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