MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , plus(s(x), y) -> s(plus(x, y)) , plus(0(), y) -> y , times(s(x), y) -> plus(y, times(x, y)) , times(0(), y) -> 0() , log(x, s(0())) -> baseError() , log(x, 0()) -> baseError() , log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0()), 0()) , log(0(), s(s(b))) -> logZeroError() , loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z) , if(false(), x, b, y, z) -> loop(x, b, times(b, y), s(z)) , if(true(), x, b, y, z) -> z } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..