t)), circ(cons(lift(), s), cons(lift(), t)) -> cons(lift(), circ(s, t)), circ(cons(lift(), s), circ(cons(lift(), t), u)) -> circ(cons(lift(), circ(s, t)), u), circ(circ(s, t), u) -> circ(s, circ(t, u)), circ(id(), s) -> s, subst(a, id()) -> a } Fail