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