MAYBE MAYBE TRS: { a(lambda(x), y) -> lambda(a(x, p(1(), a(y, t())))), a(a(x, y), z) -> a(x, a(y, z)), a(p(x, y), z) -> p(a(x, z), a(y, z)), a(1(), p(x, y)) -> x, a(1(), id()) -> 1(), a(t(), p(x, y)) -> y, a(t(), id()) -> t(), a(id(), x) -> x } DUP: We consider a duplicating system. Trs: { a(lambda(x), y) -> lambda(a(x, p(1(), a(y, t())))), a(a(x, y), z) -> a(x, a(y, z)), a(p(x, y), z) -> p(a(x, z), a(y, z)), a(1(), p(x, y)) -> x, a(1(), id()) -> 1(), a(t(), p(x, y)) -> y, a(t(), id()) -> t(), a(id(), x) -> x } Fail