MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , zero(0()) -> true() , zero(s(x)) -> false() , id(0()) -> 0() , id(s(x)) -> s(id(x)) , minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)) , if_mod(true(), b1, b2, x, y) -> 0() , if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y) , if2(true(), b2, x, y) -> 0() , if2(false(), b2, x, y) -> if3(b2, x, y) , if3(true(), x, y) -> mod(minus(x, y), s(y)) , if3(false(), x, y) -> x } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..