MAYBE 704.25/297.30 MAYBE 704.25/297.30 704.25/297.30 We are left with following problem, upon which TcT provides the 704.25/297.30 certificate MAYBE. 704.25/297.30 704.25/297.30 Strict Trs: 704.25/297.30 { a__f(X, X) -> a__f(a(), b()) 704.25/297.30 , a__f(X1, X2) -> f(X1, X2) 704.25/297.30 , a__b() -> a() 704.25/297.30 , a__b() -> b() 704.25/297.30 , mark(a()) -> a() 704.25/297.30 , mark(b()) -> a__b() 704.25/297.30 , mark(f(X1, X2)) -> a__f(mark(X1), X2) } 704.25/297.30 Obligation: 704.25/297.30 derivational complexity 704.25/297.30 Answer: 704.25/297.30 MAYBE 704.25/297.30 704.25/297.30 None of the processors succeeded. 704.25/297.30 704.25/297.30 Details of failed attempt(s): 704.25/297.30 ----------------------------- 704.25/297.30 1) 'iteProgress (timeout of 297 seconds)' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 Computation stopped due to timeout after 297.0 seconds. 704.25/297.30 704.25/297.30 2) 'Fastest (timeout of 60 seconds)' failed due to the following 704.25/297.30 reason: 704.25/297.30 704.25/297.30 Computation stopped due to timeout after 60.0 seconds. 704.25/297.30 704.25/297.30 3) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 704.25/297.30 the following reason: 704.25/297.30 704.25/297.30 We use the processor 'matrix interpretation of dimension 1' to 704.25/297.30 orient following rules strictly. 704.25/297.30 704.25/297.30 Trs: 704.25/297.30 { a__b() -> a() 704.25/297.30 , a__b() -> b() 704.25/297.30 , mark(a()) -> a() 704.25/297.30 , mark(b()) -> a__b() } 704.25/297.30 704.25/297.30 The induced complexity on above rules (modulo remaining rules) is 704.25/297.30 YES(?,O(n^1)) . These rules are moved into the corresponding weak 704.25/297.30 component(s). 704.25/297.30 704.25/297.30 Sub-proof: 704.25/297.30 ---------- 704.25/297.30 TcT has computed the following triangular matrix interpretation. 704.25/297.30 704.25/297.30 [a__f](x1, x2) = [1] x1 + [1] x2 + [2] 704.25/297.30 704.25/297.30 [a] = [0] 704.25/297.30 704.25/297.30 [b] = [0] 704.25/297.30 704.25/297.30 [a__b] = [1] 704.25/297.30 704.25/297.30 [mark](x1) = [1] x1 + [2] 704.25/297.30 704.25/297.30 [f](x1, x2) = [1] x1 + [1] x2 + [2] 704.25/297.30 704.25/297.30 The order satisfies the following ordering constraints: 704.25/297.30 704.25/297.30 [a__f(X, X)] = [2] X + [2] 704.25/297.30 >= [2] 704.25/297.30 = [a__f(a(), b())] 704.25/297.30 704.25/297.30 [a__f(X1, X2)] = [1] X1 + [1] X2 + [2] 704.25/297.30 >= [1] X1 + [1] X2 + [2] 704.25/297.30 = [f(X1, X2)] 704.25/297.30 704.25/297.30 [a__b()] = [1] 704.25/297.30 > [0] 704.25/297.30 = [a()] 704.25/297.30 704.25/297.30 [a__b()] = [1] 704.25/297.30 > [0] 704.25/297.30 = [b()] 704.25/297.30 704.25/297.30 [mark(a())] = [2] 704.25/297.30 > [0] 704.25/297.30 = [a()] 704.25/297.30 704.25/297.30 [mark(b())] = [2] 704.25/297.30 > [1] 704.25/297.30 = [a__b()] 704.25/297.30 704.25/297.30 [mark(f(X1, X2))] = [1] X1 + [1] X2 + [4] 704.25/297.30 >= [1] X1 + [1] X2 + [4] 704.25/297.30 = [a__f(mark(X1), X2)] 704.25/297.30 704.25/297.30 704.25/297.30 We return to the main proof. 704.25/297.30 704.25/297.30 We are left with following problem, upon which TcT provides the 704.25/297.30 certificate MAYBE. 704.25/297.30 704.25/297.30 Strict Trs: 704.25/297.30 { a__f(X, X) -> a__f(a(), b()) 704.25/297.30 , a__f(X1, X2) -> f(X1, X2) 704.25/297.30 , mark(f(X1, X2)) -> a__f(mark(X1), X2) } 704.25/297.30 Weak Trs: 704.25/297.30 { a__b() -> a() 704.25/297.30 , a__b() -> b() 704.25/297.30 , mark(a()) -> a() 704.25/297.30 , mark(b()) -> a__b() } 704.25/297.30 Obligation: 704.25/297.30 derivational complexity 704.25/297.30 Answer: 704.25/297.30 MAYBE 704.25/297.30 704.25/297.30 The weightgap principle applies (using the following nonconstant 704.25/297.30 growth matrix-interpretation) 704.25/297.30 704.25/297.30 TcT has computed the following triangular matrix interpretation. 704.25/297.30 Note that the diagonal of the component-wise maxima of 704.25/297.30 interpretation-entries contains no more than 1 non-zero entries. 704.25/297.30 704.25/297.30 [a__f](x1, x2) = [1] x1 + [1] x2 + [1] 704.25/297.30 704.25/297.30 [a] = [2] 704.25/297.30 704.25/297.30 [b] = [2] 704.25/297.30 704.25/297.30 [a__b] = [2] 704.25/297.30 704.25/297.30 [mark](x1) = [1] x1 + [0] 704.25/297.30 704.25/297.30 [f](x1, x2) = [1] x1 + [1] x2 + [0] 704.25/297.30 704.25/297.30 The order satisfies the following ordering constraints: 704.25/297.30 704.25/297.30 [a__f(X, X)] = [2] X + [1] 704.25/297.30 ? [5] 704.25/297.30 = [a__f(a(), b())] 704.25/297.30 704.25/297.30 [a__f(X1, X2)] = [1] X1 + [1] X2 + [1] 704.25/297.30 > [1] X1 + [1] X2 + [0] 704.25/297.30 = [f(X1, X2)] 704.25/297.30 704.25/297.30 [a__b()] = [2] 704.25/297.30 >= [2] 704.25/297.30 = [a()] 704.25/297.30 704.25/297.30 [a__b()] = [2] 704.25/297.30 >= [2] 704.25/297.30 = [b()] 704.25/297.30 704.25/297.30 [mark(a())] = [2] 704.25/297.30 >= [2] 704.25/297.30 = [a()] 704.25/297.30 704.25/297.30 [mark(b())] = [2] 704.25/297.30 >= [2] 704.25/297.30 = [a__b()] 704.25/297.30 704.25/297.30 [mark(f(X1, X2))] = [1] X1 + [1] X2 + [0] 704.25/297.30 ? [1] X1 + [1] X2 + [1] 704.25/297.30 = [a__f(mark(X1), X2)] 704.25/297.30 704.25/297.30 704.25/297.30 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 704.25/297.30 704.25/297.30 We are left with following problem, upon which TcT provides the 704.25/297.30 certificate MAYBE. 704.25/297.30 704.25/297.30 Strict Trs: 704.25/297.30 { a__f(X, X) -> a__f(a(), b()) 704.25/297.30 , mark(f(X1, X2)) -> a__f(mark(X1), X2) } 704.25/297.30 Weak Trs: 704.25/297.30 { a__f(X1, X2) -> f(X1, X2) 704.25/297.30 , a__b() -> a() 704.25/297.30 , a__b() -> b() 704.25/297.30 , mark(a()) -> a() 704.25/297.30 , mark(b()) -> a__b() } 704.25/297.30 Obligation: 704.25/297.30 derivational complexity 704.25/297.30 Answer: 704.25/297.30 MAYBE 704.25/297.30 704.25/297.30 We use the processor 'matrix interpretation of dimension 2' to 704.25/297.30 orient following rules strictly. 704.25/297.30 704.25/297.30 Trs: { mark(f(X1, X2)) -> a__f(mark(X1), X2) } 704.25/297.30 704.25/297.30 The induced complexity on above rules (modulo remaining rules) is 704.25/297.30 YES(?,O(n^2)) . These rules are moved into the corresponding weak 704.25/297.30 component(s). 704.25/297.30 704.25/297.30 Sub-proof: 704.25/297.30 ---------- 704.25/297.30 TcT has computed the following triangular matrix interpretation. 704.25/297.30 704.25/297.30 [a__f](x1, x2) = [1 0] x1 + [1 0] x2 + [2] 704.25/297.30 [0 1] [0 0] [2] 704.25/297.30 704.25/297.30 [a] = [0] 704.25/297.30 [0] 704.25/297.30 704.25/297.30 [b] = [0] 704.25/297.30 [2] 704.25/297.30 704.25/297.30 [a__b] = [1] 704.25/297.30 [2] 704.25/297.30 704.25/297.30 [mark](x1) = [1 1] x1 + [0] 704.25/297.30 [0 1] [0] 704.25/297.30 704.25/297.30 [f](x1, x2) = [1 0] x1 + [1 0] x2 + [2] 704.25/297.30 [0 1] [0 0] [2] 704.25/297.30 704.25/297.30 The order satisfies the following ordering constraints: 704.25/297.30 704.25/297.30 [a__f(X, X)] = [2 0] X + [2] 704.25/297.30 [0 1] [2] 704.25/297.30 >= [2] 704.25/297.30 [2] 704.25/297.30 = [a__f(a(), b())] 704.25/297.30 704.25/297.30 [a__f(X1, X2)] = [1 0] X1 + [1 0] X2 + [2] 704.25/297.30 [0 1] [0 0] [2] 704.25/297.30 >= [1 0] X1 + [1 0] X2 + [2] 704.25/297.30 [0 1] [0 0] [2] 704.25/297.30 = [f(X1, X2)] 704.25/297.30 704.25/297.30 [a__b()] = [1] 704.25/297.30 [2] 704.25/297.30 > [0] 704.25/297.30 [0] 704.25/297.30 = [a()] 704.25/297.30 704.25/297.30 [a__b()] = [1] 704.25/297.30 [2] 704.25/297.30 > [0] 704.25/297.30 [2] 704.25/297.30 = [b()] 704.25/297.30 704.25/297.30 [mark(a())] = [0] 704.25/297.30 [0] 704.25/297.30 >= [0] 704.25/297.30 [0] 704.25/297.30 = [a()] 704.25/297.30 704.25/297.30 [mark(b())] = [2] 704.25/297.30 [2] 704.25/297.30 > [1] 704.25/297.30 [2] 704.25/297.30 = [a__b()] 704.25/297.30 704.25/297.30 [mark(f(X1, X2))] = [1 1] X1 + [1 0] X2 + [4] 704.25/297.30 [0 1] [0 0] [2] 704.25/297.30 > [1 1] X1 + [1 0] X2 + [2] 704.25/297.30 [0 1] [0 0] [2] 704.25/297.30 = [a__f(mark(X1), X2)] 704.25/297.30 704.25/297.30 704.25/297.30 We return to the main proof. 704.25/297.30 704.25/297.30 We are left with following problem, upon which TcT provides the 704.25/297.30 certificate MAYBE. 704.25/297.30 704.25/297.30 Strict Trs: { a__f(X, X) -> a__f(a(), b()) } 704.25/297.30 Weak Trs: 704.25/297.30 { a__f(X1, X2) -> f(X1, X2) 704.25/297.30 , a__b() -> a() 704.25/297.30 , a__b() -> b() 704.25/297.30 , mark(a()) -> a() 704.25/297.30 , mark(b()) -> a__b() 704.25/297.30 , mark(f(X1, X2)) -> a__f(mark(X1), X2) } 704.25/297.30 Obligation: 704.25/297.30 derivational complexity 704.25/297.30 Answer: 704.25/297.30 MAYBE 704.25/297.30 704.25/297.30 None of the processors succeeded. 704.25/297.30 704.25/297.30 Details of failed attempt(s): 704.25/297.30 ----------------------------- 704.25/297.30 1) 'empty' failed due to the following reason: 704.25/297.30 704.25/297.30 Empty strict component of the problem is NOT empty. 704.25/297.30 704.25/297.30 2) 'Fastest' failed due to the following reason: 704.25/297.30 704.25/297.30 None of the processors succeeded. 704.25/297.30 704.25/297.30 Details of failed attempt(s): 704.25/297.30 ----------------------------- 704.25/297.30 1) 'Fastest (timeout of 30 seconds)' failed due to the following 704.25/297.30 reason: 704.25/297.30 704.25/297.30 Computation stopped due to timeout after 30.0 seconds. 704.25/297.30 704.25/297.30 2) 'Fastest' failed due to the following reason: 704.25/297.30 704.25/297.30 None of the processors succeeded. 704.25/297.30 704.25/297.30 Details of failed attempt(s): 704.25/297.30 ----------------------------- 704.25/297.30 1) 'matrix interpretation of dimension 6' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 2) 'matrix interpretation of dimension 5' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 3) 'matrix interpretation of dimension 4' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 4) 'matrix interpretation of dimension 3' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 5) 'matrix interpretation of dimension 2' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 6) 'matrix interpretation of dimension 1' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 704.25/297.30 3) 'iteProgress' failed due to the following reason: 704.25/297.30 704.25/297.30 Fail 704.25/297.30 704.25/297.30 4) 'bsearch-matrix' failed due to the following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 704.25/297.30 704.25/297.30 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 704.25/297.30 following reason: 704.25/297.30 704.25/297.30 The input cannot be shown compatible 704.25/297.30 704.25/297.30 704.25/297.30 Arrrr.. 704.25/297.37 EOF