YES(O(1),O(n^1)) 495.29/193.58 YES(O(1),O(n^1)) 495.29/193.58 495.29/193.58 We are left with following problem, upon which TcT provides the 495.29/193.58 certificate YES(O(1),O(n^1)). 495.29/193.58 495.29/193.58 Strict Trs: 495.29/193.58 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.29/193.58 Obligation: 495.29/193.58 derivational complexity 495.29/193.58 Answer: 495.29/193.58 YES(O(1),O(n^1)) 495.29/193.58 495.29/193.58 The weightgap principle applies (using the following nonconstant 495.29/193.58 growth matrix-interpretation) 495.29/193.58 495.29/193.58 TcT has computed the following triangular matrix interpretation. 495.29/193.58 Note that the diagonal of the component-wise maxima of 495.29/193.58 interpretation-entries contains no more than 1 non-zero entries. 495.29/193.58 495.29/193.58 [0](x1) = [1] x1 + [0] 495.29/193.58 495.29/193.58 [1](x1) = [1] x1 + [2] 495.29/193.58 495.29/193.58 [2](x1) = [1] x1 + [1] 495.29/193.58 495.29/193.58 The order satisfies the following ordering constraints: 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [0(1(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(1(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [0(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [0(2(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [1(0(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [1(0(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [4] 495.29/193.58 = [1(0(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [1(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [1(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 >= [1] x1 + [4] 495.29/193.58 = [0(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [0(1(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 >= [1] x1 + [4] 495.29/193.58 = [0(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 >= [1] x1 + [4] 495.29/193.58 = [0(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [0(2(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [1(0(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [1(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [1(0(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [1(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [1(0(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [1(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 ? [1] x1 + [6] 495.29/193.58 = [1(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(1(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(2(0(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(2(1(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [0(2(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [1(0(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 >= [1] x1 + [6] 495.29/193.58 = [1(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [1(0(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 >= [1] x1 + [6] 495.29/193.58 = [1(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [1(0(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 >= [1] x1 + [6] 495.29/193.58 = [1(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 >= [1] x1 + [6] 495.29/193.58 = [1(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(2(0(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [1(2(2(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(1(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(0(1(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(1(2(0(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.58 ? [1] x1 + [5] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [4] 495.29/193.58 = [2(0(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [6] 495.29/193.58 > [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [5] 495.29/193.58 >= [1] x1 + [5] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 495.29/193.58 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 495.29/193.58 495.29/193.58 We are left with following problem, upon which TcT provides the 495.29/193.58 certificate YES(O(1),O(n^1)). 495.29/193.58 495.29/193.58 Strict Trs: 495.29/193.58 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.29/193.58 Weak Trs: 495.29/193.58 { 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) } 495.29/193.58 Obligation: 495.29/193.58 derivational complexity 495.29/193.58 Answer: 495.29/193.58 YES(O(1),O(n^1)) 495.29/193.58 495.29/193.58 The weightgap principle applies (using the following nonconstant 495.29/193.58 growth matrix-interpretation) 495.29/193.58 495.29/193.58 TcT has computed the following triangular matrix interpretation. 495.29/193.58 Note that the diagonal of the component-wise maxima of 495.29/193.58 interpretation-entries contains no more than 1 non-zero entries. 495.29/193.58 495.29/193.58 [0](x1) = [1] x1 + [0] 495.29/193.58 495.29/193.58 [1](x1) = [1] x1 + [1] 495.29/193.58 495.29/193.58 [2](x1) = [1] x1 + [0] 495.29/193.58 495.29/193.58 The order satisfies the following ordering constraints: 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 ? [1] x1 + [2] 495.29/193.58 = [0(1(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(1(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 ? [1] x1 + [2] 495.29/193.58 = [1(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 ? [1] x1 + [2] 495.29/193.58 = [1(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 ? [1] x1 + [2] 495.29/193.58 = [0(1(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [0(2(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [0(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(1(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(0(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(1(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(0(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [0(1(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [0(2(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [0(2(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(2(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 >= [1] x1 + [2] 495.29/193.58 = [1(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(2(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [1(2(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(0(1(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [1(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [1(2(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [1(0(2(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(1(2(2(0(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(0(1(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(1(2(0(x1)))))] 495.29/193.58 495.29/193.58 [2(0(1(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(0(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(0(2(1(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(1(2(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(1(0(2(x1)))))] = [1] x1 + [2] 495.29/193.58 > [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(0(1(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(1(0(2(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(1(0(2(x1)))))] 495.29/193.58 495.29/193.58 [2(1(2(0(2(x1)))))] = [1] x1 + [1] 495.29/193.58 >= [1] x1 + [1] 495.29/193.58 = [2(2(2(1(0(x1)))))] 495.29/193.58 495.29/193.58 495.29/193.58 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 495.29/193.58 495.29/193.58 We are left with following problem, upon which TcT provides the 495.29/193.58 certificate YES(O(1),O(n^1)). 495.29/193.58 495.29/193.58 Strict Trs: 495.29/193.58 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.58 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.58 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.58 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.29/193.59 Weak Trs: 495.29/193.59 { 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) } 495.29/193.59 Obligation: 495.29/193.59 derivational complexity 495.29/193.59 Answer: 495.29/193.59 YES(O(1),O(n^1)) 495.29/193.59 495.29/193.59 The weightgap principle applies (using the following nonconstant 495.29/193.59 growth matrix-interpretation) 495.29/193.59 495.29/193.59 TcT has computed the following triangular matrix interpretation. 495.29/193.59 Note that the diagonal of the component-wise maxima of 495.29/193.59 interpretation-entries contains no more than 1 non-zero entries. 495.29/193.59 495.29/193.59 [0](x1) = [1] x1 + [1] 495.29/193.59 495.29/193.59 [1](x1) = [1] x1 + [1] 495.29/193.59 495.29/193.59 [2](x1) = [1] x1 + [0] 495.29/193.59 495.29/193.59 The order satisfies the following ordering constraints: 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(1(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(1(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(1(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [0(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [0(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [0(1(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [0(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [0(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(0(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [3] 495.29/193.59 = [1(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(0(1(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1] x1 + [4] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [0(2(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(0(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(0(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(0(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [1(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(0(1(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [1(1(2(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [1(2(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.59 >= [1] x1 + [2] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(0(1(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(2(0(x1)))))] 495.29/193.59 495.29/193.59 [2(0(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [2(1(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 >= [1] x1 + [3] 495.29/193.59 = [2(0(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(1(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(1(0(2(x1)))))] = [1] x1 + [3] 495.29/193.59 > [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.59 >= [1] x1 + [2] 495.29/193.59 = [2(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.59 >= [1] x1 + [2] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.59 >= [1] x1 + [2] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [2(1(2(0(2(x1)))))] = [1] x1 + [2] 495.29/193.59 >= [1] x1 + [2] 495.29/193.59 = [2(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 495.29/193.59 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 495.29/193.59 495.29/193.59 We are left with following problem, upon which TcT provides the 495.29/193.59 certificate YES(O(1),O(n^1)). 495.29/193.59 495.29/193.59 Strict Trs: 495.29/193.59 { 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.59 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.29/193.59 Weak Trs: 495.29/193.59 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.59 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.59 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.59 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) } 495.29/193.59 Obligation: 495.29/193.59 derivational complexity 495.29/193.59 Answer: 495.29/193.59 YES(O(1),O(n^1)) 495.29/193.59 495.29/193.59 We use the processor 'matrix interpretation of dimension 3' to 495.29/193.59 orient following rules strictly. 495.29/193.59 495.29/193.59 Trs: 495.29/193.59 { 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.59 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.59 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.59 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.59 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.29/193.59 495.29/193.59 The induced complexity on above rules (modulo remaining rules) is 495.29/193.59 YES(?,O(n^1)) . These rules are moved into the corresponding weak 495.29/193.59 component(s). 495.29/193.59 495.29/193.59 Sub-proof: 495.29/193.59 ---------- 495.29/193.59 TcT has computed the following triangular matrix interpretation. 495.29/193.59 Note that the diagonal of the component-wise maxima of 495.29/193.59 interpretation-entries contains no more than 1 non-zero entries. 495.29/193.59 495.29/193.59 [1 1 0] [0] 495.29/193.59 [0](x1) = [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 495.29/193.59 [1 0 0] [1] 495.29/193.59 [1](x1) = [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 495.29/193.59 [1 1 0] [0] 495.29/193.59 [2](x1) = [0 0 0] x1 + [0] 495.29/193.59 [0 0 0] [0] 495.29/193.59 495.29/193.59 The order satisfies the following ordering constraints: 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(0(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(0(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [1] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [0] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [2(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [0] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [2(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [0] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [2(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(1(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(2(1(0(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(2(1(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [1] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(2(0(2(x1)))))] 495.29/193.59 495.29/193.59 [0(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(2(2(2(0(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(1(2(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [0(2(1(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 > [1 1 0] [2] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(0(2(2(x1)))))] 495.29/193.59 495.29/193.59 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 >= [1 1 0] [3] 495.29/193.59 [0 0 0] x1 + [1] 495.29/193.59 [0 0 0] [0] 495.29/193.59 = [1(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [1] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(0(1(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(2(1(0(x1)))))] 495.29/193.60 495.29/193.60 [1(0(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [1] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(0(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(0(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [0(1(2(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [0(2(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [0(2(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [1] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(2(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(0(1(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [1(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(2(1(0(x1)))))] 495.29/193.60 495.29/193.60 [1(2(2(0(2(x1)))))] = [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [1] 495.29/193.60 [0 0 0] x1 + [1] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [1(0(2(2(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(0(1(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(2(0(x1)))))] 495.29/193.60 495.29/193.60 [2(0(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(2(1(0(x1)))))] 495.29/193.60 495.29/193.60 [2(1(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(1(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 >= [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [2(1(2(0(2(x1)))))] = [1 1 0] [3] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 > [1 1 0] [2] 495.29/193.60 [0 0 0] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 = [2(2(2(1(0(x1)))))] 495.29/193.60 495.29/193.60 495.29/193.60 We return to the main proof. 495.29/193.60 495.29/193.60 We are left with following problem, upon which TcT provides the 495.29/193.60 certificate YES(O(1),O(n^1)). 495.29/193.60 495.29/193.60 Strict Trs: 495.29/193.60 { 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.60 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) } 495.29/193.60 Weak Trs: 495.29/193.60 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.60 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.60 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.60 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.60 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.60 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.60 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.60 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.60 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.60 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.29/193.60 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.29/193.60 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.29/193.60 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.29/193.60 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.29/193.60 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.29/193.60 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.29/193.60 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.29/193.60 Obligation: 495.29/193.60 derivational complexity 495.29/193.60 Answer: 495.29/193.60 YES(O(1),O(n^1)) 495.29/193.60 495.29/193.60 We use the processor 'matrix interpretation of dimension 3' to 495.29/193.60 orient following rules strictly. 495.29/193.60 495.29/193.60 Trs: 495.29/193.60 { 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.29/193.60 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.29/193.60 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) } 495.29/193.60 495.29/193.60 The induced complexity on above rules (modulo remaining rules) is 495.29/193.60 YES(?,O(n^1)) . These rules are moved into the corresponding weak 495.29/193.60 component(s). 495.29/193.60 495.29/193.60 Sub-proof: 495.29/193.60 ---------- 495.29/193.60 TcT has computed the following triangular matrix interpretation. 495.29/193.60 Note that the diagonal of the component-wise maxima of 495.29/193.60 interpretation-entries contains no more than 1 non-zero entries. 495.29/193.60 495.29/193.60 [1 1 0] [0] 495.29/193.60 [0](x1) = [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 495.29/193.60 [1 1 0] [0] 495.29/193.60 [1](x1) = [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 495.29/193.60 [1 1 0] [0] 495.29/193.60 [2](x1) = [0 0 1] x1 + [0] 495.29/193.60 [0 0 0] [0] 495.29/193.60 495.29/193.60 The order satisfies the following ordering constraints: 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [4] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(0(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(0(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [4] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(1(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [4] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(1(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(1(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 0] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(1(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [2] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(1(2(2(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(2(1(0(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [3] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(2(1(2(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 0] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(2(2(1(0(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [3] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [0(2(2(1(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [4] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [1(0(0(2(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [1(0(2(0(2(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 0] [5] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 = [1(0(2(2(0(x1)))))] 495.29/193.60 495.29/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.29/193.60 > [1 1 1] [2] 495.29/193.60 [0 0 0] x1 + [2] 495.29/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(2(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [4] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(1(0(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(0(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(1(0(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(2(0(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 0] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(2(2(0(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [4] 495.50/193.60 [0 0 0] x1 + [1] 495.50/193.60 [0 0 0] [0] 495.50/193.60 = [2(1(0(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [0] 495.50/193.60 [0 0 0] [0] 495.50/193.60 = [2(2(1(0(2(x1)))))] 495.50/193.60 495.50/193.60 [0(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 0] [5] 495.50/193.60 [0 0 0] x1 + [0] 495.50/193.60 [0 0 0] [0] 495.50/193.60 = [2(2(2(1(0(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [4] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(1(0(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [4] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(1(1(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [2] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(1(2(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 >= [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(2(1(0(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(2(1(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 >= [1 1 0] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(2(2(1(0(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(2(2(1(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [2] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(2(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(0(2(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(2(0(2(x1)))))] 495.50/193.60 495.50/193.60 [0(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 0] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(2(2(2(0(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [2] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(1(2(2(2(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [3] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [0(2(1(2(2(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [4] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(0(2(2(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [4] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(1(2(2(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(2(0(2(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(2(1(2(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 0] [5] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 = [1(0(2(2(0(x1)))))] 495.50/193.60 495.50/193.60 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.60 > [1 1 1] [2] 495.50/193.60 [0 0 0] x1 + [2] 495.50/193.60 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 0] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(0(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 0] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 0] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 0] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(0(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [1(2(2(0(2(x1)))))] = [1 1 1] [3] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 1 1] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(0(1(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 >= [1 1 0] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(2(0(x1)))))] 495.50/193.61 495.50/193.61 [2(0(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [2(1(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 >= [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(1(0(2(x1)))))] = [1 1 1] [6] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 > [1 1 1] [4] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 >= [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [2(1(2(0(2(x1)))))] = [1 1 1] [5] 495.50/193.61 [0 0 0] x1 + [1] 495.50/193.61 [0 0 0] [0] 495.50/193.61 >= [1 1 0] [5] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 495.50/193.61 We return to the main proof. 495.50/193.61 495.50/193.61 We are left with following problem, upon which TcT provides the 495.50/193.61 certificate YES(O(1),O(n^1)). 495.50/193.61 495.50/193.61 Strict Trs: 495.50/193.61 { 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) } 495.50/193.61 Weak Trs: 495.50/193.61 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.61 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.50/193.61 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.61 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.61 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.61 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.61 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.61 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.61 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.61 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.50/193.61 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.61 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.50/193.61 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.50/193.61 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.61 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.61 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.61 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.61 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.50/193.61 Obligation: 495.50/193.61 derivational complexity 495.50/193.61 Answer: 495.50/193.61 YES(O(1),O(n^1)) 495.50/193.61 495.50/193.61 We use the processor 'matrix interpretation of dimension 3' to 495.50/193.61 orient following rules strictly. 495.50/193.61 495.50/193.61 Trs: 495.50/193.61 { 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.50/193.61 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) } 495.50/193.61 495.50/193.61 The induced complexity on above rules (modulo remaining rules) is 495.50/193.61 YES(?,O(n^1)) . These rules are moved into the corresponding weak 495.50/193.61 component(s). 495.50/193.61 495.50/193.61 Sub-proof: 495.50/193.61 ---------- 495.50/193.61 TcT has computed the following triangular matrix interpretation. 495.50/193.61 Note that the diagonal of the component-wise maxima of 495.50/193.61 interpretation-entries contains no more than 1 non-zero entries. 495.50/193.61 495.50/193.61 [1 0 0] [2] 495.50/193.61 [0](x1) = [0 0 2] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 495.50/193.61 [1 1 0] [0] 495.50/193.61 [1](x1) = [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 495.50/193.61 [1 0 2] [0] 495.50/193.61 [2](x1) = [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 495.50/193.61 The order satisfies the following ordering constraints: 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 0] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 0] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 0] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [0(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 0] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 0] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 0] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 0] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(0(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 0] [6] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(2(1(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 0] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(0(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [0] 495.50/193.61 = [2(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(1(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [0] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [0(2(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(1(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(1(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 >= [1 0 0] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(0(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [2] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(0(2(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(1(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(0(2(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(1(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 > [1 0 2] [4] 495.50/193.61 [0 0 0] x1 + [2] 495.50/193.61 [0 0 0] [1] 495.50/193.61 = [1(2(2(0(2(x1)))))] 495.50/193.61 495.50/193.61 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 0] [4] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 = [1(2(2(2(0(x1)))))] 495.50/193.62 495.50/193.62 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(0(1(2(2(x1)))))] 495.50/193.62 495.50/193.62 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(0(2(2(x1)))))] 495.50/193.62 495.50/193.62 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 >= [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(2(0(2(x1)))))] 495.50/193.62 495.50/193.62 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(0(1(2(x1)))))] 495.50/193.62 495.50/193.62 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(1(0(2(x1)))))] 495.50/193.62 495.50/193.62 [1(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(2(1(0(x1)))))] 495.50/193.62 495.50/193.62 [1(2(2(0(2(x1)))))] = [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 > [1 0 2] [2] 495.50/193.62 [0 0 0] x1 + [2] 495.50/193.62 [0 0 0] [1] 495.50/193.62 = [1(0(2(2(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(0(1(2(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(0(2(1(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(0(2(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(2(0(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 0] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(2(2(0(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(0(1(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(1(0(2(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 0] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(1(2(0(x1)))))] 495.50/193.62 495.50/193.62 [2(0(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(2(1(0(x1)))))] 495.50/193.62 495.50/193.62 [2(1(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(0(1(0(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(0(2(1(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 >= [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(2(0(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(1(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(1(0(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(0(1(2(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(1(0(2(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(1(0(2(x1)))))] 495.50/193.62 495.50/193.62 [2(1(2(0(2(x1)))))] = [1 0 2] [6] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 > [1 0 2] [4] 495.50/193.62 [0 0 0] x1 + [0] 495.50/193.62 [0 0 0] [0] 495.50/193.62 = [2(2(2(1(0(x1)))))] 495.50/193.62 495.50/193.62 495.50/193.62 We return to the main proof. 495.50/193.62 495.50/193.62 We are left with following problem, upon which TcT provides the 495.50/193.62 certificate YES(O(1),O(1)). 495.50/193.62 495.50/193.62 Weak Trs: 495.50/193.62 { 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.62 , 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.50/193.62 , 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.62 , 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.62 , 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.62 , 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.62 , 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.62 , 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.62 , 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.62 , 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 495.50/193.62 , 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 495.50/193.62 , 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 495.50/193.62 , 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 495.50/193.62 , 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 495.50/193.62 , 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 495.50/193.62 , 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 495.50/193.62 , 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 495.50/193.62 , 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) } 495.50/193.62 Obligation: 495.50/193.62 derivational complexity 495.50/193.62 Answer: 495.50/193.62 YES(O(1),O(1)) 495.50/193.62 495.50/193.62 Empty rules are trivially bounded 495.50/193.62 495.50/193.62 Hurray, we answered YES(O(1),O(n^1)) 495.50/193.62 EOF