MAYBE 444.94/297.03 MAYBE 444.94/297.03 444.94/297.03 We are left with following problem, upon which TcT provides the 444.94/297.03 certificate MAYBE. 444.94/297.03 444.94/297.03 Strict Trs: 444.94/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 444.94/297.03 , a__f(X) -> f(X) 444.94/297.03 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 444.94/297.03 , mark(f(X)) -> a__f(mark(X)) 444.94/297.03 , mark(g(X)) -> a__g(mark(X)) 444.94/297.03 , mark(0()) -> 0() 444.94/297.03 , mark(s(X)) -> s(mark(X)) 444.94/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 444.94/297.03 , a__g(X) -> g(X) 444.94/297.03 , a__g(0()) -> s(0()) 444.94/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) 444.94/297.03 , a__sel(X1, X2) -> sel(X1, X2) 444.94/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 444.94/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 444.94/297.03 Obligation: 444.94/297.03 innermost runtime complexity 444.94/297.03 Answer: 444.94/297.03 MAYBE 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'Best' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 444.94/297.03 following reason: 444.94/297.03 444.94/297.03 Computation stopped due to timeout after 297.0 seconds. 444.94/297.03 444.94/297.03 2) 'Best' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 444.94/297.03 seconds)' failed due to the following reason: 444.94/297.03 444.94/297.03 The weightgap principle applies (using the following nonconstant 444.94/297.03 growth matrix-interpretation) 444.94/297.03 444.94/297.03 The following argument positions are usable: 444.94/297.03 Uargs(a__f) = {1}, Uargs(cons) = {1}, Uargs(a__g) = {1}, 444.94/297.03 Uargs(s) = {1}, Uargs(a__sel) = {1, 2} 444.94/297.03 444.94/297.03 TcT has computed the following matrix interpretation satisfying 444.94/297.03 not(EDA) and not(IDA(1)). 444.94/297.03 444.94/297.03 [a__f](x1) = [1] x1 + [7] 444.94/297.03 444.94/297.03 [cons](x1, x2) = [1] x1 + [7] 444.94/297.03 444.94/297.03 [mark](x1) = [7] 444.94/297.03 444.94/297.03 [f](x1) = [1] x1 + [6] 444.94/297.03 444.94/297.03 [g](x1) = [1] x1 + [6] 444.94/297.03 444.94/297.03 [a__g](x1) = [1] x1 + [7] 444.94/297.03 444.94/297.03 [0] = [7] 444.94/297.03 444.94/297.03 [s](x1) = [1] x1 + [0] 444.94/297.03 444.94/297.03 [a__sel](x1, x2) = [1] x1 + [1] x2 + [1] 444.94/297.03 444.94/297.03 [sel](x1, x2) = [1] x1 + [1] x2 + [0] 444.94/297.03 444.94/297.03 The order satisfies the following ordering constraints: 444.94/297.03 444.94/297.03 [a__f(X)] = [1] X + [7] 444.94/297.03 ? [14] 444.94/297.03 = [cons(mark(X), f(g(X)))] 444.94/297.03 444.94/297.03 [a__f(X)] = [1] X + [7] 444.94/297.03 > [1] X + [6] 444.94/297.03 = [f(X)] 444.94/297.03 444.94/297.03 [mark(cons(X1, X2))] = [7] 444.94/297.03 ? [14] 444.94/297.03 = [cons(mark(X1), X2)] 444.94/297.03 444.94/297.03 [mark(f(X))] = [7] 444.94/297.03 ? [14] 444.94/297.03 = [a__f(mark(X))] 444.94/297.03 444.94/297.03 [mark(g(X))] = [7] 444.94/297.03 ? [14] 444.94/297.03 = [a__g(mark(X))] 444.94/297.03 444.94/297.03 [mark(0())] = [7] 444.94/297.03 >= [7] 444.94/297.03 = [0()] 444.94/297.03 444.94/297.03 [mark(s(X))] = [7] 444.94/297.03 >= [7] 444.94/297.03 = [s(mark(X))] 444.94/297.03 444.94/297.03 [mark(sel(X1, X2))] = [7] 444.94/297.03 ? [15] 444.94/297.03 = [a__sel(mark(X1), mark(X2))] 444.94/297.03 444.94/297.03 [a__g(X)] = [1] X + [7] 444.94/297.03 > [1] X + [6] 444.94/297.03 = [g(X)] 444.94/297.03 444.94/297.03 [a__g(0())] = [14] 444.94/297.03 > [7] 444.94/297.03 = [s(0())] 444.94/297.03 444.94/297.03 [a__g(s(X))] = [1] X + [7] 444.94/297.03 ? [14] 444.94/297.03 = [s(s(a__g(mark(X))))] 444.94/297.03 444.94/297.03 [a__sel(X1, X2)] = [1] X1 + [1] X2 + [1] 444.94/297.03 > [1] X1 + [1] X2 + [0] 444.94/297.03 = [sel(X1, X2)] 444.94/297.03 444.94/297.03 [a__sel(0(), cons(X, Y))] = [1] X + [15] 444.94/297.03 > [7] 444.94/297.03 = [mark(X)] 444.94/297.03 444.94/297.03 [a__sel(s(X), cons(Y, Z))] = [1] X + [1] Y + [8] 444.94/297.03 ? [15] 444.94/297.03 = [a__sel(mark(X), mark(Z))] 444.94/297.03 444.94/297.03 444.94/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 444.94/297.03 444.94/297.03 We are left with following problem, upon which TcT provides the 444.94/297.03 certificate MAYBE. 444.94/297.03 444.94/297.03 Strict Trs: 444.94/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 444.94/297.03 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 444.94/297.03 , mark(f(X)) -> a__f(mark(X)) 444.94/297.03 , mark(g(X)) -> a__g(mark(X)) 444.94/297.03 , mark(0()) -> 0() 444.94/297.03 , mark(s(X)) -> s(mark(X)) 444.94/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 444.94/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) 444.94/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 444.94/297.03 Weak Trs: 444.94/297.03 { a__f(X) -> f(X) 444.94/297.03 , a__g(X) -> g(X) 444.94/297.03 , a__g(0()) -> s(0()) 444.94/297.03 , a__sel(X1, X2) -> sel(X1, X2) 444.94/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) } 444.94/297.03 Obligation: 444.94/297.03 innermost runtime complexity 444.94/297.03 Answer: 444.94/297.03 MAYBE 444.94/297.03 444.94/297.03 The weightgap principle applies (using the following nonconstant 444.94/297.03 growth matrix-interpretation) 444.94/297.03 444.94/297.03 The following argument positions are usable: 444.94/297.03 Uargs(a__f) = {1}, Uargs(cons) = {1}, Uargs(a__g) = {1}, 444.94/297.03 Uargs(s) = {1}, Uargs(a__sel) = {1, 2} 444.94/297.03 444.94/297.03 TcT has computed the following matrix interpretation satisfying 444.94/297.03 not(EDA) and not(IDA(1)). 444.94/297.03 444.94/297.03 [a__f](x1) = [1] x1 + [5] 444.94/297.03 444.94/297.03 [cons](x1, x2) = [1] x1 + [4] 444.94/297.03 444.94/297.03 [mark](x1) = [0] 444.94/297.03 444.94/297.03 [f](x1) = [1] x1 + [5] 444.94/297.03 444.94/297.03 [g](x1) = [1] x1 + [0] 444.94/297.03 444.94/297.03 [a__g](x1) = [1] x1 + [0] 444.94/297.03 444.94/297.03 [0] = [0] 444.94/297.03 444.94/297.03 [s](x1) = [1] x1 + [0] 444.94/297.03 444.94/297.03 [a__sel](x1, x2) = [1] x1 + [1] x2 + [0] 444.94/297.03 444.94/297.03 [sel](x1, x2) = [1] x1 + [1] x2 + [0] 444.94/297.03 444.94/297.03 The order satisfies the following ordering constraints: 444.94/297.03 444.94/297.03 [a__f(X)] = [1] X + [5] 444.94/297.03 > [4] 444.94/297.03 = [cons(mark(X), f(g(X)))] 444.94/297.03 444.94/297.03 [a__f(X)] = [1] X + [5] 444.94/297.03 >= [1] X + [5] 444.94/297.03 = [f(X)] 444.94/297.03 444.94/297.03 [mark(cons(X1, X2))] = [0] 444.94/297.03 ? [4] 444.94/297.03 = [cons(mark(X1), X2)] 444.94/297.03 444.94/297.03 [mark(f(X))] = [0] 444.94/297.03 ? [5] 444.94/297.03 = [a__f(mark(X))] 444.94/297.03 444.94/297.03 [mark(g(X))] = [0] 444.94/297.03 >= [0] 444.94/297.03 = [a__g(mark(X))] 444.94/297.03 444.94/297.03 [mark(0())] = [0] 444.94/297.03 >= [0] 444.94/297.03 = [0()] 444.94/297.03 444.94/297.03 [mark(s(X))] = [0] 444.94/297.03 >= [0] 444.94/297.03 = [s(mark(X))] 444.94/297.03 444.94/297.03 [mark(sel(X1, X2))] = [0] 444.94/297.03 >= [0] 444.94/297.03 = [a__sel(mark(X1), mark(X2))] 444.94/297.03 444.94/297.03 [a__g(X)] = [1] X + [0] 444.94/297.03 >= [1] X + [0] 444.94/297.03 = [g(X)] 444.94/297.03 444.94/297.03 [a__g(0())] = [0] 444.94/297.03 >= [0] 444.94/297.03 = [s(0())] 444.94/297.03 444.94/297.03 [a__g(s(X))] = [1] X + [0] 444.94/297.03 >= [0] 444.94/297.03 = [s(s(a__g(mark(X))))] 444.94/297.03 444.94/297.03 [a__sel(X1, X2)] = [1] X1 + [1] X2 + [0] 444.94/297.03 >= [1] X1 + [1] X2 + [0] 444.94/297.03 = [sel(X1, X2)] 444.94/297.03 444.94/297.03 [a__sel(0(), cons(X, Y))] = [1] X + [4] 444.94/297.03 > [0] 444.94/297.03 = [mark(X)] 444.94/297.03 444.94/297.03 [a__sel(s(X), cons(Y, Z))] = [1] X + [1] Y + [4] 444.94/297.03 > [0] 444.94/297.03 = [a__sel(mark(X), mark(Z))] 444.94/297.03 444.94/297.03 444.94/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 444.94/297.03 444.94/297.03 We are left with following problem, upon which TcT provides the 444.94/297.03 certificate MAYBE. 444.94/297.03 444.94/297.03 Strict Trs: 444.94/297.03 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 444.94/297.03 , mark(f(X)) -> a__f(mark(X)) 444.94/297.03 , mark(g(X)) -> a__g(mark(X)) 444.94/297.03 , mark(0()) -> 0() 444.94/297.03 , mark(s(X)) -> s(mark(X)) 444.94/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 444.94/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) } 444.94/297.03 Weak Trs: 444.94/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 444.94/297.03 , a__f(X) -> f(X) 444.94/297.03 , a__g(X) -> g(X) 444.94/297.03 , a__g(0()) -> s(0()) 444.94/297.03 , a__sel(X1, X2) -> sel(X1, X2) 444.94/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 444.94/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 444.94/297.03 Obligation: 444.94/297.03 innermost runtime complexity 444.94/297.03 Answer: 444.94/297.03 MAYBE 444.94/297.03 444.94/297.03 The weightgap principle applies (using the following nonconstant 444.94/297.03 growth matrix-interpretation) 444.94/297.03 444.94/297.03 The following argument positions are usable: 444.94/297.03 Uargs(a__f) = {1}, Uargs(cons) = {1}, Uargs(a__g) = {1}, 444.94/297.03 Uargs(s) = {1}, Uargs(a__sel) = {1, 2} 444.94/297.03 444.94/297.03 TcT has computed the following matrix interpretation satisfying 444.94/297.03 not(EDA) and not(IDA(1)). 444.94/297.03 444.94/297.03 [a__f](x1) = [1] x1 + [6] 444.94/297.03 444.94/297.03 [cons](x1, x2) = [1] x1 + [2] 444.94/297.03 444.94/297.03 [mark](x1) = [2] 444.94/297.03 444.94/297.03 [f](x1) = [1] x1 + [5] 444.94/297.03 444.94/297.03 [g](x1) = [1] x1 + [1] 444.94/297.03 444.94/297.03 [a__g](x1) = [1] x1 + [2] 444.94/297.03 444.94/297.03 [0] = [0] 444.94/297.03 444.94/297.03 [s](x1) = [1] x1 + [2] 444.94/297.03 444.94/297.03 [a__sel](x1, x2) = [1] x1 + [1] x2 + [4] 444.94/297.03 444.94/297.03 [sel](x1, x2) = [1] x1 + [1] x2 + [4] 444.94/297.03 444.94/297.03 The order satisfies the following ordering constraints: 444.94/297.03 444.94/297.03 [a__f(X)] = [1] X + [6] 444.94/297.03 > [4] 444.94/297.03 = [cons(mark(X), f(g(X)))] 444.94/297.03 444.94/297.03 [a__f(X)] = [1] X + [6] 444.94/297.03 > [1] X + [5] 444.94/297.03 = [f(X)] 444.94/297.03 444.94/297.03 [mark(cons(X1, X2))] = [2] 444.94/297.03 ? [4] 444.94/297.03 = [cons(mark(X1), X2)] 444.94/297.03 444.94/297.03 [mark(f(X))] = [2] 444.94/297.03 ? [8] 444.94/297.03 = [a__f(mark(X))] 444.94/297.03 444.94/297.03 [mark(g(X))] = [2] 444.94/297.03 ? [4] 444.94/297.03 = [a__g(mark(X))] 444.94/297.03 444.94/297.03 [mark(0())] = [2] 444.94/297.03 > [0] 444.94/297.03 = [0()] 444.94/297.03 444.94/297.03 [mark(s(X))] = [2] 444.94/297.03 ? [4] 444.94/297.03 = [s(mark(X))] 444.94/297.03 444.94/297.03 [mark(sel(X1, X2))] = [2] 444.94/297.03 ? [8] 444.94/297.03 = [a__sel(mark(X1), mark(X2))] 444.94/297.03 444.94/297.03 [a__g(X)] = [1] X + [2] 444.94/297.03 > [1] X + [1] 444.94/297.03 = [g(X)] 444.94/297.03 444.94/297.03 [a__g(0())] = [2] 444.94/297.03 >= [2] 444.94/297.03 = [s(0())] 444.94/297.03 444.94/297.03 [a__g(s(X))] = [1] X + [4] 444.94/297.03 ? [8] 444.94/297.03 = [s(s(a__g(mark(X))))] 444.94/297.03 444.94/297.03 [a__sel(X1, X2)] = [1] X1 + [1] X2 + [4] 444.94/297.03 >= [1] X1 + [1] X2 + [4] 444.94/297.03 = [sel(X1, X2)] 444.94/297.03 444.94/297.03 [a__sel(0(), cons(X, Y))] = [1] X + [6] 444.94/297.03 > [2] 444.94/297.03 = [mark(X)] 444.94/297.03 444.94/297.03 [a__sel(s(X), cons(Y, Z))] = [1] X + [1] Y + [8] 444.94/297.03 >= [8] 444.94/297.03 = [a__sel(mark(X), mark(Z))] 444.94/297.03 444.94/297.03 444.94/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 444.94/297.03 444.94/297.03 We are left with following problem, upon which TcT provides the 444.94/297.03 certificate MAYBE. 444.94/297.03 444.94/297.03 Strict Trs: 444.94/297.03 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 444.94/297.03 , mark(f(X)) -> a__f(mark(X)) 444.94/297.03 , mark(g(X)) -> a__g(mark(X)) 444.94/297.03 , mark(s(X)) -> s(mark(X)) 444.94/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) 444.94/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) } 444.94/297.03 Weak Trs: 444.94/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 444.94/297.03 , a__f(X) -> f(X) 444.94/297.03 , mark(0()) -> 0() 444.94/297.03 , a__g(X) -> g(X) 444.94/297.03 , a__g(0()) -> s(0()) 444.94/297.03 , a__sel(X1, X2) -> sel(X1, X2) 444.94/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 444.94/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 444.94/297.03 Obligation: 444.94/297.03 innermost runtime complexity 444.94/297.03 Answer: 444.94/297.03 MAYBE 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'Fastest' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 The weightgap principle applies (using the following nonconstant 444.94/297.03 growth matrix-interpretation) 444.94/297.03 444.94/297.03 The following argument positions are usable: 444.94/297.03 Uargs(a__f) = {1}, Uargs(cons) = {1}, Uargs(a__g) = {1}, 444.94/297.03 Uargs(s) = {1}, Uargs(a__sel) = {1, 2} 444.94/297.03 444.94/297.03 TcT has computed the following matrix interpretation satisfying 444.94/297.03 not(EDA) and not(IDA(1)). 444.94/297.03 444.94/297.03 [a__f](x1) = [1 0] x1 + [0] 444.94/297.03 [0 0] [4] 444.94/297.03 444.94/297.03 [cons](x1, x2) = [1 0] x1 + [0] 444.94/297.03 [0 0] [0] 444.94/297.03 444.94/297.03 [mark](x1) = [0] 444.94/297.03 [0] 444.94/297.03 444.94/297.03 [f](x1) = [0] 444.94/297.03 [0] 444.94/297.03 444.94/297.03 [g](x1) = [0] 444.94/297.03 [0] 444.94/297.03 444.94/297.03 [a__g](x1) = [1 1] x1 + [0] 444.94/297.03 [0 0] [1] 444.94/297.03 444.94/297.03 [0] = [0] 444.94/297.03 [0] 444.94/297.03 444.94/297.03 [s](x1) = [1 0] x1 + [0] 444.94/297.03 [0 0] [1] 444.94/297.03 444.94/297.03 [a__sel](x1, x2) = [1 0] x1 + [1 0] x2 + [0] 444.94/297.03 [0 0] [0 0] [0] 444.94/297.03 444.94/297.03 [sel](x1, x2) = [0] 444.94/297.03 [0] 444.94/297.03 444.94/297.03 The order satisfies the following ordering constraints: 444.94/297.03 444.94/297.03 [a__f(X)] = [1 0] X + [0] 444.94/297.03 [0 0] [4] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [cons(mark(X), f(g(X)))] 444.94/297.03 444.94/297.03 [a__f(X)] = [1 0] X + [0] 444.94/297.03 [0 0] [4] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [f(X)] 444.94/297.03 444.94/297.03 [mark(cons(X1, X2))] = [0] 444.94/297.03 [0] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [cons(mark(X1), X2)] 444.94/297.03 444.94/297.03 [mark(f(X))] = [0] 444.94/297.03 [0] 444.94/297.03 ? [0] 444.94/297.03 [4] 444.94/297.03 = [a__f(mark(X))] 444.94/297.03 444.94/297.03 [mark(g(X))] = [0] 444.94/297.03 [0] 444.94/297.03 ? [0] 444.94/297.03 [1] 444.94/297.03 = [a__g(mark(X))] 444.94/297.03 444.94/297.03 [mark(0())] = [0] 444.94/297.03 [0] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [0()] 444.94/297.03 444.94/297.03 [mark(s(X))] = [0] 444.94/297.03 [0] 444.94/297.03 ? [0] 444.94/297.03 [1] 444.94/297.03 = [s(mark(X))] 444.94/297.03 444.94/297.03 [mark(sel(X1, X2))] = [0] 444.94/297.03 [0] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [a__sel(mark(X1), mark(X2))] 444.94/297.03 444.94/297.03 [a__g(X)] = [1 1] X + [0] 444.94/297.03 [0 0] [1] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [g(X)] 444.94/297.03 444.94/297.03 [a__g(0())] = [0] 444.94/297.03 [1] 444.94/297.03 >= [0] 444.94/297.03 [1] 444.94/297.03 = [s(0())] 444.94/297.03 444.94/297.03 [a__g(s(X))] = [1 0] X + [1] 444.94/297.03 [0 0] [1] 444.94/297.03 > [0] 444.94/297.03 [1] 444.94/297.03 = [s(s(a__g(mark(X))))] 444.94/297.03 444.94/297.03 [a__sel(X1, X2)] = [1 0] X1 + [1 0] X2 + [0] 444.94/297.03 [0 0] [0 0] [0] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [sel(X1, X2)] 444.94/297.03 444.94/297.03 [a__sel(0(), cons(X, Y))] = [1 0] X + [0] 444.94/297.03 [0 0] [0] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [mark(X)] 444.94/297.03 444.94/297.03 [a__sel(s(X), cons(Y, Z))] = [1 0] X + [1 0] Y + [0] 444.94/297.03 [0 0] [0 0] [0] 444.94/297.03 >= [0] 444.94/297.03 [0] 444.94/297.03 = [a__sel(mark(X), mark(Z))] 444.94/297.03 444.94/297.03 444.94/297.03 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 444.94/297.03 444.94/297.03 We are left with following problem, upon which TcT provides the 444.94/297.03 certificate MAYBE. 444.94/297.03 444.94/297.03 Strict Trs: 444.94/297.03 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 444.94/297.03 , mark(f(X)) -> a__f(mark(X)) 444.94/297.03 , mark(g(X)) -> a__g(mark(X)) 444.94/297.03 , mark(s(X)) -> s(mark(X)) 444.94/297.03 , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) } 444.94/297.03 Weak Trs: 444.94/297.03 { a__f(X) -> cons(mark(X), f(g(X))) 444.94/297.03 , a__f(X) -> f(X) 444.94/297.03 , mark(0()) -> 0() 444.94/297.03 , a__g(X) -> g(X) 444.94/297.03 , a__g(0()) -> s(0()) 444.94/297.03 , a__g(s(X)) -> s(s(a__g(mark(X)))) 444.94/297.03 , a__sel(X1, X2) -> sel(X1, X2) 444.94/297.03 , a__sel(0(), cons(X, Y)) -> mark(X) 444.94/297.03 , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) } 444.94/297.03 Obligation: 444.94/297.03 innermost runtime complexity 444.94/297.03 Answer: 444.94/297.03 MAYBE 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 2) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'empty' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 2) 'With Problem ...' failed due to the following reason: 444.94/297.03 444.94/297.03 Empty strict component of the problem is NOT empty. 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 2) 'Best' failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 444.94/297.03 following reason: 444.94/297.03 444.94/297.03 The input cannot be shown compatible 444.94/297.03 444.94/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 444.94/297.03 to the following reason: 444.94/297.03 444.94/297.03 The input cannot be shown compatible 444.94/297.03 444.94/297.03 444.94/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 444.94/297.03 failed due to the following reason: 444.94/297.03 444.94/297.03 None of the processors succeeded. 444.94/297.03 444.94/297.03 Details of failed attempt(s): 444.94/297.03 ----------------------------- 444.94/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 444.94/297.03 failed due to the following reason: 444.94/297.03 444.94/297.03 match-boundness of the problem could not be verified. 444.94/297.03 444.94/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 444.94/297.03 failed due to the following reason: 444.94/297.03 444.94/297.03 match-boundness of the problem could not be verified. 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 444.94/297.03 Arrrr.. 445.07/297.14 EOF