MAYBE MAYBE TRS: { lt(x, 0()) -> false(), lt(0(), s(y)) -> true(), lt(s(x), s(y)) -> lt(x, y), plus(x, 0()) -> x, plus(x, s(y)) -> s(plus(x, y)), help(x, s(y), c) -> if(lt(c, x), x, s(y), c), quot(x, s(y)) -> help(x, s(y), 0()), if(false(), x, s(y), c) -> 0(), if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } DUP: We consider a duplicating system. Trs: { lt(x, 0()) -> false(), lt(0(), s(y)) -> true(), lt(s(x), s(y)) -> lt(x, y), plus(x, 0()) -> x, plus(x, s(y)) -> s(plus(x, y)), help(x, s(y), c) -> if(lt(c, x), x, s(y), c), quot(x, s(y)) -> help(x, s(y), 0()), if(false(), x, s(y), c) -> 0(), if(true(), x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) } Fail