YES(?,POLY) 'Pop* with parameter subtitution (timeout of 60.0 seconds)' ----------------------------------------------------------- Answer: YES(?,POLY) Input Problem: innermost runtime-complexity with respect to Rules: { +(0(), y) -> y , +(s(x), y) -> s(+(x, y)) , +(s(x), y) -> +(x, s(y))} Proof Output: The input was oriented with the instance of POP* as induced by the precedence empty and safe mapping safe(+) = {2}, safe(0) = {}, safe(s) = {1} . For your convenience, here is the input in predicative notation: Rules: { +(0(); y) -> y , +(s(; x); y) -> s(; +(x; y)) , +(s(; x); y) -> +(x; s(; y))}