YES(?,POLY) 'Pop* with parameter subtitution (timeout of 60.0 seconds)' ----------------------------------------------------------- Answer: YES(?,POLY) Input Problem: innermost runtime-complexity with respect to Rules: { g(0()) -> 0() , g(s(x)) -> f(g(x)) , f(0()) -> 0()} Proof Output: The input was oriented with the instance of POP* as induced by the precedence g > f and safe mapping safe(g) = {}, safe(0) = {}, safe(s) = {1}, safe(f) = {1} . For your convenience, here is the input in predicative notation: Rules: { g(0();) -> 0() , g(s(; x);) -> f(; g(x;)) , f(; 0()) -> 0()}