MAYBE 477.80/129.02 MAYBE 477.80/129.02 477.80/129.02 We are left with following problem, upon which TcT provides the 477.80/129.02 certificate MAYBE. 477.80/129.02 477.80/129.02 Strict Trs: 477.80/129.02 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.02 , a(b(x1)) -> C(x1) 477.80/129.02 , a(A(x1)) -> x1 477.80/129.02 , b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.02 , b(c(x1)) -> A(x1) 477.80/129.02 , b(B(x1)) -> x1 477.80/129.02 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.02 , C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.02 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.02 , C(c(x1)) -> x1 477.80/129.02 , C(B(x1)) -> a(x1) 477.80/129.02 , c(a(x1)) -> B(x1) 477.80/129.02 , c(C(x1)) -> x1 477.80/129.02 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.02 , A(a(x1)) -> x1 477.80/129.02 , A(C(x1)) -> b(x1) 477.80/129.02 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.02 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) 477.80/129.02 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.02 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.02 , B(b(x1)) -> x1 477.80/129.02 , B(A(x1)) -> c(x1) 477.80/129.02 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) 477.80/129.02 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.02 Obligation: 477.80/129.02 derivational complexity 477.80/129.02 Answer: 477.80/129.02 MAYBE 477.80/129.02 477.80/129.02 None of the processors succeeded. 477.80/129.02 477.80/129.02 Details of failed attempt(s): 477.80/129.02 ----------------------------- 477.80/129.02 1) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 477.80/129.02 the following reason: 477.80/129.02 477.80/129.02 The weightgap principle applies (using the following nonconstant 477.80/129.02 growth matrix-interpretation) 477.80/129.02 477.80/129.02 TcT has computed the following triangular matrix interpretation. 477.80/129.02 Note that the diagonal of the component-wise maxima of 477.80/129.02 interpretation-entries contains no more than 1 non-zero entries. 477.80/129.02 477.80/129.02 [a](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [b](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [C](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [c](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 [A](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [B](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 The order satisfies the following ordering constraints: 477.80/129.02 477.80/129.02 [a(a(a(a(a(x1)))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [A(A(A(x1)))] 477.80/129.02 477.80/129.02 [a(b(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [C(x1)] 477.80/129.02 477.80/129.02 [a(A(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [b(b(b(b(b(x1)))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [B(B(B(x1)))] 477.80/129.02 477.80/129.02 [b(c(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [A(x1)] 477.80/129.02 477.80/129.02 [b(B(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [C(b(b(b(b(x1)))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [a(B(B(B(x1))))] 477.80/129.02 477.80/129.02 [C(C(C(a(x1))))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [4] 477.80/129.02 = [c(c(c(c(B(x1)))))] 477.80/129.02 477.80/129.02 [C(C(C(C(x1))))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [4] 477.80/129.02 = [c(c(c(c(x1))))] 477.80/129.02 477.80/129.02 [C(c(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [C(B(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [a(x1)] 477.80/129.02 477.80/129.02 [c(a(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [B(x1)] 477.80/129.02 477.80/129.02 [c(C(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [c(c(c(c(c(x1)))))] = [1] x1 + [5] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [C(C(C(x1)))] 477.80/129.02 477.80/129.02 [A(a(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [A(C(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [b(x1)] 477.80/129.02 477.80/129.02 [A(c(c(c(c(x1)))))] = [1] x1 + [4] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [b(C(C(C(x1))))] 477.80/129.02 477.80/129.02 [A(A(A(b(x1))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [a(a(a(a(C(x1)))))] 477.80/129.02 477.80/129.02 [A(A(A(A(x1))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [a(a(a(a(x1))))] 477.80/129.02 477.80/129.02 [B(a(a(a(a(x1)))))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [1] 477.80/129.02 = [c(A(A(A(x1))))] 477.80/129.02 477.80/129.02 [B(b(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [B(A(x1))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [1] 477.80/129.02 = [c(x1)] 477.80/129.02 477.80/129.02 [B(B(B(c(x1))))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [b(b(b(b(A(x1)))))] 477.80/129.02 477.80/129.02 [B(B(B(B(x1))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [b(b(b(b(x1))))] 477.80/129.02 477.80/129.02 477.80/129.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 477.80/129.02 477.80/129.02 We are left with following problem, upon which TcT provides the 477.80/129.02 certificate MAYBE. 477.80/129.02 477.80/129.02 Strict Trs: 477.80/129.02 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.02 , a(b(x1)) -> C(x1) 477.80/129.02 , a(A(x1)) -> x1 477.80/129.02 , b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.02 , b(B(x1)) -> x1 477.80/129.02 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.02 , C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.02 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.02 , C(B(x1)) -> a(x1) 477.80/129.02 , A(a(x1)) -> x1 477.80/129.02 , A(C(x1)) -> b(x1) 477.80/129.02 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) 477.80/129.02 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.02 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.02 , B(b(x1)) -> x1 477.80/129.02 , B(A(x1)) -> c(x1) 477.80/129.02 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.02 Weak Trs: 477.80/129.02 { b(c(x1)) -> A(x1) 477.80/129.02 , C(c(x1)) -> x1 477.80/129.02 , c(a(x1)) -> B(x1) 477.80/129.02 , c(C(x1)) -> x1 477.80/129.02 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.02 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.02 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) } 477.80/129.02 Obligation: 477.80/129.02 derivational complexity 477.80/129.02 Answer: 477.80/129.02 MAYBE 477.80/129.02 477.80/129.02 The weightgap principle applies (using the following nonconstant 477.80/129.02 growth matrix-interpretation) 477.80/129.02 477.80/129.02 TcT has computed the following triangular matrix interpretation. 477.80/129.02 Note that the diagonal of the component-wise maxima of 477.80/129.02 interpretation-entries contains no more than 1 non-zero entries. 477.80/129.02 477.80/129.02 [a](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [b](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [C](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 [c](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 [A](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [B](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 The order satisfies the following ordering constraints: 477.80/129.02 477.80/129.02 [a(a(a(a(a(x1)))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [A(A(A(x1)))] 477.80/129.02 477.80/129.02 [a(b(x1))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [1] 477.80/129.02 = [C(x1)] 477.80/129.02 477.80/129.02 [a(A(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [b(b(b(b(b(x1)))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [B(B(B(x1)))] 477.80/129.02 477.80/129.02 [b(c(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [A(x1)] 477.80/129.02 477.80/129.02 [b(B(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [C(b(b(b(b(x1)))))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [a(B(B(B(x1))))] 477.80/129.02 477.80/129.02 [C(C(C(a(x1))))] = [1] x1 + [3] 477.80/129.02 ? [1] x1 + [4] 477.80/129.02 = [c(c(c(c(B(x1)))))] 477.80/129.02 477.80/129.02 [C(C(C(C(x1))))] = [1] x1 + [4] 477.80/129.02 >= [1] x1 + [4] 477.80/129.02 = [c(c(c(c(x1))))] 477.80/129.02 477.80/129.02 [C(c(x1))] = [1] x1 + [2] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [C(B(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [a(x1)] 477.80/129.02 477.80/129.02 [c(a(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [B(x1)] 477.80/129.02 477.80/129.02 [c(C(x1))] = [1] x1 + [2] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [c(c(c(c(c(x1)))))] = [1] x1 + [5] 477.80/129.02 > [1] x1 + [3] 477.80/129.02 = [C(C(C(x1)))] 477.80/129.02 477.80/129.02 [A(a(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [A(C(x1))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [b(x1)] 477.80/129.02 477.80/129.02 [A(c(c(c(c(x1)))))] = [1] x1 + [4] 477.80/129.02 > [1] x1 + [3] 477.80/129.02 = [b(C(C(C(x1))))] 477.80/129.02 477.80/129.02 [A(A(A(b(x1))))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [1] 477.80/129.02 = [a(a(a(a(C(x1)))))] 477.80/129.02 477.80/129.02 [A(A(A(A(x1))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [a(a(a(a(x1))))] 477.80/129.02 477.80/129.02 [B(a(a(a(a(x1)))))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [1] 477.80/129.02 = [c(A(A(A(x1))))] 477.80/129.02 477.80/129.02 [B(b(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [B(A(x1))] = [1] x1 + [0] 477.80/129.02 ? [1] x1 + [1] 477.80/129.02 = [c(x1)] 477.80/129.02 477.80/129.02 [B(B(B(c(x1))))] = [1] x1 + [1] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [b(b(b(b(A(x1)))))] 477.80/129.02 477.80/129.02 [B(B(B(B(x1))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [b(b(b(b(x1))))] 477.80/129.02 477.80/129.02 477.80/129.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 477.80/129.02 477.80/129.02 We are left with following problem, upon which TcT provides the 477.80/129.02 certificate MAYBE. 477.80/129.02 477.80/129.02 Strict Trs: 477.80/129.02 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.02 , a(b(x1)) -> C(x1) 477.80/129.02 , a(A(x1)) -> x1 477.80/129.02 , b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.02 , b(B(x1)) -> x1 477.80/129.02 , C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.02 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.02 , A(a(x1)) -> x1 477.80/129.02 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) 477.80/129.02 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.02 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.02 , B(b(x1)) -> x1 477.80/129.02 , B(A(x1)) -> c(x1) 477.80/129.02 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.02 Weak Trs: 477.80/129.02 { b(c(x1)) -> A(x1) 477.80/129.02 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.02 , C(c(x1)) -> x1 477.80/129.02 , C(B(x1)) -> a(x1) 477.80/129.02 , c(a(x1)) -> B(x1) 477.80/129.02 , c(C(x1)) -> x1 477.80/129.02 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.02 , A(C(x1)) -> b(x1) 477.80/129.02 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.02 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) } 477.80/129.02 Obligation: 477.80/129.02 derivational complexity 477.80/129.02 Answer: 477.80/129.02 MAYBE 477.80/129.02 477.80/129.02 The weightgap principle applies (using the following nonconstant 477.80/129.02 growth matrix-interpretation) 477.80/129.02 477.80/129.02 TcT has computed the following triangular matrix interpretation. 477.80/129.02 Note that the diagonal of the component-wise maxima of 477.80/129.02 interpretation-entries contains no more than 1 non-zero entries. 477.80/129.02 477.80/129.02 [a](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [b](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 [C](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 [c](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 [A](x1) = [1] x1 + [0] 477.80/129.02 477.80/129.02 [B](x1) = [1] x1 + [1] 477.80/129.02 477.80/129.02 The order satisfies the following ordering constraints: 477.80/129.02 477.80/129.02 [a(a(a(a(a(x1)))))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [A(A(A(x1)))] 477.80/129.02 477.80/129.02 [a(b(x1))] = [1] x1 + [1] 477.80/129.02 >= [1] x1 + [1] 477.80/129.02 = [C(x1)] 477.80/129.02 477.80/129.02 [a(A(x1))] = [1] x1 + [0] 477.80/129.02 >= [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [b(b(b(b(b(x1)))))] = [1] x1 + [5] 477.80/129.02 > [1] x1 + [3] 477.80/129.02 = [B(B(B(x1)))] 477.80/129.02 477.80/129.02 [b(c(x1))] = [1] x1 + [2] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [A(x1)] 477.80/129.02 477.80/129.02 [b(B(x1))] = [1] x1 + [2] 477.80/129.02 > [1] x1 + [0] 477.80/129.02 = [x1] 477.80/129.02 477.80/129.02 [C(b(b(b(b(x1)))))] = [1] x1 + [5] 477.80/129.02 > [1] x1 + [3] 477.80/129.02 = [a(B(B(B(x1))))] 477.80/129.02 477.80/129.02 [C(C(C(a(x1))))] = [1] x1 + [3] 477.80/129.02 ? [1] x1 + [5] 477.80/129.02 = [c(c(c(c(B(x1)))))] 477.80/129.02 477.80/129.02 [C(C(C(C(x1))))] = [1] x1 + [4] 477.80/129.02 >= [1] x1 + [4] 477.80/129.02 = [c(c(c(c(x1))))] 477.80/129.02 477.80/129.03 [C(c(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(B(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [a(x1)] 477.80/129.03 477.80/129.03 [c(a(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [B(x1)] 477.80/129.03 477.80/129.03 [c(C(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [c(c(c(c(c(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [C(C(C(x1)))] 477.80/129.03 477.80/129.03 [A(a(x1))] = [1] x1 + [0] 477.80/129.03 >= [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [A(C(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [b(x1)] 477.80/129.03 477.80/129.03 [A(c(c(c(c(x1)))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [b(C(C(C(x1))))] 477.80/129.03 477.80/129.03 [A(A(A(b(x1))))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [a(a(a(a(C(x1)))))] 477.80/129.03 477.80/129.03 [A(A(A(A(x1))))] = [1] x1 + [0] 477.80/129.03 >= [1] x1 + [0] 477.80/129.03 = [a(a(a(a(x1))))] 477.80/129.03 477.80/129.03 [B(a(a(a(a(x1)))))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [c(A(A(A(x1))))] 477.80/129.03 477.80/129.03 [B(b(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [B(A(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [c(x1)] 477.80/129.03 477.80/129.03 [B(B(B(c(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [b(b(b(b(A(x1)))))] 477.80/129.03 477.80/129.03 [B(B(B(B(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [b(b(b(b(x1))))] 477.80/129.03 477.80/129.03 477.80/129.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 477.80/129.03 477.80/129.03 We are left with following problem, upon which TcT provides the 477.80/129.03 certificate MAYBE. 477.80/129.03 477.80/129.03 Strict Trs: 477.80/129.03 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.03 , a(b(x1)) -> C(x1) 477.80/129.03 , a(A(x1)) -> x1 477.80/129.03 , C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.03 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.03 , A(a(x1)) -> x1 477.80/129.03 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) 477.80/129.03 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.03 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.03 , B(A(x1)) -> c(x1) 477.80/129.03 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.03 Weak Trs: 477.80/129.03 { b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.03 , b(c(x1)) -> A(x1) 477.80/129.03 , b(B(x1)) -> x1 477.80/129.03 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.03 , C(c(x1)) -> x1 477.80/129.03 , C(B(x1)) -> a(x1) 477.80/129.03 , c(a(x1)) -> B(x1) 477.80/129.03 , c(C(x1)) -> x1 477.80/129.03 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.03 , A(C(x1)) -> b(x1) 477.80/129.03 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.03 , B(b(x1)) -> x1 477.80/129.03 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) } 477.80/129.03 Obligation: 477.80/129.03 derivational complexity 477.80/129.03 Answer: 477.80/129.03 MAYBE 477.80/129.03 477.80/129.03 The weightgap principle applies (using the following nonconstant 477.80/129.03 growth matrix-interpretation) 477.80/129.03 477.80/129.03 TcT has computed the following triangular matrix interpretation. 477.80/129.03 Note that the diagonal of the component-wise maxima of 477.80/129.03 interpretation-entries contains no more than 1 non-zero entries. 477.80/129.03 477.80/129.03 [a](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [b](x1) = [1] x1 + [0] 477.80/129.03 477.80/129.03 [C](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [c](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [A](x1) = [1] x1 + [0] 477.80/129.03 477.80/129.03 [B](x1) = [1] x1 + [0] 477.80/129.03 477.80/129.03 The order satisfies the following ordering constraints: 477.80/129.03 477.80/129.03 [a(a(a(a(a(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [A(A(A(x1)))] 477.80/129.03 477.80/129.03 [a(b(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [C(x1)] 477.80/129.03 477.80/129.03 [a(A(x1))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [b(b(b(b(b(x1)))))] = [1] x1 + [0] 477.80/129.03 >= [1] x1 + [0] 477.80/129.03 = [B(B(B(x1)))] 477.80/129.03 477.80/129.03 [b(c(x1))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [A(x1)] 477.80/129.03 477.80/129.03 [b(B(x1))] = [1] x1 + [0] 477.80/129.03 >= [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(b(b(b(b(x1)))))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [a(B(B(B(x1))))] 477.80/129.03 477.80/129.03 [C(C(C(a(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [c(c(c(c(B(x1)))))] 477.80/129.03 477.80/129.03 [C(C(C(C(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [c(c(c(c(x1))))] 477.80/129.03 477.80/129.03 [C(c(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(B(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [a(x1)] 477.80/129.03 477.80/129.03 [c(a(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [B(x1)] 477.80/129.03 477.80/129.03 [c(C(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [c(c(c(c(c(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [C(C(C(x1)))] 477.80/129.03 477.80/129.03 [A(a(x1))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [A(C(x1))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [b(x1)] 477.80/129.03 477.80/129.03 [A(c(c(c(c(x1)))))] = [1] x1 + [4] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [b(C(C(C(x1))))] 477.80/129.03 477.80/129.03 [A(A(A(b(x1))))] = [1] x1 + [0] 477.80/129.03 ? [1] x1 + [5] 477.80/129.03 = [a(a(a(a(C(x1)))))] 477.80/129.03 477.80/129.03 [A(A(A(A(x1))))] = [1] x1 + [0] 477.80/129.03 ? [1] x1 + [4] 477.80/129.03 = [a(a(a(a(x1))))] 477.80/129.03 477.80/129.03 [B(a(a(a(a(x1)))))] = [1] x1 + [4] 477.80/129.03 > [1] x1 + [1] 477.80/129.03 = [c(A(A(A(x1))))] 477.80/129.03 477.80/129.03 [B(b(x1))] = [1] x1 + [0] 477.80/129.03 >= [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [B(A(x1))] = [1] x1 + [0] 477.80/129.03 ? [1] x1 + [1] 477.80/129.03 = [c(x1)] 477.80/129.03 477.80/129.03 [B(B(B(c(x1))))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [b(b(b(b(A(x1)))))] 477.80/129.03 477.80/129.03 [B(B(B(B(x1))))] = [1] x1 + [0] 477.80/129.03 >= [1] x1 + [0] 477.80/129.03 = [b(b(b(b(x1))))] 477.80/129.03 477.80/129.03 477.80/129.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 477.80/129.03 477.80/129.03 We are left with following problem, upon which TcT provides the 477.80/129.03 certificate MAYBE. 477.80/129.03 477.80/129.03 Strict Trs: 477.80/129.03 { a(b(x1)) -> C(x1) 477.80/129.03 , C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.03 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.03 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) 477.80/129.03 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.03 , B(A(x1)) -> c(x1) 477.80/129.03 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.03 Weak Trs: 477.80/129.03 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.03 , a(A(x1)) -> x1 477.80/129.03 , b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.03 , b(c(x1)) -> A(x1) 477.80/129.03 , b(B(x1)) -> x1 477.80/129.03 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.03 , C(c(x1)) -> x1 477.80/129.03 , C(B(x1)) -> a(x1) 477.80/129.03 , c(a(x1)) -> B(x1) 477.80/129.03 , c(C(x1)) -> x1 477.80/129.03 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.03 , A(a(x1)) -> x1 477.80/129.03 , A(C(x1)) -> b(x1) 477.80/129.03 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.03 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.03 , B(b(x1)) -> x1 477.80/129.03 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) } 477.80/129.03 Obligation: 477.80/129.03 derivational complexity 477.80/129.03 Answer: 477.80/129.03 MAYBE 477.80/129.03 477.80/129.03 The weightgap principle applies (using the following nonconstant 477.80/129.03 growth matrix-interpretation) 477.80/129.03 477.80/129.03 TcT has computed the following triangular matrix interpretation. 477.80/129.03 Note that the diagonal of the component-wise maxima of 477.80/129.03 interpretation-entries contains no more than 1 non-zero entries. 477.80/129.03 477.80/129.03 [a](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [b](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [C](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [c](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 [A](x1) = [1] x1 + [0] 477.80/129.03 477.80/129.03 [B](x1) = [1] x1 + [1] 477.80/129.03 477.80/129.03 The order satisfies the following ordering constraints: 477.80/129.03 477.80/129.03 [a(a(a(a(a(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [A(A(A(x1)))] 477.80/129.03 477.80/129.03 [a(b(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [1] 477.80/129.03 = [C(x1)] 477.80/129.03 477.80/129.03 [a(A(x1))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [b(b(b(b(b(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [B(B(B(x1)))] 477.80/129.03 477.80/129.03 [b(c(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [A(x1)] 477.80/129.03 477.80/129.03 [b(B(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(b(b(b(b(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [4] 477.80/129.03 = [a(B(B(B(x1))))] 477.80/129.03 477.80/129.03 [C(C(C(a(x1))))] = [1] x1 + [4] 477.80/129.03 ? [1] x1 + [5] 477.80/129.03 = [c(c(c(c(B(x1)))))] 477.80/129.03 477.80/129.03 [C(C(C(C(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [c(c(c(c(x1))))] 477.80/129.03 477.80/129.03 [C(c(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(B(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [1] 477.80/129.03 = [a(x1)] 477.80/129.03 477.80/129.03 [c(a(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [1] 477.80/129.03 = [B(x1)] 477.80/129.03 477.80/129.03 [c(C(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [c(c(c(c(c(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [C(C(C(x1)))] 477.80/129.03 477.80/129.03 [A(a(x1))] = [1] x1 + [1] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [A(C(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [b(x1)] 477.80/129.03 477.80/129.03 [A(c(c(c(c(x1)))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [b(C(C(C(x1))))] 477.80/129.03 477.80/129.03 [A(A(A(b(x1))))] = [1] x1 + [1] 477.80/129.03 ? [1] x1 + [5] 477.80/129.03 = [a(a(a(a(C(x1)))))] 477.80/129.03 477.80/129.03 [A(A(A(A(x1))))] = [1] x1 + [0] 477.80/129.03 ? [1] x1 + [4] 477.80/129.03 = [a(a(a(a(x1))))] 477.80/129.03 477.80/129.03 [B(a(a(a(a(x1)))))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [1] 477.80/129.03 = [c(A(A(A(x1))))] 477.80/129.03 477.80/129.03 [B(b(x1))] = [1] x1 + [2] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [B(A(x1))] = [1] x1 + [1] 477.80/129.03 >= [1] x1 + [1] 477.80/129.03 = [c(x1)] 477.80/129.03 477.80/129.03 [B(B(B(c(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [b(b(b(b(A(x1)))))] 477.80/129.03 477.80/129.03 [B(B(B(B(x1))))] = [1] x1 + [4] 477.80/129.03 >= [1] x1 + [4] 477.80/129.03 = [b(b(b(b(x1))))] 477.80/129.03 477.80/129.03 477.80/129.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 477.80/129.03 477.80/129.03 We are left with following problem, upon which TcT provides the 477.80/129.03 certificate MAYBE. 477.80/129.03 477.80/129.03 Strict Trs: 477.80/129.03 { C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.03 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.03 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) 477.80/129.03 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.03 , B(A(x1)) -> c(x1) 477.80/129.03 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.03 Weak Trs: 477.80/129.03 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.03 , a(b(x1)) -> C(x1) 477.80/129.03 , a(A(x1)) -> x1 477.80/129.03 , b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.03 , b(c(x1)) -> A(x1) 477.80/129.03 , b(B(x1)) -> x1 477.80/129.03 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.03 , C(c(x1)) -> x1 477.80/129.03 , C(B(x1)) -> a(x1) 477.80/129.03 , c(a(x1)) -> B(x1) 477.80/129.03 , c(C(x1)) -> x1 477.80/129.03 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.03 , A(a(x1)) -> x1 477.80/129.03 , A(C(x1)) -> b(x1) 477.80/129.03 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.03 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.03 , B(b(x1)) -> x1 477.80/129.03 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) } 477.80/129.03 Obligation: 477.80/129.03 derivational complexity 477.80/129.03 Answer: 477.80/129.03 MAYBE 477.80/129.03 477.80/129.03 We use the processor 'matrix interpretation of dimension 1' to 477.80/129.03 orient following rules strictly. 477.80/129.03 477.80/129.03 Trs: 477.80/129.03 { C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.03 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.03 , B(A(x1)) -> c(x1) 477.80/129.03 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.03 477.80/129.03 The induced complexity on above rules (modulo remaining rules) is 477.80/129.03 YES(?,O(n^1)) . These rules are moved into the corresponding weak 477.80/129.03 component(s). 477.80/129.03 477.80/129.03 Sub-proof: 477.80/129.03 ---------- 477.80/129.03 TcT has computed the following triangular matrix interpretation. 477.80/129.03 477.80/129.03 [a](x1) = [1] x1 + [2] 477.80/129.03 477.80/129.03 [b](x1) = [1] x1 + [2] 477.80/129.03 477.80/129.03 [C](x1) = [1] x1 + [3] 477.80/129.03 477.80/129.03 [c](x1) = [1] x1 + [2] 477.80/129.03 477.80/129.03 [A](x1) = [1] x1 + [3] 477.80/129.03 477.80/129.03 [B](x1) = [1] x1 + [3] 477.80/129.03 477.80/129.03 The order satisfies the following ordering constraints: 477.80/129.03 477.80/129.03 [a(a(a(a(a(x1)))))] = [1] x1 + [10] 477.80/129.03 > [1] x1 + [9] 477.80/129.03 = [A(A(A(x1)))] 477.80/129.03 477.80/129.03 [a(b(x1))] = [1] x1 + [4] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [C(x1)] 477.80/129.03 477.80/129.03 [a(A(x1))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [b(b(b(b(b(x1)))))] = [1] x1 + [10] 477.80/129.03 > [1] x1 + [9] 477.80/129.03 = [B(B(B(x1)))] 477.80/129.03 477.80/129.03 [b(c(x1))] = [1] x1 + [4] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [A(x1)] 477.80/129.03 477.80/129.03 [b(B(x1))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(b(b(b(b(x1)))))] = [1] x1 + [11] 477.80/129.03 >= [1] x1 + [11] 477.80/129.03 = [a(B(B(B(x1))))] 477.80/129.03 477.80/129.03 [C(C(C(a(x1))))] = [1] x1 + [11] 477.80/129.03 >= [1] x1 + [11] 477.80/129.03 = [c(c(c(c(B(x1)))))] 477.80/129.03 477.80/129.03 [C(C(C(C(x1))))] = [1] x1 + [12] 477.80/129.03 > [1] x1 + [8] 477.80/129.03 = [c(c(c(c(x1))))] 477.80/129.03 477.80/129.03 [C(c(x1))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [C(B(x1))] = [1] x1 + [6] 477.80/129.03 > [1] x1 + [2] 477.80/129.03 = [a(x1)] 477.80/129.03 477.80/129.03 [c(a(x1))] = [1] x1 + [4] 477.80/129.03 > [1] x1 + [3] 477.80/129.03 = [B(x1)] 477.80/129.03 477.80/129.03 [c(C(x1))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [c(c(c(c(c(x1)))))] = [1] x1 + [10] 477.80/129.03 > [1] x1 + [9] 477.80/129.03 = [C(C(C(x1)))] 477.80/129.03 477.80/129.03 [A(a(x1))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [A(C(x1))] = [1] x1 + [6] 477.80/129.03 > [1] x1 + [2] 477.80/129.03 = [b(x1)] 477.80/129.03 477.80/129.03 [A(c(c(c(c(x1)))))] = [1] x1 + [11] 477.80/129.03 >= [1] x1 + [11] 477.80/129.03 = [b(C(C(C(x1))))] 477.80/129.03 477.80/129.03 [A(A(A(b(x1))))] = [1] x1 + [11] 477.80/129.03 >= [1] x1 + [11] 477.80/129.03 = [a(a(a(a(C(x1)))))] 477.80/129.03 477.80/129.03 [A(A(A(A(x1))))] = [1] x1 + [12] 477.80/129.03 > [1] x1 + [8] 477.80/129.03 = [a(a(a(a(x1))))] 477.80/129.03 477.80/129.03 [B(a(a(a(a(x1)))))] = [1] x1 + [11] 477.80/129.03 >= [1] x1 + [11] 477.80/129.03 = [c(A(A(A(x1))))] 477.80/129.03 477.80/129.03 [B(b(x1))] = [1] x1 + [5] 477.80/129.03 > [1] x1 + [0] 477.80/129.03 = [x1] 477.80/129.03 477.80/129.03 [B(A(x1))] = [1] x1 + [6] 477.80/129.03 > [1] x1 + [2] 477.80/129.03 = [c(x1)] 477.80/129.03 477.80/129.03 [B(B(B(c(x1))))] = [1] x1 + [11] 477.80/129.03 >= [1] x1 + [11] 477.80/129.03 = [b(b(b(b(A(x1)))))] 477.80/129.03 477.80/129.03 [B(B(B(B(x1))))] = [1] x1 + [12] 477.80/129.03 > [1] x1 + [8] 477.80/129.03 = [b(b(b(b(x1))))] 477.80/129.03 477.80/129.03 477.80/129.03 We return to the main proof. 477.80/129.03 477.80/129.03 We are left with following problem, upon which TcT provides the 477.80/129.03 certificate MAYBE. 477.80/129.03 477.80/129.03 Strict Trs: 477.80/129.03 { C(C(C(a(x1)))) -> c(c(c(c(B(x1))))) 477.80/129.03 , A(A(A(b(x1)))) -> a(a(a(a(C(x1))))) } 477.80/129.03 Weak Trs: 477.80/129.03 { a(a(a(a(a(x1))))) -> A(A(A(x1))) 477.80/129.03 , a(b(x1)) -> C(x1) 477.80/129.03 , a(A(x1)) -> x1 477.80/129.03 , b(b(b(b(b(x1))))) -> B(B(B(x1))) 477.80/129.03 , b(c(x1)) -> A(x1) 477.80/129.03 , b(B(x1)) -> x1 477.80/129.03 , C(b(b(b(b(x1))))) -> a(B(B(B(x1)))) 477.80/129.03 , C(C(C(C(x1)))) -> c(c(c(c(x1)))) 477.80/129.03 , C(c(x1)) -> x1 477.80/129.03 , C(B(x1)) -> a(x1) 477.80/129.03 , c(a(x1)) -> B(x1) 477.80/129.03 , c(C(x1)) -> x1 477.80/129.03 , c(c(c(c(c(x1))))) -> C(C(C(x1))) 477.80/129.03 , A(a(x1)) -> x1 477.80/129.03 , A(C(x1)) -> b(x1) 477.80/129.03 , A(c(c(c(c(x1))))) -> b(C(C(C(x1)))) 477.80/129.03 , A(A(A(A(x1)))) -> a(a(a(a(x1)))) 477.80/129.03 , B(a(a(a(a(x1))))) -> c(A(A(A(x1)))) 477.80/129.03 , B(b(x1)) -> x1 477.80/129.03 , B(A(x1)) -> c(x1) 477.80/129.03 , B(B(B(c(x1)))) -> b(b(b(b(A(x1))))) 477.80/129.03 , B(B(B(B(x1)))) -> b(b(b(b(x1)))) } 477.80/129.03 Obligation: 477.80/129.03 derivational complexity 477.80/129.03 Answer: 477.80/129.03 MAYBE 477.80/129.03 477.80/129.03 None of the processors succeeded. 477.80/129.03 477.80/129.03 Details of failed attempt(s): 477.80/129.03 ----------------------------- 477.80/129.03 1) 'empty' failed due to the following reason: 477.80/129.03 477.80/129.03 Empty strict component of the problem is NOT empty. 477.80/129.03 477.80/129.03 2) 'Fastest' failed due to the following reason: 477.80/129.03 477.80/129.03 None of the processors succeeded. 477.80/129.03 477.80/129.03 Details of failed attempt(s): 477.80/129.03 ----------------------------- 477.80/129.03 1) 'bsearch-matrix' failed due to the following reason: 477.80/129.03 477.80/129.03 Following exception was raised: 477.80/129.03 stack overflow 477.80/129.03 477.80/129.03 2) 'iteProgress' failed due to the following reason: 477.80/129.03 477.80/129.03 Fail 477.80/129.03 477.80/129.03 3) 'Fastest' failed due to the following reason: 477.80/129.03 477.80/129.03 None of the processors succeeded. 477.80/129.03 477.80/129.03 Details of failed attempt(s): 477.80/129.03 ----------------------------- 477.80/129.03 1) 'matrix interpretation of dimension 6' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 Following exception was raised: 477.80/129.03 stack overflow 477.80/129.03 477.80/129.03 2) 'matrix interpretation of dimension 4' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 The input cannot be shown compatible 477.80/129.03 477.80/129.03 3) 'matrix interpretation of dimension 5' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 Following exception was raised: 477.80/129.03 stack overflow 477.80/129.03 477.80/129.03 4) 'matrix interpretation of dimension 3' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 The input cannot be shown compatible 477.80/129.03 477.80/129.03 5) 'matrix interpretation of dimension 2' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 The input cannot be shown compatible 477.80/129.03 477.80/129.03 6) 'matrix interpretation of dimension 1' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 The input cannot be shown compatible 477.80/129.03 477.80/129.03 477.80/129.03 4) 'Fastest (timeout of 30 seconds)' failed due to the following 477.80/129.03 reason: 477.80/129.03 477.80/129.03 Computation stopped due to timeout after 30.0 seconds. 477.80/129.03 477.80/129.03 477.80/129.03 477.80/129.03 2) 'iteProgress (timeout of 297 seconds)' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 Fail 477.80/129.03 477.80/129.03 3) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 477.80/129.03 following reason: 477.80/129.03 477.80/129.03 Following exception was raised: 477.80/129.03 stack overflow 477.80/129.03 477.80/129.03 4) 'Fastest (timeout of 60 seconds)' failed due to the following 477.80/129.03 reason: 477.80/129.03 477.80/129.03 Computation stopped due to timeout after 60.0 seconds. 477.80/129.03 477.80/129.03 477.80/129.03 Arrrr.. 477.98/129.14 EOF