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