MAYBE MAYBE TRS: { prime(0()) -> false(), prime(s(0())) -> false(), prime(s(s(x))) -> prime1(s(s(x)), s(x)), prime1(x, 0()) -> false(), prime1(x, s(0())) -> true(), prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))), divp(x, y) -> =(rem(x, y), 0()) } DUP: We consider a duplicating system. Trs: { prime(0()) -> false(), prime(s(0())) -> false(), prime(s(s(x))) -> prime1(s(s(x)), s(x)), prime1(x, 0()) -> false(), prime1(x, s(0())) -> true(), prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))), divp(x, y) -> =(rem(x, y), 0()) } Fail