MAYBE 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 We are left with following problem, upon which TcT provides the 198.29/60.05 certificate MAYBE. 198.29/60.05 198.29/60.05 Strict Trs: 198.29/60.05 { f(X) -> if(X, c(), n__f(n__true())) 198.29/60.05 , f(X) -> n__f(X) 198.29/60.05 , if(true(), X, Y) -> X 198.29/60.05 , if(false(), X, Y) -> activate(Y) 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X 198.29/60.05 , activate(n__f(X)) -> f(activate(X)) 198.29/60.05 , activate(n__true()) -> true() } 198.29/60.05 Obligation: 198.29/60.05 derivational complexity 198.29/60.05 Answer: 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 None of the processors succeeded. 198.29/60.05 198.29/60.05 Details of failed attempt(s): 198.29/60.05 ----------------------------- 198.29/60.05 1) 'Fastest (timeout of 60 seconds)' failed due to the following 198.29/60.05 reason: 198.29/60.05 198.29/60.05 Computation stopped due to timeout after 60.0 seconds. 198.29/60.05 198.29/60.05 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 198.29/60.05 the following reason: 198.29/60.05 198.29/60.05 We use the processor 'matrix interpretation of dimension 1' to 198.29/60.05 orient following rules strictly. 198.29/60.05 198.29/60.05 Trs: { if(false(), X, Y) -> activate(Y) } 198.29/60.05 198.29/60.05 The induced complexity on above rules (modulo remaining rules) is 198.29/60.05 YES(?,O(n^1)) . These rules are moved into the corresponding weak 198.29/60.05 component(s). 198.29/60.05 198.29/60.05 Sub-proof: 198.29/60.05 ---------- 198.29/60.05 TcT has computed the following triangular matrix interpretation. 198.29/60.05 198.29/60.05 [f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 198.29/60.05 198.29/60.05 [c] = [0] 198.29/60.05 198.29/60.05 [n__f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [n__true] = [0] 198.29/60.05 198.29/60.05 [true] = [0] 198.29/60.05 198.29/60.05 [false] = [2] 198.29/60.05 198.29/60.05 [activate](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 The order satisfies the following ordering constraints: 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [if(X, c(), n__f(n__true()))] 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [n__f(X)] 198.29/60.05 198.29/60.05 [if(true(), X, Y)] = [1] X + [1] Y + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [if(false(), X, Y)] = [1] X + [1] Y + [2] 198.29/60.05 > [1] Y + [0] 198.29/60.05 = [activate(Y)] 198.29/60.05 198.29/60.05 [true()] = [0] 198.29/60.05 >= [0] 198.29/60.05 = [n__true()] 198.29/60.05 198.29/60.05 [activate(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [activate(n__f(X))] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [f(activate(X))] 198.29/60.05 198.29/60.05 [activate(n__true())] = [0] 198.29/60.05 >= [0] 198.29/60.05 = [true()] 198.29/60.05 198.29/60.05 198.29/60.05 We return to the main proof. 198.29/60.05 198.29/60.05 We are left with following problem, upon which TcT provides the 198.29/60.05 certificate MAYBE. 198.29/60.05 198.29/60.05 Strict Trs: 198.29/60.05 { f(X) -> if(X, c(), n__f(n__true())) 198.29/60.05 , f(X) -> n__f(X) 198.29/60.05 , if(true(), X, Y) -> X 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X 198.29/60.05 , activate(n__f(X)) -> f(activate(X)) 198.29/60.05 , activate(n__true()) -> true() } 198.29/60.05 Weak Trs: { if(false(), X, Y) -> activate(Y) } 198.29/60.05 Obligation: 198.29/60.05 derivational complexity 198.29/60.05 Answer: 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 We use the processor 'matrix interpretation of dimension 1' to 198.29/60.05 orient following rules strictly. 198.29/60.05 198.29/60.05 Trs: 198.29/60.05 { if(true(), X, Y) -> X 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X } 198.29/60.05 198.29/60.05 The induced complexity on above rules (modulo remaining rules) is 198.29/60.05 YES(?,O(n^1)) . These rules are moved into the corresponding weak 198.29/60.05 component(s). 198.29/60.05 198.29/60.05 Sub-proof: 198.29/60.05 ---------- 198.29/60.05 TcT has computed the following triangular matrix interpretation. 198.29/60.05 198.29/60.05 [f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 198.29/60.05 198.29/60.05 [c] = [0] 198.29/60.05 198.29/60.05 [n__f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [n__true] = [0] 198.29/60.05 198.29/60.05 [true] = [1] 198.29/60.05 198.29/60.05 [false] = [2] 198.29/60.05 198.29/60.05 [activate](x1) = [1] x1 + [1] 198.29/60.05 198.29/60.05 The order satisfies the following ordering constraints: 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [if(X, c(), n__f(n__true()))] 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [n__f(X)] 198.29/60.05 198.29/60.05 [if(true(), X, Y)] = [1] X + [1] Y + [1] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [if(false(), X, Y)] = [1] X + [1] Y + [2] 198.29/60.05 > [1] Y + [1] 198.29/60.05 = [activate(Y)] 198.29/60.05 198.29/60.05 [true()] = [1] 198.29/60.05 > [0] 198.29/60.05 = [n__true()] 198.29/60.05 198.29/60.05 [activate(X)] = [1] X + [1] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [activate(n__f(X))] = [1] X + [1] 198.29/60.05 >= [1] X + [1] 198.29/60.05 = [f(activate(X))] 198.29/60.05 198.29/60.05 [activate(n__true())] = [1] 198.29/60.05 >= [1] 198.29/60.05 = [true()] 198.29/60.05 198.29/60.05 198.29/60.05 We return to the main proof. 198.29/60.05 198.29/60.05 We are left with following problem, upon which TcT provides the 198.29/60.05 certificate MAYBE. 198.29/60.05 198.29/60.05 Strict Trs: 198.29/60.05 { f(X) -> if(X, c(), n__f(n__true())) 198.29/60.05 , f(X) -> n__f(X) 198.29/60.05 , activate(n__f(X)) -> f(activate(X)) 198.29/60.05 , activate(n__true()) -> true() } 198.29/60.05 Weak Trs: 198.29/60.05 { if(true(), X, Y) -> X 198.29/60.05 , if(false(), X, Y) -> activate(Y) 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X } 198.29/60.05 Obligation: 198.29/60.05 derivational complexity 198.29/60.05 Answer: 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 We use the processor 'matrix interpretation of dimension 1' to 198.29/60.05 orient following rules strictly. 198.29/60.05 198.29/60.05 Trs: { activate(n__true()) -> true() } 198.29/60.05 198.29/60.05 The induced complexity on above rules (modulo remaining rules) is 198.29/60.05 YES(?,O(n^1)) . These rules are moved into the corresponding weak 198.29/60.05 component(s). 198.29/60.05 198.29/60.05 Sub-proof: 198.29/60.05 ---------- 198.29/60.05 TcT has computed the following triangular matrix interpretation. 198.29/60.05 198.29/60.05 [f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 198.29/60.05 198.29/60.05 [c] = [0] 198.29/60.05 198.29/60.05 [n__f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [n__true] = [0] 198.29/60.05 198.29/60.05 [true] = [0] 198.29/60.05 198.29/60.05 [false] = [2] 198.29/60.05 198.29/60.05 [activate](x1) = [1] x1 + [1] 198.29/60.05 198.29/60.05 The order satisfies the following ordering constraints: 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [if(X, c(), n__f(n__true()))] 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [n__f(X)] 198.29/60.05 198.29/60.05 [if(true(), X, Y)] = [1] X + [1] Y + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [if(false(), X, Y)] = [1] X + [1] Y + [2] 198.29/60.05 > [1] Y + [1] 198.29/60.05 = [activate(Y)] 198.29/60.05 198.29/60.05 [true()] = [0] 198.29/60.05 >= [0] 198.29/60.05 = [n__true()] 198.29/60.05 198.29/60.05 [activate(X)] = [1] X + [1] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [activate(n__f(X))] = [1] X + [1] 198.29/60.05 >= [1] X + [1] 198.29/60.05 = [f(activate(X))] 198.29/60.05 198.29/60.05 [activate(n__true())] = [1] 198.29/60.05 > [0] 198.29/60.05 = [true()] 198.29/60.05 198.29/60.05 198.29/60.05 We return to the main proof. 198.29/60.05 198.29/60.05 We are left with following problem, upon which TcT provides the 198.29/60.05 certificate MAYBE. 198.29/60.05 198.29/60.05 Strict Trs: 198.29/60.05 { f(X) -> if(X, c(), n__f(n__true())) 198.29/60.05 , f(X) -> n__f(X) 198.29/60.05 , activate(n__f(X)) -> f(activate(X)) } 198.29/60.05 Weak Trs: 198.29/60.05 { if(true(), X, Y) -> X 198.29/60.05 , if(false(), X, Y) -> activate(Y) 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X 198.29/60.05 , activate(n__true()) -> true() } 198.29/60.05 Obligation: 198.29/60.05 derivational complexity 198.29/60.05 Answer: 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 The weightgap principle applies (using the following nonconstant 198.29/60.05 growth matrix-interpretation) 198.29/60.05 198.29/60.05 TcT has computed the following triangular matrix interpretation. 198.29/60.05 Note that the diagonal of the component-wise maxima of 198.29/60.05 interpretation-entries contains no more than 1 non-zero entries. 198.29/60.05 198.29/60.05 [f](x1) = [1] x1 + [1] 198.29/60.05 198.29/60.05 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 198.29/60.05 198.29/60.05 [c] = [1] 198.29/60.05 198.29/60.05 [n__f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [n__true] = [2] 198.29/60.05 198.29/60.05 [true] = [2] 198.29/60.05 198.29/60.05 [false] = [2] 198.29/60.05 198.29/60.05 [activate](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 The order satisfies the following ordering constraints: 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [1] 198.29/60.05 ? [1] X + [3] 198.29/60.05 = [if(X, c(), n__f(n__true()))] 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [1] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [n__f(X)] 198.29/60.05 198.29/60.05 [if(true(), X, Y)] = [1] X + [1] Y + [2] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [if(false(), X, Y)] = [1] X + [1] Y + [2] 198.29/60.05 > [1] Y + [0] 198.29/60.05 = [activate(Y)] 198.29/60.05 198.29/60.05 [true()] = [2] 198.29/60.05 >= [2] 198.29/60.05 = [n__true()] 198.29/60.05 198.29/60.05 [activate(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [activate(n__f(X))] = [1] X + [0] 198.29/60.05 ? [1] X + [1] 198.29/60.05 = [f(activate(X))] 198.29/60.05 198.29/60.05 [activate(n__true())] = [2] 198.29/60.05 >= [2] 198.29/60.05 = [true()] 198.29/60.05 198.29/60.05 198.29/60.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 198.29/60.05 198.29/60.05 We are left with following problem, upon which TcT provides the 198.29/60.05 certificate MAYBE. 198.29/60.05 198.29/60.05 Strict Trs: 198.29/60.05 { f(X) -> if(X, c(), n__f(n__true())) 198.29/60.05 , activate(n__f(X)) -> f(activate(X)) } 198.29/60.05 Weak Trs: 198.29/60.05 { f(X) -> n__f(X) 198.29/60.05 , if(true(), X, Y) -> X 198.29/60.05 , if(false(), X, Y) -> activate(Y) 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X 198.29/60.05 , activate(n__true()) -> true() } 198.29/60.05 Obligation: 198.29/60.05 derivational complexity 198.29/60.05 Answer: 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 The weightgap principle applies (using the following nonconstant 198.29/60.05 growth matrix-interpretation) 198.29/60.05 198.29/60.05 TcT has computed the following triangular matrix interpretation. 198.29/60.05 Note that the diagonal of the component-wise maxima of 198.29/60.05 interpretation-entries contains no more than 1 non-zero entries. 198.29/60.05 198.29/60.05 [f](x1) = [1] x1 + [1] 198.29/60.05 198.29/60.05 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 198.29/60.05 198.29/60.05 [c] = [0] 198.29/60.05 198.29/60.05 [n__f](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 [n__true] = [0] 198.29/60.05 198.29/60.05 [true] = [0] 198.29/60.05 198.29/60.05 [false] = [2] 198.29/60.05 198.29/60.05 [activate](x1) = [1] x1 + [0] 198.29/60.05 198.29/60.05 The order satisfies the following ordering constraints: 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [1] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [if(X, c(), n__f(n__true()))] 198.29/60.05 198.29/60.05 [f(X)] = [1] X + [1] 198.29/60.05 > [1] X + [0] 198.29/60.05 = [n__f(X)] 198.29/60.05 198.29/60.05 [if(true(), X, Y)] = [1] X + [1] Y + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [if(false(), X, Y)] = [1] X + [1] Y + [2] 198.29/60.05 > [1] Y + [0] 198.29/60.05 = [activate(Y)] 198.29/60.05 198.29/60.05 [true()] = [0] 198.29/60.05 >= [0] 198.29/60.05 = [n__true()] 198.29/60.05 198.29/60.05 [activate(X)] = [1] X + [0] 198.29/60.05 >= [1] X + [0] 198.29/60.05 = [X] 198.29/60.05 198.29/60.05 [activate(n__f(X))] = [1] X + [0] 198.29/60.05 ? [1] X + [1] 198.29/60.05 = [f(activate(X))] 198.29/60.05 198.29/60.05 [activate(n__true())] = [0] 198.29/60.05 >= [0] 198.29/60.05 = [true()] 198.29/60.05 198.29/60.05 198.29/60.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 198.29/60.05 198.29/60.05 We are left with following problem, upon which TcT provides the 198.29/60.05 certificate MAYBE. 198.29/60.05 198.29/60.05 Strict Trs: { activate(n__f(X)) -> f(activate(X)) } 198.29/60.05 Weak Trs: 198.29/60.05 { f(X) -> if(X, c(), n__f(n__true())) 198.29/60.05 , f(X) -> n__f(X) 198.29/60.05 , if(true(), X, Y) -> X 198.29/60.05 , if(false(), X, Y) -> activate(Y) 198.29/60.05 , true() -> n__true() 198.29/60.05 , activate(X) -> X 198.29/60.05 , activate(n__true()) -> true() } 198.29/60.05 Obligation: 198.29/60.05 derivational complexity 198.29/60.05 Answer: 198.29/60.05 MAYBE 198.29/60.05 198.29/60.05 None of the processors succeeded. 198.29/60.05 198.29/60.05 Details of failed attempt(s): 198.29/60.05 ----------------------------- 198.29/60.05 1) 'empty' failed due to the following reason: 198.29/60.05 198.29/60.05 Empty strict component of the problem is NOT empty. 198.29/60.05 198.29/60.05 2) 'Fastest' failed due to the following reason: 198.29/60.05 198.29/60.05 None of the processors succeeded. 198.29/60.05 198.29/60.05 Details of failed attempt(s): 198.29/60.05 ----------------------------- 198.29/60.05 1) 'Fastest (timeout of 30 seconds)' failed due to the following 198.29/60.05 reason: 198.29/60.05 198.29/60.05 Computation stopped due to timeout after 30.0 seconds. 198.29/60.05 198.29/60.05 2) 'Fastest' failed due to the following reason: 198.29/60.05 198.29/60.05 None of the processors succeeded. 198.29/60.05 198.29/60.05 Details of failed attempt(s): 198.29/60.05 ----------------------------- 198.29/60.05 1) 'matrix interpretation of dimension 6' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 2) 'matrix interpretation of dimension 5' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 3) 'matrix interpretation of dimension 4' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 4) 'matrix interpretation of dimension 3' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 5) 'matrix interpretation of dimension 2' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 6) 'matrix interpretation of dimension 1' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 198.29/60.05 3) 'iteProgress' failed due to the following reason: 198.29/60.05 198.29/60.05 Fail 198.29/60.05 198.29/60.05 4) 'bsearch-matrix' failed due to the following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 198.29/60.05 198.29/60.05 3) 'iteProgress (timeout of 297 seconds)' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 Fail 198.29/60.05 198.29/60.05 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 198.29/60.05 following reason: 198.29/60.05 198.29/60.05 The input cannot be shown compatible 198.29/60.05 198.29/60.05 198.29/60.05 Arrrr.. 198.29/60.06 EOF