MAYBE 201.18/60.03 MAYBE 201.18/60.03 201.18/60.03 We are left with following problem, upon which TcT provides the 201.18/60.03 certificate MAYBE. 201.18/60.03 201.18/60.03 Strict Trs: 201.18/60.03 { if(x, y, y) -> y 201.18/60.03 , if(if(x, y, z), u(), v()) -> 201.18/60.03 if(x, if(y, u(), v()), if(z, u(), v())) 201.18/60.03 , if(true(), x, y) -> x 201.18/60.03 , if(false(), x, y) -> y } 201.18/60.03 Obligation: 201.18/60.03 derivational complexity 201.18/60.03 Answer: 201.18/60.03 MAYBE 201.18/60.03 201.18/60.03 None of the processors succeeded. 201.18/60.03 201.18/60.03 Details of failed attempt(s): 201.18/60.03 ----------------------------- 201.18/60.03 1) 'Fastest (timeout of 60 seconds)' failed due to the following 201.18/60.03 reason: 201.18/60.03 201.18/60.03 Computation stopped due to timeout after 60.0 seconds. 201.18/60.03 201.18/60.03 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 201.18/60.03 the following reason: 201.18/60.03 201.18/60.03 We use the processor 'matrix interpretation of dimension 1' to 201.18/60.03 orient following rules strictly. 201.18/60.03 201.18/60.03 Trs: 201.18/60.03 { if(true(), x, y) -> x 201.18/60.03 , if(false(), x, y) -> y } 201.18/60.03 201.18/60.03 The induced complexity on above rules (modulo remaining rules) is 201.18/60.03 YES(?,O(n^1)) . These rules are moved into the corresponding weak 201.18/60.03 component(s). 201.18/60.03 201.18/60.03 Sub-proof: 201.18/60.03 ---------- 201.18/60.03 TcT has computed the following triangular matrix interpretation. 201.18/60.03 201.18/60.03 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 201.18/60.03 201.18/60.03 [true] = [2] 201.18/60.03 201.18/60.03 [false] = [2] 201.18/60.03 201.18/60.03 [u] = [0] 201.18/60.03 201.18/60.03 [v] = [0] 201.18/60.03 201.18/60.03 The order satisfies the following ordering constraints: 201.18/60.03 201.18/60.03 [if(x, y, y)] = [1] x + [2] y + [0] 201.18/60.03 >= [1] y + [0] 201.18/60.03 = [y] 201.18/60.03 201.18/60.03 [if(if(x, y, z), u(), v())] = [1] x + [1] y + [1] z + [0] 201.18/60.03 >= [1] x + [1] y + [1] z + [0] 201.18/60.03 = [if(x, if(y, u(), v()), if(z, u(), v()))] 201.18/60.03 201.18/60.03 [if(true(), x, y)] = [1] x + [1] y + [2] 201.18/60.03 > [1] x + [0] 201.18/60.03 = [x] 201.18/60.03 201.18/60.03 [if(false(), x, y)] = [1] x + [1] y + [2] 201.18/60.03 > [1] y + [0] 201.18/60.03 = [y] 201.18/60.03 201.18/60.03 201.18/60.03 We return to the main proof. 201.18/60.03 201.18/60.03 We are left with following problem, upon which TcT provides the 201.18/60.03 certificate MAYBE. 201.18/60.03 201.18/60.03 Strict Trs: 201.18/60.03 { if(x, y, y) -> y 201.18/60.03 , if(if(x, y, z), u(), v()) -> 201.18/60.03 if(x, if(y, u(), v()), if(z, u(), v())) } 201.18/60.03 Weak Trs: 201.18/60.03 { if(true(), x, y) -> x 201.18/60.03 , if(false(), x, y) -> y } 201.18/60.03 Obligation: 201.18/60.03 derivational complexity 201.18/60.03 Answer: 201.18/60.03 MAYBE 201.18/60.03 201.18/60.03 The weightgap principle applies (using the following nonconstant 201.18/60.03 growth matrix-interpretation) 201.18/60.03 201.18/60.03 TcT has computed the following triangular matrix interpretation. 201.18/60.03 Note that the diagonal of the component-wise maxima of 201.18/60.03 interpretation-entries contains no more than 1 non-zero entries. 201.18/60.03 201.18/60.03 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [2] 201.18/60.03 201.18/60.03 [true] = [1] 201.18/60.03 201.18/60.03 [false] = [1] 201.18/60.03 201.18/60.03 [u] = [0] 201.18/60.03 201.18/60.03 [v] = [0] 201.18/60.03 201.18/60.03 The order satisfies the following ordering constraints: 201.18/60.03 201.18/60.03 [if(x, y, y)] = [1] x + [2] y + [2] 201.18/60.03 > [1] y + [0] 201.18/60.03 = [y] 201.18/60.03 201.18/60.03 [if(if(x, y, z), u(), v())] = [1] x + [1] y + [1] z + [4] 201.18/60.03 ? [1] x + [1] y + [1] z + [6] 201.18/60.03 = [if(x, if(y, u(), v()), if(z, u(), v()))] 201.18/60.03 201.18/60.03 [if(true(), x, y)] = [1] x + [1] y + [3] 201.18/60.03 > [1] x + [0] 201.18/60.03 = [x] 201.18/60.03 201.18/60.03 [if(false(), x, y)] = [1] x + [1] y + [3] 201.18/60.03 > [1] y + [0] 201.18/60.03 = [y] 201.18/60.03 201.18/60.03 201.18/60.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 201.18/60.03 201.18/60.03 We are left with following problem, upon which TcT provides the 201.18/60.03 certificate MAYBE. 201.18/60.03 201.18/60.03 Strict Trs: 201.18/60.03 { if(if(x, y, z), u(), v()) -> 201.18/60.03 if(x, if(y, u(), v()), if(z, u(), v())) } 201.18/60.03 Weak Trs: 201.18/60.03 { if(x, y, y) -> y 201.18/60.03 , if(true(), x, y) -> x 201.18/60.03 , if(false(), x, y) -> y } 201.18/60.03 Obligation: 201.18/60.03 derivational complexity 201.18/60.03 Answer: 201.18/60.03 MAYBE 201.18/60.03 201.18/60.03 None of the processors succeeded. 201.18/60.03 201.18/60.03 Details of failed attempt(s): 201.18/60.03 ----------------------------- 201.18/60.03 1) 'empty' failed due to the following reason: 201.18/60.03 201.18/60.03 Empty strict component of the problem is NOT empty. 201.18/60.03 201.18/60.03 2) 'Fastest' failed due to the following reason: 201.18/60.03 201.18/60.03 None of the processors succeeded. 201.18/60.03 201.18/60.03 Details of failed attempt(s): 201.18/60.03 ----------------------------- 201.18/60.03 1) 'Fastest (timeout of 30 seconds)' failed due to the following 201.18/60.03 reason: 201.18/60.03 201.18/60.03 Computation stopped due to timeout after 30.0 seconds. 201.18/60.03 201.18/60.03 2) 'Fastest' failed due to the following reason: 201.18/60.03 201.18/60.03 None of the processors succeeded. 201.18/60.03 201.18/60.03 Details of failed attempt(s): 201.18/60.03 ----------------------------- 201.18/60.03 1) 'matrix interpretation of dimension 6' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 2) 'matrix interpretation of dimension 5' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 3) 'matrix interpretation of dimension 4' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 4) 'matrix interpretation of dimension 3' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 5) 'matrix interpretation of dimension 2' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 6) 'matrix interpretation of dimension 1' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 201.18/60.03 3) 'iteProgress' failed due to the following reason: 201.18/60.03 201.18/60.03 Fail 201.18/60.03 201.18/60.03 4) 'bsearch-matrix' failed due to the following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 201.18/60.03 201.18/60.03 3) 'iteProgress (timeout of 297 seconds)' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 Fail 201.18/60.03 201.18/60.03 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 201.18/60.03 following reason: 201.18/60.03 201.18/60.03 The input cannot be shown compatible 201.18/60.03 201.18/60.03 201.18/60.03 Arrrr.. 201.18/60.03 EOF