YES(?,O(n^1)) 667.36/225.16 YES(?,O(n^1)) 667.36/225.16 667.36/225.16 We are left with following problem, upon which TcT provides the 667.36/225.16 certificate YES(?,O(n^1)). 667.36/225.16 667.36/225.16 Strict Trs: 667.36/225.16 { a(a(f(x, y))) -> f(a(b(a(b(a(x))))), a(b(a(b(a(y)))))) 667.36/225.16 , f(a(x), a(y)) -> a(f(x, y)) 667.36/225.16 , f(b(x), b(y)) -> b(f(x, y)) } 667.36/225.16 Obligation: 667.36/225.16 innermost runtime complexity 667.36/225.16 Answer: 667.36/225.16 YES(?,O(n^1)) 667.36/225.16 667.36/225.16 The problem is match-bounded by 1. The enriched problem is 667.36/225.16 compatible with the following automaton. 667.36/225.16 { a_0(2) -> 1 667.36/225.16 , f_0(2, 2) -> 1 667.36/225.16 , f_1(2, 2) -> 3 667.36/225.16 , b_0(2) -> 2 667.36/225.16 , b_1(3) -> 1 667.36/225.16 , b_1(3) -> 3 } 667.36/225.16 667.36/225.16 Hurray, we answered YES(?,O(n^1)) 667.82/225.45 EOF