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