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)) , mult(0(), x) -> 0() , mult(s(x), y) -> add(y, mult(x, y))} Proof Output: The input was oriented with the instance of POP* as induced by the precedence mult > add and safe mapping safe(add) = {2}, safe(0) = {}, safe(s) = {1}, safe(mult) = {} . For your convenience, here is the input in predicative notation: Rules: { add(0(); x) -> x , add(s(; x); y) -> s(; add(x; y)) , mult(0(), x;) -> 0() , mult(s(; x), y;) -> add(y; mult(x, y;))}