YES(O(1),O(n^2)) 160.83/60.06 YES(O(1),O(n^2)) 160.83/60.06 160.83/60.06 We are left with following problem, upon which TcT provides the 160.83/60.06 certificate YES(O(1),O(n^2)). 160.83/60.06 160.83/60.06 Strict Trs: 160.83/60.06 { f(f(a(), f(x, a())), a()) -> f(a(), f(f(x, a()), a())) } 160.83/60.06 Obligation: 160.83/60.06 derivational complexity 160.83/60.06 Answer: 160.83/60.06 YES(O(1),O(n^2)) 160.83/60.06 160.83/60.06 We use the processor 'matrix interpretation of dimension 2' to 160.83/60.06 orient following rules strictly. 160.83/60.06 160.83/60.06 Trs: { f(f(a(), f(x, a())), a()) -> f(a(), f(f(x, a()), a())) } 160.83/60.06 160.83/60.06 The induced complexity on above rules (modulo remaining rules) is 160.83/60.06 YES(?,O(n^2)) . These rules are moved into the corresponding weak 160.83/60.06 component(s). 160.83/60.06 160.83/60.06 Sub-proof: 160.83/60.06 ---------- 160.83/60.06 TcT has computed the following triangular matrix interpretation. 160.83/60.06 160.83/60.06 [f](x1, x2) = [1 2] x1 + [1 0] x2 + [0] 160.83/60.06 [0 1] [0 1] [1] 160.83/60.06 160.83/60.06 [a] = [0] 160.83/60.06 [0] 160.83/60.06 160.83/60.06 The order satisfies the following ordering constraints: 160.83/60.06 160.83/60.06 [f(f(a(), f(x, a())), a())] = [1 4] x + [4] 160.83/60.06 [0 1] [3] 160.83/60.06 > [1 4] x + [2] 160.83/60.06 [0 1] [3] 160.83/60.06 = [f(a(), f(f(x, a()), a()))] 160.83/60.06 160.83/60.06 160.83/60.06 We return to the main proof. 160.83/60.06 160.83/60.06 We are left with following problem, upon which TcT provides the 160.83/60.06 certificate YES(O(1),O(1)). 160.83/60.06 160.83/60.06 Weak Trs: 160.83/60.06 { f(f(a(), f(x, a())), a()) -> f(a(), f(f(x, a()), a())) } 160.83/60.06 Obligation: 160.83/60.06 derivational complexity 160.83/60.06 Answer: 160.83/60.06 YES(O(1),O(1)) 160.83/60.06 160.83/60.06 Empty rules are trivially bounded 160.83/60.06 160.83/60.06 Hurray, we answered YES(O(1),O(n^2)) 160.83/60.07 EOF