MAYBE MAYBE TRS: { p(s(x)) -> x, s(p(x)) -> x, +(p(x), y) -> p(+(x, y)), +(s(x), y) -> s(+(x, y)), +(0(), y) -> y, minus(p(x)) -> s(minus(x)), minus(s(x)) -> p(minus(x)), minus(0()) -> 0(), *(p(x), y) -> +(*(x, y), minus(y)), *(s(x), y) -> +(*(x, y), y), *(0(), y) -> 0() } DUP: We consider a duplicating system. Trs: { p(s(x)) -> x, s(p(x)) -> x, +(p(x), y) -> p(+(x, y)), +(s(x), y) -> s(+(x, y)), +(0(), y) -> y, minus(p(x)) -> s(minus(x)), minus(s(x)) -> p(minus(x)), minus(0()) -> 0(), *(p(x), y) -> +(*(x, y), minus(y)), *(s(x), y) -> +(*(x, y), y), *(0(), y) -> 0() } Fail