YES(?,O(1)) 0.00/0.19 YES(?,O(1)) 0.00/0.19 0.00/0.19 We are left with following problem, upon which TcT provides the 0.00/0.19 certificate YES(?,O(1)). 0.00/0.19 0.00/0.19 Strict Trs: 0.00/0.19 { a__c() -> a__f(g(c())) 0.00/0.19 , a__c() -> c() 0.00/0.19 , a__f(X) -> f(X) 0.00/0.19 , a__f(g(X)) -> g(X) 0.00/0.19 , mark(g(X)) -> g(X) 0.00/0.19 , mark(c()) -> a__c() 0.00/0.19 , mark(f(X)) -> a__f(X) } 0.00/0.19 Obligation: 0.00/0.19 runtime complexity 0.00/0.19 Answer: 0.00/0.19 YES(?,O(1)) 0.00/0.19 0.00/0.19 The input is overlay and right-linear. Switching to innermost 0.00/0.19 rewriting. 0.00/0.19 0.00/0.19 We are left with following problem, upon which TcT provides the 0.00/0.19 certificate YES(?,O(1)). 0.00/0.19 0.00/0.19 Strict Trs: 0.00/0.19 { a__c() -> a__f(g(c())) 0.00/0.19 , a__c() -> c() 0.00/0.19 , a__f(X) -> f(X) 0.00/0.19 , a__f(g(X)) -> g(X) 0.00/0.19 , mark(g(X)) -> g(X) 0.00/0.19 , mark(c()) -> a__c() 0.00/0.19 , mark(f(X)) -> a__f(X) } 0.00/0.19 Obligation: 0.00/0.19 innermost runtime complexity 0.00/0.19 Answer: 0.00/0.19 YES(?,O(1)) 0.00/0.19 0.00/0.19 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.19 Order (PS,0-bounded)' as induced by the safe mapping 0.00/0.19 0.00/0.19 safe(a__c) = {}, safe(a__f) = {1}, safe(g) = {1}, safe(c) = {}, 0.00/0.19 safe(mark) = {}, safe(f) = {1} 0.00/0.19 0.00/0.19 and precedence 0.00/0.19 0.00/0.19 a__c > a__f, mark > a__c, mark > a__f . 0.00/0.19 0.00/0.19 Following symbols are considered recursive: 0.00/0.19 0.00/0.19 {} 0.00/0.19 0.00/0.19 The recursion depth is 0. 0.00/0.19 0.00/0.19 For your convenience, here are the satisfied ordering constraints: 0.00/0.19 0.00/0.19 a__c() > a__f(; g(; c())) 0.00/0.19 0.00/0.19 a__c() > c() 0.00/0.19 0.00/0.19 a__f(; X) > f(; X) 0.00/0.19 0.00/0.19 a__f(; g(; X)) > g(; X) 0.00/0.19 0.00/0.19 mark(g(; X);) > g(; X) 0.00/0.19 0.00/0.19 mark(c();) > a__c() 0.00/0.19 0.00/0.19 mark(f(; X);) > a__f(; X) 0.00/0.19 0.00/0.19 0.00/0.19 Hurray, we answered YES(?,O(1)) 0.00/0.19 EOF