MAYBE 204.60/60.04 MAYBE 204.60/60.04 204.60/60.04 We are left with following problem, upon which TcT provides the 204.60/60.04 certificate MAYBE. 204.60/60.04 204.60/60.04 Strict Trs: 204.60/60.04 { a____(X1, X2) -> __(X1, X2) 204.60/60.04 , a____(X, nil()) -> mark(X) 204.60/60.04 , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 204.60/60.04 , a____(nil(), X) -> mark(X) 204.60/60.04 , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 204.60/60.04 , mark(nil()) -> nil() 204.60/60.04 , mark(tt()) -> tt() 204.60/60.04 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 204.60/60.04 , mark(isNePal(X)) -> a__isNePal(mark(X)) 204.60/60.04 , a__and(X1, X2) -> and(X1, X2) 204.60/60.04 , a__and(tt(), X) -> mark(X) 204.60/60.04 , a__isNePal(X) -> isNePal(X) 204.60/60.04 , a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.04 Obligation: 204.60/60.04 derivational complexity 204.60/60.04 Answer: 204.60/60.04 MAYBE 204.60/60.04 204.60/60.04 None of the processors succeeded. 204.60/60.04 204.60/60.04 Details of failed attempt(s): 204.60/60.04 ----------------------------- 204.60/60.04 1) 'Fastest (timeout of 60 seconds)' failed due to the following 204.60/60.04 reason: 204.60/60.04 204.60/60.04 Computation stopped due to timeout after 60.0 seconds. 204.60/60.04 204.60/60.04 2) 'Inspecting Problem... (timeout of 297 seconds)' failed due to 204.60/60.04 the following reason: 204.60/60.04 204.60/60.04 We use the processor 'matrix interpretation of dimension 1' to 204.60/60.04 orient following rules strictly. 204.60/60.04 204.60/60.04 Trs: { a__and(tt(), X) -> mark(X) } 204.60/60.04 204.60/60.04 The induced complexity on above rules (modulo remaining rules) is 204.60/60.04 YES(?,O(n^1)) . These rules are moved into the corresponding weak 204.60/60.04 component(s). 204.60/60.04 204.60/60.04 Sub-proof: 204.60/60.04 ---------- 204.60/60.04 TcT has computed the following triangular matrix interpretation. 204.60/60.04 204.60/60.04 [a____](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [__](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [mark](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 [nil] = [0] 204.60/60.04 204.60/60.04 [a__and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [tt] = [1] 204.60/60.04 204.60/60.04 [a__isNePal](x1) = [1] x1 + [1] 204.60/60.04 204.60/60.04 [and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [isNePal](x1) = [1] x1 + [1] 204.60/60.04 204.60/60.04 The order satisfies the following ordering constraints: 204.60/60.04 204.60/60.04 [a____(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [__(X1, X2)] 204.60/60.04 204.60/60.04 [a____(X, nil())] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a____(__(X, Y), Z)] = [1] X + [1] Y + [1] Z + [0] 204.60/60.04 >= [1] X + [1] Y + [1] Z + [0] 204.60/60.04 = [a____(mark(X), a____(mark(Y), mark(Z)))] 204.60/60.04 204.60/60.04 [a____(nil(), X)] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [mark(__(X1, X2))] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [a____(mark(X1), mark(X2))] 204.60/60.04 204.60/60.04 [mark(nil())] = [0] 204.60/60.04 >= [0] 204.60/60.04 = [nil()] 204.60/60.04 204.60/60.04 [mark(tt())] = [1] 204.60/60.04 >= [1] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 [mark(and(X1, X2))] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [a__and(mark(X1), X2)] 204.60/60.04 204.60/60.04 [mark(isNePal(X))] = [1] X + [1] 204.60/60.04 >= [1] X + [1] 204.60/60.04 = [a__isNePal(mark(X))] 204.60/60.04 204.60/60.04 [a__and(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [and(X1, X2)] 204.60/60.04 204.60/60.04 [a__and(tt(), X)] = [1] X + [1] 204.60/60.04 > [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a__isNePal(X)] = [1] X + [1] 204.60/60.04 >= [1] X + [1] 204.60/60.04 = [isNePal(X)] 204.60/60.04 204.60/60.04 [a__isNePal(__(I, __(P, I)))] = [2] I + [1] P + [1] 204.60/60.04 >= [1] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 204.60/60.04 We return to the main proof. 204.60/60.04 204.60/60.04 We are left with following problem, upon which TcT provides the 204.60/60.04 certificate MAYBE. 204.60/60.04 204.60/60.04 Strict Trs: 204.60/60.04 { a____(X1, X2) -> __(X1, X2) 204.60/60.04 , a____(X, nil()) -> mark(X) 204.60/60.04 , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 204.60/60.04 , a____(nil(), X) -> mark(X) 204.60/60.04 , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 204.60/60.04 , mark(nil()) -> nil() 204.60/60.04 , mark(tt()) -> tt() 204.60/60.04 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 204.60/60.04 , mark(isNePal(X)) -> a__isNePal(mark(X)) 204.60/60.04 , a__and(X1, X2) -> and(X1, X2) 204.60/60.04 , a__isNePal(X) -> isNePal(X) 204.60/60.04 , a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.04 Weak Trs: { a__and(tt(), X) -> mark(X) } 204.60/60.04 Obligation: 204.60/60.04 derivational complexity 204.60/60.04 Answer: 204.60/60.04 MAYBE 204.60/60.04 204.60/60.04 We use the processor 'matrix interpretation of dimension 1' to 204.60/60.04 orient following rules strictly. 204.60/60.04 204.60/60.04 Trs: { a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.04 204.60/60.04 The induced complexity on above rules (modulo remaining rules) is 204.60/60.04 YES(?,O(n^1)) . These rules are moved into the corresponding weak 204.60/60.04 component(s). 204.60/60.04 204.60/60.04 Sub-proof: 204.60/60.04 ---------- 204.60/60.04 TcT has computed the following triangular matrix interpretation. 204.60/60.04 204.60/60.04 [a____](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [__](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [mark](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 [nil] = [0] 204.60/60.04 204.60/60.04 [a__and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [tt] = [0] 204.60/60.04 204.60/60.04 [a__isNePal](x1) = [1] x1 + [1] 204.60/60.04 204.60/60.04 [and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [isNePal](x1) = [1] x1 + [1] 204.60/60.04 204.60/60.04 The order satisfies the following ordering constraints: 204.60/60.04 204.60/60.04 [a____(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [__(X1, X2)] 204.60/60.04 204.60/60.04 [a____(X, nil())] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a____(__(X, Y), Z)] = [1] X + [1] Y + [1] Z + [0] 204.60/60.04 >= [1] X + [1] Y + [1] Z + [0] 204.60/60.04 = [a____(mark(X), a____(mark(Y), mark(Z)))] 204.60/60.04 204.60/60.04 [a____(nil(), X)] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [mark(__(X1, X2))] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [a____(mark(X1), mark(X2))] 204.60/60.04 204.60/60.04 [mark(nil())] = [0] 204.60/60.04 >= [0] 204.60/60.04 = [nil()] 204.60/60.04 204.60/60.04 [mark(tt())] = [0] 204.60/60.04 >= [0] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 [mark(and(X1, X2))] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [a__and(mark(X1), X2)] 204.60/60.04 204.60/60.04 [mark(isNePal(X))] = [1] X + [1] 204.60/60.04 >= [1] X + [1] 204.60/60.04 = [a__isNePal(mark(X))] 204.60/60.04 204.60/60.04 [a__and(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [and(X1, X2)] 204.60/60.04 204.60/60.04 [a__and(tt(), X)] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a__isNePal(X)] = [1] X + [1] 204.60/60.04 >= [1] X + [1] 204.60/60.04 = [isNePal(X)] 204.60/60.04 204.60/60.04 [a__isNePal(__(I, __(P, I)))] = [2] I + [1] P + [1] 204.60/60.04 > [0] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 204.60/60.04 We return to the main proof. 204.60/60.04 204.60/60.04 We are left with following problem, upon which TcT provides the 204.60/60.04 certificate MAYBE. 204.60/60.04 204.60/60.04 Strict Trs: 204.60/60.04 { a____(X1, X2) -> __(X1, X2) 204.60/60.04 , a____(X, nil()) -> mark(X) 204.60/60.04 , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 204.60/60.04 , a____(nil(), X) -> mark(X) 204.60/60.04 , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 204.60/60.04 , mark(nil()) -> nil() 204.60/60.04 , mark(tt()) -> tt() 204.60/60.04 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 204.60/60.04 , mark(isNePal(X)) -> a__isNePal(mark(X)) 204.60/60.04 , a__and(X1, X2) -> and(X1, X2) 204.60/60.04 , a__isNePal(X) -> isNePal(X) } 204.60/60.04 Weak Trs: 204.60/60.04 { a__and(tt(), X) -> mark(X) 204.60/60.04 , a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.04 Obligation: 204.60/60.04 derivational complexity 204.60/60.04 Answer: 204.60/60.04 MAYBE 204.60/60.04 204.60/60.04 The weightgap principle applies (using the following nonconstant 204.60/60.04 growth matrix-interpretation) 204.60/60.04 204.60/60.04 TcT has computed the following triangular matrix interpretation. 204.60/60.04 Note that the diagonal of the component-wise maxima of 204.60/60.04 interpretation-entries contains no more than 1 non-zero entries. 204.60/60.04 204.60/60.04 [a____](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [__](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [mark](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 [nil] = [1] 204.60/60.04 204.60/60.04 [a__and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [tt] = [0] 204.60/60.04 204.60/60.04 [a__isNePal](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 [and](x1, x2) = [1] x1 + [1] x2 + [1] 204.60/60.04 204.60/60.04 [isNePal](x1) = [1] x1 + [1] 204.60/60.04 204.60/60.04 The order satisfies the following ordering constraints: 204.60/60.04 204.60/60.04 [a____(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [__(X1, X2)] 204.60/60.04 204.60/60.04 [a____(X, nil())] = [1] X + [1] 204.60/60.04 > [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a____(__(X, Y), Z)] = [1] X + [1] Y + [1] Z + [0] 204.60/60.04 >= [1] X + [1] Y + [1] Z + [0] 204.60/60.04 = [a____(mark(X), a____(mark(Y), mark(Z)))] 204.60/60.04 204.60/60.04 [a____(nil(), X)] = [1] X + [1] 204.60/60.04 > [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [mark(__(X1, X2))] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [a____(mark(X1), mark(X2))] 204.60/60.04 204.60/60.04 [mark(nil())] = [1] 204.60/60.04 >= [1] 204.60/60.04 = [nil()] 204.60/60.04 204.60/60.04 [mark(tt())] = [0] 204.60/60.04 >= [0] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 [mark(and(X1, X2))] = [1] X1 + [1] X2 + [1] 204.60/60.04 > [1] X1 + [1] X2 + [0] 204.60/60.04 = [a__and(mark(X1), X2)] 204.60/60.04 204.60/60.04 [mark(isNePal(X))] = [1] X + [1] 204.60/60.04 > [1] X + [0] 204.60/60.04 = [a__isNePal(mark(X))] 204.60/60.04 204.60/60.04 [a__and(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 ? [1] X1 + [1] X2 + [1] 204.60/60.04 = [and(X1, X2)] 204.60/60.04 204.60/60.04 [a__and(tt(), X)] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a__isNePal(X)] = [1] X + [0] 204.60/60.04 ? [1] X + [1] 204.60/60.04 = [isNePal(X)] 204.60/60.04 204.60/60.04 [a__isNePal(__(I, __(P, I)))] = [2] I + [1] P + [0] 204.60/60.04 >= [0] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 204.60/60.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 204.60/60.04 204.60/60.04 We are left with following problem, upon which TcT provides the 204.60/60.04 certificate MAYBE. 204.60/60.04 204.60/60.04 Strict Trs: 204.60/60.04 { a____(X1, X2) -> __(X1, X2) 204.60/60.04 , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 204.60/60.04 , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 204.60/60.04 , mark(nil()) -> nil() 204.60/60.04 , mark(tt()) -> tt() 204.60/60.04 , a__and(X1, X2) -> and(X1, X2) 204.60/60.04 , a__isNePal(X) -> isNePal(X) } 204.60/60.04 Weak Trs: 204.60/60.04 { a____(X, nil()) -> mark(X) 204.60/60.04 , a____(nil(), X) -> mark(X) 204.60/60.04 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 204.60/60.04 , mark(isNePal(X)) -> a__isNePal(mark(X)) 204.60/60.04 , a__and(tt(), X) -> mark(X) 204.60/60.04 , a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.04 Obligation: 204.60/60.04 derivational complexity 204.60/60.04 Answer: 204.60/60.04 MAYBE 204.60/60.04 204.60/60.04 The weightgap principle applies (using the following nonconstant 204.60/60.04 growth matrix-interpretation) 204.60/60.04 204.60/60.04 TcT has computed the following triangular matrix interpretation. 204.60/60.04 Note that the diagonal of the component-wise maxima of 204.60/60.04 interpretation-entries contains no more than 1 non-zero entries. 204.60/60.04 204.60/60.04 [a____](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [__](x1, x2) = [1] x1 + [1] x2 + [1] 204.60/60.04 204.60/60.04 [mark](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 [nil] = [1] 204.60/60.04 204.60/60.04 [a__and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [tt] = [0] 204.60/60.04 204.60/60.04 [a__isNePal](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 [and](x1, x2) = [1] x1 + [1] x2 + [0] 204.60/60.04 204.60/60.04 [isNePal](x1) = [1] x1 + [0] 204.60/60.04 204.60/60.04 The order satisfies the following ordering constraints: 204.60/60.04 204.60/60.04 [a____(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 ? [1] X1 + [1] X2 + [1] 204.60/60.04 = [__(X1, X2)] 204.60/60.04 204.60/60.04 [a____(X, nil())] = [1] X + [1] 204.60/60.04 > [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [a____(__(X, Y), Z)] = [1] X + [1] Y + [1] Z + [1] 204.60/60.04 > [1] X + [1] Y + [1] Z + [0] 204.60/60.04 = [a____(mark(X), a____(mark(Y), mark(Z)))] 204.60/60.04 204.60/60.04 [a____(nil(), X)] = [1] X + [1] 204.60/60.04 > [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.04 204.60/60.04 [mark(__(X1, X2))] = [1] X1 + [1] X2 + [1] 204.60/60.04 > [1] X1 + [1] X2 + [0] 204.60/60.04 = [a____(mark(X1), mark(X2))] 204.60/60.04 204.60/60.04 [mark(nil())] = [1] 204.60/60.04 >= [1] 204.60/60.04 = [nil()] 204.60/60.04 204.60/60.04 [mark(tt())] = [0] 204.60/60.04 >= [0] 204.60/60.04 = [tt()] 204.60/60.04 204.60/60.04 [mark(and(X1, X2))] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [a__and(mark(X1), X2)] 204.60/60.04 204.60/60.04 [mark(isNePal(X))] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [a__isNePal(mark(X))] 204.60/60.04 204.60/60.04 [a__and(X1, X2)] = [1] X1 + [1] X2 + [0] 204.60/60.04 >= [1] X1 + [1] X2 + [0] 204.60/60.04 = [and(X1, X2)] 204.60/60.04 204.60/60.04 [a__and(tt(), X)] = [1] X + [0] 204.60/60.04 >= [1] X + [0] 204.60/60.04 = [mark(X)] 204.60/60.05 204.60/60.05 [a__isNePal(X)] = [1] X + [0] 204.60/60.05 >= [1] X + [0] 204.60/60.05 = [isNePal(X)] 204.60/60.05 204.60/60.05 [a__isNePal(__(I, __(P, I)))] = [2] I + [1] P + [2] 204.60/60.05 > [0] 204.60/60.05 = [tt()] 204.60/60.05 204.60/60.05 204.60/60.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 204.60/60.05 204.60/60.05 We are left with following problem, upon which TcT provides the 204.60/60.05 certificate MAYBE. 204.60/60.05 204.60/60.05 Strict Trs: 204.60/60.05 { a____(X1, X2) -> __(X1, X2) 204.60/60.05 , mark(nil()) -> nil() 204.60/60.05 , mark(tt()) -> tt() 204.60/60.05 , a__and(X1, X2) -> and(X1, X2) 204.60/60.05 , a__isNePal(X) -> isNePal(X) } 204.60/60.05 Weak Trs: 204.60/60.05 { a____(X, nil()) -> mark(X) 204.60/60.05 , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 204.60/60.05 , a____(nil(), X) -> mark(X) 204.60/60.05 , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 204.60/60.05 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 204.60/60.05 , mark(isNePal(X)) -> a__isNePal(mark(X)) 204.60/60.05 , a__and(tt(), X) -> mark(X) 204.60/60.05 , a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.05 Obligation: 204.60/60.05 derivational complexity 204.60/60.05 Answer: 204.60/60.05 MAYBE 204.60/60.05 204.60/60.05 The weightgap principle applies (using the following nonconstant 204.60/60.05 growth matrix-interpretation) 204.60/60.05 204.60/60.05 TcT has computed the following triangular matrix interpretation. 204.60/60.05 Note that the diagonal of the component-wise maxima of 204.60/60.05 interpretation-entries contains no more than 1 non-zero entries. 204.60/60.05 204.60/60.05 [a____](x1, x2) = [1 2] x1 + [1 0] x2 + [0] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 204.60/60.05 [__](x1, x2) = [1 2] x1 + [1 0] x2 + [2] 204.60/60.05 [0 0] [0 0] [2] 204.60/60.05 204.60/60.05 [mark](x1) = [1 0] x1 + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 204.60/60.05 [nil] = [2] 204.60/60.05 [0] 204.60/60.05 204.60/60.05 [a__and](x1, x2) = [1 0] x1 + [1 2] x2 + [2] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 204.60/60.05 [tt] = [2] 204.60/60.05 [0] 204.60/60.05 204.60/60.05 [a__isNePal](x1) = [1 0] x1 + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 204.60/60.05 [and](x1, x2) = [1 0] x1 + [1 2] x2 + [2] 204.60/60.05 [0 0] [0 0] [2] 204.60/60.05 204.60/60.05 [isNePal](x1) = [1 0] x1 + [2] 204.60/60.05 [0 0] [1] 204.60/60.05 204.60/60.05 The order satisfies the following ordering constraints: 204.60/60.05 204.60/60.05 [a____(X1, X2)] = [1 2] X1 + [1 0] X2 + [0] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 ? [1 2] X1 + [1 0] X2 + [2] 204.60/60.05 [0 0] [0 0] [2] 204.60/60.05 = [__(X1, X2)] 204.60/60.05 204.60/60.05 [a____(X, nil())] = [1 2] X + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 >= [1 0] X + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 = [mark(X)] 204.60/60.05 204.60/60.05 [a____(__(X, Y), Z)] = [1 2] X + [1 0] Y + [1 0] Z + [6] 204.60/60.05 [0 0] [0 0] [0 0] [0] 204.60/60.05 >= [1 0] X + [1 0] Y + [1 0] Z + [6] 204.60/60.05 [0 0] [0 0] [0 0] [0] 204.60/60.05 = [a____(mark(X), a____(mark(Y), mark(Z)))] 204.60/60.05 204.60/60.05 [a____(nil(), X)] = [1 0] X + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 >= [1 0] X + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 = [mark(X)] 204.60/60.05 204.60/60.05 [mark(__(X1, X2))] = [1 2] X1 + [1 0] X2 + [4] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 >= [1 0] X1 + [1 0] X2 + [4] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 = [a____(mark(X1), mark(X2))] 204.60/60.05 204.60/60.05 [mark(nil())] = [4] 204.60/60.05 [0] 204.60/60.05 > [2] 204.60/60.05 [0] 204.60/60.05 = [nil()] 204.60/60.05 204.60/60.05 [mark(tt())] = [4] 204.60/60.05 [0] 204.60/60.05 > [2] 204.60/60.05 [0] 204.60/60.05 = [tt()] 204.60/60.05 204.60/60.05 [mark(and(X1, X2))] = [1 0] X1 + [1 2] X2 + [4] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 >= [1 0] X1 + [1 2] X2 + [4] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 = [a__and(mark(X1), X2)] 204.60/60.05 204.60/60.05 [mark(isNePal(X))] = [1 0] X + [4] 204.60/60.05 [0 0] [0] 204.60/60.05 >= [1 0] X + [4] 204.60/60.05 [0 0] [0] 204.60/60.05 = [a__isNePal(mark(X))] 204.60/60.05 204.60/60.05 [a__and(X1, X2)] = [1 0] X1 + [1 2] X2 + [2] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 ? [1 0] X1 + [1 2] X2 + [2] 204.60/60.05 [0 0] [0 0] [2] 204.60/60.05 = [and(X1, X2)] 204.60/60.05 204.60/60.05 [a__and(tt(), X)] = [1 2] X + [4] 204.60/60.05 [0 0] [0] 204.60/60.05 > [1 0] X + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 = [mark(X)] 204.60/60.05 204.60/60.05 [a__isNePal(X)] = [1 0] X + [2] 204.60/60.05 [0 0] [0] 204.60/60.05 ? [1 0] X + [2] 204.60/60.05 [0 0] [1] 204.60/60.05 = [isNePal(X)] 204.60/60.05 204.60/60.05 [a__isNePal(__(I, __(P, I)))] = [2 2] I + [1 2] P + [6] 204.60/60.05 [0 0] [0 0] [0] 204.60/60.05 > [2] 204.60/60.05 [0] 204.60/60.05 = [tt()] 204.60/60.05 204.60/60.05 204.60/60.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 204.60/60.05 204.60/60.05 We are left with following problem, upon which TcT provides the 204.60/60.05 certificate MAYBE. 204.60/60.05 204.60/60.05 Strict Trs: 204.60/60.05 { a____(X1, X2) -> __(X1, X2) 204.60/60.05 , a__and(X1, X2) -> and(X1, X2) 204.60/60.05 , a__isNePal(X) -> isNePal(X) } 204.60/60.05 Weak Trs: 204.60/60.05 { a____(X, nil()) -> mark(X) 204.60/60.05 , a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z))) 204.60/60.05 , a____(nil(), X) -> mark(X) 204.60/60.05 , mark(__(X1, X2)) -> a____(mark(X1), mark(X2)) 204.60/60.05 , mark(nil()) -> nil() 204.60/60.05 , mark(tt()) -> tt() 204.60/60.05 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 204.60/60.05 , mark(isNePal(X)) -> a__isNePal(mark(X)) 204.60/60.05 , a__and(tt(), X) -> mark(X) 204.60/60.05 , a__isNePal(__(I, __(P, I))) -> tt() } 204.60/60.05 Obligation: 204.60/60.05 derivational complexity 204.60/60.05 Answer: 204.60/60.05 MAYBE 204.60/60.05 204.60/60.05 None of the processors succeeded. 204.60/60.05 204.60/60.05 Details of failed attempt(s): 204.60/60.05 ----------------------------- 204.60/60.05 1) 'empty' failed due to the following reason: 204.60/60.05 204.60/60.05 Empty strict component of the problem is NOT empty. 204.60/60.05 204.60/60.05 2) 'Fastest' failed due to the following reason: 204.60/60.05 204.60/60.05 None of the processors succeeded. 204.60/60.05 204.60/60.05 Details of failed attempt(s): 204.60/60.05 ----------------------------- 204.60/60.05 1) 'Fastest (timeout of 30 seconds)' failed due to the following 204.60/60.05 reason: 204.60/60.05 204.60/60.05 Computation stopped due to timeout after 30.0 seconds. 204.60/60.05 204.60/60.05 2) 'Fastest' failed due to the following reason: 204.60/60.05 204.60/60.05 None of the processors succeeded. 204.60/60.05 204.60/60.05 Details of failed attempt(s): 204.60/60.05 ----------------------------- 204.60/60.05 1) 'matrix interpretation of dimension 6' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 2) 'matrix interpretation of dimension 5' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 3) 'matrix interpretation of dimension 4' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 4) 'matrix interpretation of dimension 3' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 5) 'matrix interpretation of dimension 2' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 6) 'matrix interpretation of dimension 1' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 204.60/60.05 3) 'iteProgress' failed due to the following reason: 204.60/60.05 204.60/60.05 Fail 204.60/60.05 204.60/60.05 4) 'bsearch-matrix' failed due to the following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 204.60/60.05 204.60/60.05 3) 'iteProgress (timeout of 297 seconds)' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 Fail 204.60/60.05 204.60/60.05 4) 'bsearch-matrix (timeout of 297 seconds)' failed due to the 204.60/60.05 following reason: 204.60/60.05 204.60/60.05 The input cannot be shown compatible 204.60/60.05 204.60/60.05 204.60/60.05 Arrrr.. 204.60/60.06 EOF