MAYBE 198.57/60.27 MAYBE 198.57/60.27 198.57/60.27 We are left with following problem, upon which TcT provides the 198.57/60.27 certificate MAYBE. 198.57/60.27 198.57/60.27 Strict Trs: 198.57/60.27 { :(x, x) -> e() 198.57/60.27 , :(x, :(y, :(i(x), z))) -> :(i(z), y) 198.57/60.27 , :(x, :(y, i(x))) -> i(y) 198.57/60.27 , :(x, e()) -> x 198.57/60.27 , :(:(x, y), z) -> :(x, :(z, i(y))) 198.57/60.27 , :(e(), x) -> i(x) 198.57/60.27 , :(i(x), :(y, x)) -> i(y) 198.57/60.27 , :(i(x), :(y, :(x, z))) -> :(i(z), y) 198.57/60.27 , i(:(x, y)) -> :(y, x) 198.57/60.27 , i(e()) -> e() 198.57/60.27 , i(i(x)) -> x } 198.57/60.27 Obligation: 198.57/60.27 derivational complexity 198.57/60.27 Answer: 198.57/60.27 MAYBE 198.57/60.27 198.57/60.27 None of the processors succeeded. 198.57/60.27 198.57/60.27 Details of failed attempt(s): 198.57/60.27 ----------------------------- 198.57/60.27 1) 'Fastest (timeout of 60 seconds)' failed due to the following 198.57/60.27 reason: 198.57/60.27 198.57/60.27 Computation stopped due to timeout after 60.0 seconds. 198.57/60.27 198.57/60.27 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 198.57/60.27 the following reason: 198.57/60.27 198.57/60.27 We use the processor 'matrix interpretation of dimension 1' to 198.57/60.27 orient following rules strictly. 198.57/60.27 198.57/60.27 Trs: 198.57/60.27 { :(x, x) -> e() 198.57/60.27 , :(x, :(y, :(i(x), z))) -> :(i(z), y) 198.57/60.27 , :(x, :(y, i(x))) -> i(y) 198.57/60.27 , :(x, e()) -> x 198.57/60.27 , :(e(), x) -> i(x) 198.57/60.27 , :(i(x), :(y, x)) -> i(y) 198.57/60.27 , :(i(x), :(y, :(x, z))) -> :(i(z), y) } 198.57/60.27 198.57/60.27 The induced complexity on above rules (modulo remaining rules) is 198.57/60.27 YES(?,O(n^1)) . These rules are moved into the corresponding weak 198.57/60.27 component(s). 198.57/60.27 198.57/60.27 Sub-proof: 198.57/60.27 ---------- 198.57/60.27 TcT has computed the following triangular matrix interpretation. 198.57/60.27 198.57/60.27 [:](x1, x2) = [1] x1 + [1] x2 + [2] 198.57/60.27 198.57/60.27 [e] = [1] 198.57/60.27 198.57/60.27 [i](x1) = [1] x1 + [0] 198.57/60.27 198.57/60.27 The order satisfies the following ordering constraints: 198.57/60.27 198.57/60.27 [:(x, x)] = [2] x + [2] 198.57/60.27 > [1] 198.57/60.27 = [e()] 198.57/60.27 198.57/60.27 [:(x, :(y, :(i(x), z)))] = [2] x + [1] y + [1] z + [6] 198.57/60.27 > [1] y + [1] z + [2] 198.57/60.27 = [:(i(z), y)] 198.57/60.27 198.57/60.27 [:(x, :(y, i(x)))] = [2] x + [1] y + [4] 198.57/60.27 > [1] y + [0] 198.57/60.27 = [i(y)] 198.57/60.27 198.57/60.27 [:(x, e())] = [1] x + [3] 198.57/60.27 > [1] x + [0] 198.57/60.27 = [x] 198.57/60.27 198.57/60.27 [:(:(x, y), z)] = [1] x + [1] y + [1] z + [4] 198.57/60.27 >= [1] x + [1] y + [1] z + [4] 198.57/60.27 = [:(x, :(z, i(y)))] 198.57/60.27 198.57/60.27 [:(e(), x)] = [1] x + [3] 198.57/60.27 > [1] x + [0] 198.57/60.27 = [i(x)] 198.57/60.27 198.57/60.27 [:(i(x), :(y, x))] = [2] x + [1] y + [4] 198.57/60.27 > [1] y + [0] 198.57/60.27 = [i(y)] 198.57/60.27 198.57/60.27 [:(i(x), :(y, :(x, z)))] = [2] x + [1] y + [1] z + [6] 198.57/60.27 > [1] y + [1] z + [2] 198.57/60.27 = [:(i(z), y)] 198.57/60.27 198.57/60.27 [i(:(x, y))] = [1] x + [1] y + [2] 198.57/60.27 >= [1] x + [1] y + [2] 198.57/60.27 = [:(y, x)] 198.57/60.27 198.57/60.27 [i(e())] = [1] 198.57/60.27 >= [1] 198.57/60.27 = [e()] 198.57/60.27 198.57/60.27 [i(i(x))] = [1] x + [0] 198.57/60.27 >= [1] x + [0] 198.57/60.27 = [x] 198.57/60.27 198.57/60.27 198.57/60.27 We return to the main proof. 198.57/60.27 198.57/60.27 We are left with following problem, upon which TcT provides the 198.57/60.27 certificate MAYBE. 198.57/60.27 198.57/60.27 Strict Trs: 198.57/60.27 { :(:(x, y), z) -> :(x, :(z, i(y))) 198.57/60.27 , i(:(x, y)) -> :(y, x) 198.57/60.27 , i(e()) -> e() 198.57/60.27 , i(i(x)) -> x } 198.57/60.27 Weak Trs: 198.57/60.27 { :(x, x) -> e() 198.57/60.27 , :(x, :(y, :(i(x), z))) -> :(i(z), y) 198.57/60.27 , :(x, :(y, i(x))) -> i(y) 198.57/60.27 , :(x, e()) -> x 198.57/60.27 , :(e(), x) -> i(x) 198.57/60.27 , :(i(x), :(y, x)) -> i(y) 198.57/60.27 , :(i(x), :(y, :(x, z))) -> :(i(z), y) } 198.57/60.27 Obligation: 198.57/60.27 derivational complexity 198.57/60.27 Answer: 198.57/60.27 MAYBE 198.57/60.27 198.57/60.27 The weightgap principle applies (using the following nonconstant 198.57/60.27 growth matrix-interpretation) 198.57/60.27 198.57/60.27 TcT has computed the following triangular matrix interpretation. 198.57/60.27 Note that the diagonal of the component-wise maxima of 198.57/60.27 interpretation-entries contains no more than 1 non-zero entries. 198.57/60.27 198.57/60.27 [:](x1, x2) = [1] x1 + [1] x2 + [2] 198.57/60.27 198.57/60.27 [e] = [1] 198.57/60.27 198.57/60.27 [i](x1) = [1] x1 + [1] 198.57/60.27 198.57/60.27 The order satisfies the following ordering constraints: 198.57/60.27 198.57/60.27 [:(x, x)] = [2] x + [2] 198.57/60.27 > [1] 198.57/60.27 = [e()] 198.57/60.27 198.57/60.27 [:(x, :(y, :(i(x), z)))] = [2] x + [1] y + [1] z + [7] 198.57/60.27 > [1] y + [1] z + [3] 198.57/60.27 = [:(i(z), y)] 198.57/60.27 198.57/60.27 [:(x, :(y, i(x)))] = [2] x + [1] y + [5] 198.57/60.27 > [1] y + [1] 198.57/60.27 = [i(y)] 198.57/60.27 198.57/60.27 [:(x, e())] = [1] x + [3] 198.57/60.27 > [1] x + [0] 198.57/60.27 = [x] 198.57/60.27 198.57/60.27 [:(:(x, y), z)] = [1] x + [1] y + [1] z + [4] 198.57/60.27 ? [1] x + [1] y + [1] z + [5] 198.57/60.27 = [:(x, :(z, i(y)))] 198.57/60.27 198.57/60.27 [:(e(), x)] = [1] x + [3] 198.57/60.27 > [1] x + [1] 198.57/60.27 = [i(x)] 198.57/60.27 198.57/60.27 [:(i(x), :(y, x))] = [2] x + [1] y + [5] 198.57/60.27 > [1] y + [1] 198.57/60.27 = [i(y)] 198.57/60.27 198.57/60.27 [:(i(x), :(y, :(x, z)))] = [2] x + [1] y + [1] z + [7] 198.57/60.27 > [1] y + [1] z + [3] 198.57/60.27 = [:(i(z), y)] 198.57/60.27 198.57/60.27 [i(:(x, y))] = [1] x + [1] y + [3] 198.57/60.27 > [1] x + [1] y + [2] 198.57/60.27 = [:(y, x)] 198.57/60.27 198.57/60.27 [i(e())] = [2] 198.57/60.27 > [1] 198.57/60.27 = [e()] 198.57/60.27 198.57/60.27 [i(i(x))] = [1] x + [2] 198.57/60.27 > [1] x + [0] 198.57/60.27 = [x] 198.57/60.27 198.57/60.27 198.57/60.27 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 198.57/60.27 198.57/60.27 We are left with following problem, upon which TcT provides the 198.57/60.27 certificate MAYBE. 198.57/60.27 198.57/60.27 Strict Trs: { :(:(x, y), z) -> :(x, :(z, i(y))) } 198.57/60.27 Weak Trs: 198.57/60.27 { :(x, x) -> e() 198.57/60.27 , :(x, :(y, :(i(x), z))) -> :(i(z), y) 198.57/60.27 , :(x, :(y, i(x))) -> i(y) 198.57/60.27 , :(x, e()) -> x 198.57/60.27 , :(e(), x) -> i(x) 198.57/60.27 , :(i(x), :(y, x)) -> i(y) 198.57/60.27 , :(i(x), :(y, :(x, z))) -> :(i(z), y) 198.57/60.27 , i(:(x, y)) -> :(y, x) 198.57/60.27 , i(e()) -> e() 198.57/60.27 , i(i(x)) -> x } 198.57/60.27 Obligation: 198.57/60.27 derivational complexity 198.57/60.27 Answer: 198.57/60.27 MAYBE 198.57/60.27 198.57/60.27 None of the processors succeeded. 198.57/60.27 198.57/60.27 Details of failed attempt(s): 198.57/60.27 ----------------------------- 198.57/60.27 1) 'empty' failed due to the following reason: 198.57/60.27 198.57/60.27 Empty strict component of the problem is NOT empty. 198.57/60.27 198.57/60.27 2) 'Fastest' failed due to the following reason: 198.57/60.27 198.57/60.27 None of the processors succeeded. 198.57/60.27 198.57/60.27 Details of failed attempt(s): 198.57/60.27 ----------------------------- 198.57/60.27 1) 'Fastest (timeout of 30 seconds)' failed due to the following 198.57/60.27 reason: 198.57/60.27 198.57/60.27 Computation stopped due to timeout after 30.0 seconds. 198.57/60.27 198.57/60.27 2) 'Fastest' failed due to the following reason: 198.57/60.27 198.57/60.27 None of the processors succeeded. 198.57/60.27 198.57/60.27 Details of failed attempt(s): 198.57/60.27 ----------------------------- 198.57/60.27 1) 'matrix interpretation of dimension 6' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 2) 'matrix interpretation of dimension 5' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 3) 'matrix interpretation of dimension 4' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 4) 'matrix interpretation of dimension 3' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 5) 'matrix interpretation of dimension 2' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 6) 'matrix interpretation of dimension 1' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 198.57/60.27 3) 'iteProgress' failed due to the following reason: 198.57/60.27 198.57/60.27 Fail 198.57/60.27 198.57/60.27 4) 'bsearch-matrix' failed due to the following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 198.57/60.27 198.57/60.27 3) 'iteProgress (timeout of 297 seconds)' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 Fail 198.57/60.27 198.57/60.27 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 198.57/60.27 following reason: 198.57/60.27 198.57/60.27 The input cannot be shown compatible 198.57/60.27 198.57/60.27 198.57/60.27 Arrrr.. 198.87/60.36 EOF