MAYBE MAYBE TRS: { g1(x, x, y, a()) -> h(x, y), g1(y, x, x, a()) -> h(x, y), f(x, y, w, w, a()) -> g1(x, x, y, w), f(x, y, w, a(), a()) -> g1(y, x, x, w), f(x, y, a(), w, w) -> g2(y, y, x, w), f(x, y, a(), a(), w) -> g2(x, y, y, w), g2(x, y, y, a()) -> h(x, y), g2(y, y, x, a()) -> h(x, y), h(x, x) -> x } DUP: We consider a duplicating system. Trs: { g1(x, x, y, a()) -> h(x, y), g1(y, x, x, a()) -> h(x, y), f(x, y, w, w, a()) -> g1(x, x, y, w), f(x, y, w, a(), a()) -> g1(y, x, x, w), f(x, y, a(), w, w) -> g2(y, y, x, w), f(x, y, a(), a(), w) -> g2(x, y, y, w), g2(x, y, y, a()) -> h(x, y), g2(y, y, x, a()) -> h(x, y), h(x, x) -> x } Fail