MAYBE 197.79/60.04 MAYBE 197.79/60.04 197.79/60.04 We are left with following problem, upon which TcT provides the 197.79/60.04 certificate MAYBE. 197.79/60.04 197.79/60.04 Strict Trs: 197.79/60.04 { a(x, y) -> x 197.79/60.04 , a(x, y) -> y 197.79/60.04 , a(a(x, y), z) -> a(x, a(y, z)) 197.79/60.04 , a(lambda(x), y) -> lambda(a(x, a(y, t()))) 197.79/60.04 , a(lambda(x), y) -> lambda(a(x, 1())) 197.79/60.04 , lambda(x) -> x } 197.79/60.04 Obligation: 197.79/60.04 derivational complexity 197.79/60.04 Answer: 197.79/60.04 MAYBE 197.79/60.04 197.79/60.04 None of the processors succeeded. 197.79/60.04 197.79/60.04 Details of failed attempt(s): 197.79/60.04 ----------------------------- 197.79/60.04 1) 'Fastest (timeout of 60 seconds)' failed due to the following 197.79/60.04 reason: 197.79/60.04 197.79/60.04 Computation stopped due to timeout after 60.0 seconds. 197.79/60.04 197.79/60.04 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 197.79/60.04 the following reason: 197.79/60.04 197.79/60.04 We use the processor 'matrix interpretation of dimension 1' to 197.79/60.04 orient following rules strictly. 197.79/60.04 197.79/60.04 Trs: { lambda(x) -> x } 197.79/60.04 197.79/60.04 The induced complexity on above rules (modulo remaining rules) is 197.79/60.04 YES(?,O(n^1)) . These rules are moved into the corresponding weak 197.79/60.04 component(s). 197.79/60.04 197.79/60.04 Sub-proof: 197.79/60.04 ---------- 197.79/60.04 TcT has computed the following triangular matrix interpretation. 197.79/60.04 197.79/60.04 [a](x1, x2) = [1] x1 + [1] x2 + [0] 197.79/60.04 197.79/60.04 [lambda](x1) = [1] x1 + [2] 197.79/60.04 197.79/60.04 [1] = [0] 197.79/60.04 197.79/60.04 [t] = [0] 197.79/60.04 197.79/60.04 The order satisfies the following ordering constraints: 197.79/60.04 197.79/60.04 [a(x, y)] = [1] x + [1] y + [0] 197.79/60.04 >= [1] x + [0] 197.79/60.04 = [x] 197.79/60.04 197.79/60.04 [a(x, y)] = [1] x + [1] y + [0] 197.79/60.04 >= [1] y + [0] 197.79/60.04 = [y] 197.79/60.04 197.79/60.04 [a(a(x, y), z)] = [1] x + [1] y + [1] z + [0] 197.79/60.04 >= [1] x + [1] y + [1] z + [0] 197.79/60.04 = [a(x, a(y, z))] 197.79/60.04 197.79/60.04 [a(lambda(x), y)] = [1] x + [1] y + [2] 197.79/60.04 >= [1] x + [1] y + [2] 197.79/60.04 = [lambda(a(x, a(y, t())))] 197.79/60.04 197.79/60.04 [a(lambda(x), y)] = [1] x + [1] y + [2] 197.79/60.04 >= [1] x + [2] 197.79/60.04 = [lambda(a(x, 1()))] 197.79/60.04 197.79/60.04 [lambda(x)] = [1] x + [2] 197.79/60.04 > [1] x + [0] 197.79/60.04 = [x] 197.79/60.04 197.79/60.04 197.79/60.04 We return to the main proof. 197.79/60.04 197.79/60.04 We are left with following problem, upon which TcT provides the 197.79/60.04 certificate MAYBE. 197.79/60.04 197.79/60.04 Strict Trs: 197.79/60.04 { a(x, y) -> x 197.79/60.04 , a(x, y) -> y 197.79/60.04 , a(a(x, y), z) -> a(x, a(y, z)) 197.79/60.04 , a(lambda(x), y) -> lambda(a(x, a(y, t()))) 197.79/60.04 , a(lambda(x), y) -> lambda(a(x, 1())) } 197.79/60.04 Weak Trs: { lambda(x) -> x } 197.79/60.04 Obligation: 197.79/60.04 derivational complexity 197.79/60.04 Answer: 197.79/60.04 MAYBE 197.79/60.04 197.79/60.04 The weightgap principle applies (using the following nonconstant 197.79/60.04 growth matrix-interpretation) 197.79/60.04 197.79/60.04 TcT has computed the following triangular matrix interpretation. 197.79/60.04 Note that the diagonal of the component-wise maxima of 197.79/60.04 interpretation-entries contains no more than 1 non-zero entries. 197.79/60.04 197.79/60.04 [a](x1, x2) = [1] x1 + [1] x2 + [2] 197.79/60.04 197.79/60.04 [lambda](x1) = [1] x1 + [0] 197.79/60.04 197.79/60.04 [1] = [2] 197.79/60.04 197.79/60.04 [t] = [0] 197.79/60.04 197.79/60.04 The order satisfies the following ordering constraints: 197.79/60.04 197.79/60.04 [a(x, y)] = [1] x + [1] y + [2] 197.79/60.04 > [1] x + [0] 197.79/60.04 = [x] 197.79/60.04 197.79/60.04 [a(x, y)] = [1] x + [1] y + [2] 197.79/60.04 > [1] y + [0] 197.79/60.04 = [y] 197.79/60.04 197.79/60.04 [a(a(x, y), z)] = [1] x + [1] y + [1] z + [4] 197.79/60.04 >= [1] x + [1] y + [1] z + [4] 197.79/60.04 = [a(x, a(y, z))] 197.79/60.04 197.79/60.04 [a(lambda(x), y)] = [1] x + [1] y + [2] 197.79/60.04 ? [1] x + [1] y + [4] 197.79/60.04 = [lambda(a(x, a(y, t())))] 197.79/60.04 197.79/60.04 [a(lambda(x), y)] = [1] x + [1] y + [2] 197.79/60.04 ? [1] x + [4] 197.79/60.04 = [lambda(a(x, 1()))] 197.79/60.04 197.79/60.04 [lambda(x)] = [1] x + [0] 197.79/60.04 >= [1] x + [0] 197.79/60.04 = [x] 197.79/60.04 197.79/60.04 197.79/60.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 197.79/60.04 197.79/60.04 We are left with following problem, upon which TcT provides the 197.79/60.04 certificate MAYBE. 197.79/60.04 197.79/60.04 Strict Trs: 197.79/60.04 { a(a(x, y), z) -> a(x, a(y, z)) 197.79/60.04 , a(lambda(x), y) -> lambda(a(x, a(y, t()))) 197.79/60.04 , a(lambda(x), y) -> lambda(a(x, 1())) } 197.79/60.04 Weak Trs: 197.79/60.04 { a(x, y) -> x 197.79/60.04 , a(x, y) -> y 197.79/60.04 , lambda(x) -> x } 197.79/60.04 Obligation: 197.79/60.04 derivational complexity 197.79/60.04 Answer: 197.79/60.04 MAYBE 197.79/60.04 197.79/60.04 None of the processors succeeded. 197.79/60.04 197.79/60.04 Details of failed attempt(s): 197.79/60.04 ----------------------------- 197.79/60.04 1) 'empty' failed due to the following reason: 197.79/60.04 197.79/60.04 Empty strict component of the problem is NOT empty. 197.79/60.04 197.79/60.04 2) 'Fastest' failed due to the following reason: 197.79/60.04 197.79/60.04 None of the processors succeeded. 197.79/60.04 197.79/60.04 Details of failed attempt(s): 197.79/60.04 ----------------------------- 197.79/60.04 1) 'Fastest (timeout of 30 seconds)' failed due to the following 197.79/60.04 reason: 197.79/60.04 197.79/60.04 Computation stopped due to timeout after 30.0 seconds. 197.79/60.04 197.79/60.04 2) 'Fastest' failed due to the following reason: 197.79/60.04 197.79/60.04 None of the processors succeeded. 197.79/60.04 197.79/60.04 Details of failed attempt(s): 197.79/60.04 ----------------------------- 197.79/60.04 1) 'matrix interpretation of dimension 5' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 2) 'matrix interpretation of dimension 6' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 3) 'matrix interpretation of dimension 4' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 4) 'matrix interpretation of dimension 3' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 5) 'matrix interpretation of dimension 2' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 6) 'matrix interpretation of dimension 1' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 197.79/60.04 3) 'bsearch-matrix' failed due to the following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 4) 'iteProgress' failed due to the following reason: 197.79/60.04 197.79/60.04 Fail 197.79/60.04 197.79/60.04 197.79/60.04 197.79/60.04 3) 'iteProgress (timeout of 297 seconds)' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 Fail 197.79/60.04 197.79/60.04 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 197.79/60.04 following reason: 197.79/60.04 197.79/60.04 The input cannot be shown compatible 197.79/60.04 197.79/60.04 197.79/60.04 Arrrr.. 197.95/60.10 EOF