MAYBE 429.04/256.22 MAYBE 429.04/256.22 429.04/256.22 We are left with following problem, upon which TcT provides the 429.04/256.22 certificate MAYBE. 429.04/256.22 429.04/256.22 Strict Trs: 429.04/256.22 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.22 , a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.22 , a__g(X) -> g(X) 429.04/256.22 , a__g(b()) -> c() 429.04/256.22 , a__b() -> b() 429.04/256.22 , a__b() -> c() 429.04/256.22 , mark(g(X)) -> a__g(mark(X)) 429.04/256.22 , mark(b()) -> a__b() 429.04/256.22 , mark(c()) -> c() 429.04/256.22 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.22 Obligation: 429.04/256.22 runtime complexity 429.04/256.22 Answer: 429.04/256.22 MAYBE 429.04/256.22 429.04/256.22 None of the processors succeeded. 429.04/256.22 429.04/256.22 Details of failed attempt(s): 429.04/256.22 ----------------------------- 429.04/256.22 1) 'Best' failed due to the following reason: 429.04/256.22 429.04/256.22 None of the processors succeeded. 429.04/256.22 429.04/256.22 Details of failed attempt(s): 429.04/256.22 ----------------------------- 429.04/256.22 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 429.04/256.22 seconds)' failed due to the following reason: 429.04/256.22 429.04/256.22 The weightgap principle applies (using the following nonconstant 429.04/256.22 growth matrix-interpretation) 429.04/256.22 429.04/256.22 The following argument positions are usable: 429.04/256.22 Uargs(g) = {1}, Uargs(a__g) = {1} 429.04/256.22 429.04/256.22 TcT has computed the following matrix interpretation satisfying 429.04/256.22 not(EDA) and not(IDA(1)). 429.04/256.22 429.04/256.22 [a__f](x1, x2, x3) = [1] x3 + [5] 429.04/256.22 429.04/256.22 [g](x1) = [1] x1 + [7] 429.04/256.22 429.04/256.22 [a__g](x1) = [1] x1 + [7] 429.04/256.22 429.04/256.22 [b] = [7] 429.04/256.22 429.04/256.22 [c] = [7] 429.04/256.22 429.04/256.22 [a__b] = [5] 429.04/256.22 429.04/256.22 [mark](x1) = [1] x1 + [7] 429.04/256.22 429.04/256.22 [f](x1, x2, x3) = [1] x3 + [7] 429.04/256.22 429.04/256.22 The order satisfies the following ordering constraints: 429.04/256.22 429.04/256.22 [a__f(X1, X2, X3)] = [1] X3 + [5] 429.04/256.22 ? [1] X3 + [7] 429.04/256.22 = [f(X1, X2, X3)] 429.04/256.22 429.04/256.22 [a__f(X, g(X), Y)] = [1] Y + [5] 429.04/256.22 >= [1] Y + [5] 429.04/256.22 = [a__f(Y, Y, Y)] 429.04/256.22 429.04/256.22 [a__g(X)] = [1] X + [7] 429.04/256.22 >= [1] X + [7] 429.04/256.22 = [g(X)] 429.04/256.22 429.04/256.22 [a__g(b())] = [14] 429.04/256.22 > [7] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [a__b()] = [5] 429.04/256.22 ? [7] 429.04/256.22 = [b()] 429.04/256.22 429.04/256.22 [a__b()] = [5] 429.04/256.22 ? [7] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(g(X))] = [1] X + [14] 429.04/256.22 >= [1] X + [14] 429.04/256.22 = [a__g(mark(X))] 429.04/256.22 429.04/256.22 [mark(b())] = [14] 429.04/256.22 > [5] 429.04/256.22 = [a__b()] 429.04/256.22 429.04/256.22 [mark(c())] = [14] 429.04/256.22 > [7] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(f(X1, X2, X3))] = [1] X3 + [14] 429.04/256.22 > [1] X3 + [5] 429.04/256.22 = [a__f(X1, X2, X3)] 429.04/256.22 429.04/256.22 429.04/256.22 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 429.04/256.22 429.04/256.22 We are left with following problem, upon which TcT provides the 429.04/256.22 certificate MAYBE. 429.04/256.22 429.04/256.22 Strict Trs: 429.04/256.22 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.22 , a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.22 , a__g(X) -> g(X) 429.04/256.22 , a__b() -> b() 429.04/256.22 , a__b() -> c() 429.04/256.22 , mark(g(X)) -> a__g(mark(X)) } 429.04/256.22 Weak Trs: 429.04/256.22 { a__g(b()) -> c() 429.04/256.22 , mark(b()) -> a__b() 429.04/256.22 , mark(c()) -> c() 429.04/256.22 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.22 Obligation: 429.04/256.22 runtime complexity 429.04/256.22 Answer: 429.04/256.22 MAYBE 429.04/256.22 429.04/256.22 The weightgap principle applies (using the following nonconstant 429.04/256.22 growth matrix-interpretation) 429.04/256.22 429.04/256.22 The following argument positions are usable: 429.04/256.22 Uargs(g) = {1}, Uargs(a__g) = {1} 429.04/256.22 429.04/256.22 TcT has computed the following matrix interpretation satisfying 429.04/256.22 not(EDA) and not(IDA(1)). 429.04/256.22 429.04/256.22 [a__f](x1, x2, x3) = [1] x3 + [7] 429.04/256.22 429.04/256.22 [g](x1) = [1] x1 + [7] 429.04/256.22 429.04/256.22 [a__g](x1) = [1] x1 + [7] 429.04/256.22 429.04/256.22 [b] = [3] 429.04/256.22 429.04/256.22 [c] = [5] 429.04/256.22 429.04/256.22 [a__b] = [6] 429.04/256.22 429.04/256.22 [mark](x1) = [1] x1 + [7] 429.04/256.22 429.04/256.22 [f](x1, x2, x3) = [1] x3 + [5] 429.04/256.22 429.04/256.22 The order satisfies the following ordering constraints: 429.04/256.22 429.04/256.22 [a__f(X1, X2, X3)] = [1] X3 + [7] 429.04/256.22 > [1] X3 + [5] 429.04/256.22 = [f(X1, X2, X3)] 429.04/256.22 429.04/256.22 [a__f(X, g(X), Y)] = [1] Y + [7] 429.04/256.22 >= [1] Y + [7] 429.04/256.22 = [a__f(Y, Y, Y)] 429.04/256.22 429.04/256.22 [a__g(X)] = [1] X + [7] 429.04/256.22 >= [1] X + [7] 429.04/256.22 = [g(X)] 429.04/256.22 429.04/256.22 [a__g(b())] = [10] 429.04/256.22 > [5] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [a__b()] = [6] 429.04/256.22 > [3] 429.04/256.22 = [b()] 429.04/256.22 429.04/256.22 [a__b()] = [6] 429.04/256.22 > [5] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(g(X))] = [1] X + [14] 429.04/256.22 >= [1] X + [14] 429.04/256.22 = [a__g(mark(X))] 429.04/256.22 429.04/256.22 [mark(b())] = [10] 429.04/256.22 > [6] 429.04/256.22 = [a__b()] 429.04/256.22 429.04/256.22 [mark(c())] = [12] 429.04/256.22 > [5] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(f(X1, X2, X3))] = [1] X3 + [12] 429.04/256.22 > [1] X3 + [7] 429.04/256.22 = [a__f(X1, X2, X3)] 429.04/256.22 429.04/256.22 429.04/256.22 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 429.04/256.22 429.04/256.22 We are left with following problem, upon which TcT provides the 429.04/256.22 certificate MAYBE. 429.04/256.22 429.04/256.22 Strict Trs: 429.04/256.22 { a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.22 , a__g(X) -> g(X) 429.04/256.22 , mark(g(X)) -> a__g(mark(X)) } 429.04/256.22 Weak Trs: 429.04/256.22 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.22 , a__g(b()) -> c() 429.04/256.22 , a__b() -> b() 429.04/256.22 , a__b() -> c() 429.04/256.22 , mark(b()) -> a__b() 429.04/256.22 , mark(c()) -> c() 429.04/256.22 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.22 Obligation: 429.04/256.22 runtime complexity 429.04/256.22 Answer: 429.04/256.22 MAYBE 429.04/256.22 429.04/256.22 The weightgap principle applies (using the following nonconstant 429.04/256.22 growth matrix-interpretation) 429.04/256.22 429.04/256.22 The following argument positions are usable: 429.04/256.22 Uargs(g) = {1}, Uargs(a__g) = {1} 429.04/256.22 429.04/256.22 TcT has computed the following matrix interpretation satisfying 429.04/256.22 not(EDA) and not(IDA(1)). 429.04/256.22 429.04/256.22 [a__f](x1, x2, x3) = [1] x3 + [7] 429.04/256.22 429.04/256.22 [g](x1) = [1] x1 + [0] 429.04/256.22 429.04/256.22 [a__g](x1) = [1] x1 + [1] 429.04/256.22 429.04/256.22 [b] = [7] 429.04/256.22 429.04/256.22 [c] = [4] 429.04/256.22 429.04/256.22 [a__b] = [7] 429.04/256.22 429.04/256.22 [mark](x1) = [1] x1 + [0] 429.04/256.22 429.04/256.22 [f](x1, x2, x3) = [1] x3 + [7] 429.04/256.22 429.04/256.22 The order satisfies the following ordering constraints: 429.04/256.22 429.04/256.22 [a__f(X1, X2, X3)] = [1] X3 + [7] 429.04/256.22 >= [1] X3 + [7] 429.04/256.22 = [f(X1, X2, X3)] 429.04/256.22 429.04/256.22 [a__f(X, g(X), Y)] = [1] Y + [7] 429.04/256.22 >= [1] Y + [7] 429.04/256.22 = [a__f(Y, Y, Y)] 429.04/256.22 429.04/256.22 [a__g(X)] = [1] X + [1] 429.04/256.22 > [1] X + [0] 429.04/256.22 = [g(X)] 429.04/256.22 429.04/256.22 [a__g(b())] = [8] 429.04/256.22 > [4] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [a__b()] = [7] 429.04/256.22 >= [7] 429.04/256.22 = [b()] 429.04/256.22 429.04/256.22 [a__b()] = [7] 429.04/256.22 > [4] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(g(X))] = [1] X + [0] 429.04/256.22 ? [1] X + [1] 429.04/256.22 = [a__g(mark(X))] 429.04/256.22 429.04/256.22 [mark(b())] = [7] 429.04/256.22 >= [7] 429.04/256.22 = [a__b()] 429.04/256.22 429.04/256.22 [mark(c())] = [4] 429.04/256.22 >= [4] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(f(X1, X2, X3))] = [1] X3 + [7] 429.04/256.22 >= [1] X3 + [7] 429.04/256.22 = [a__f(X1, X2, X3)] 429.04/256.22 429.04/256.22 429.04/256.22 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 429.04/256.22 429.04/256.22 We are left with following problem, upon which TcT provides the 429.04/256.22 certificate MAYBE. 429.04/256.22 429.04/256.22 Strict Trs: 429.04/256.22 { a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.22 , mark(g(X)) -> a__g(mark(X)) } 429.04/256.22 Weak Trs: 429.04/256.22 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.22 , a__g(X) -> g(X) 429.04/256.22 , a__g(b()) -> c() 429.04/256.22 , a__b() -> b() 429.04/256.22 , a__b() -> c() 429.04/256.22 , mark(b()) -> a__b() 429.04/256.22 , mark(c()) -> c() 429.04/256.22 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.22 Obligation: 429.04/256.22 runtime complexity 429.04/256.22 Answer: 429.04/256.22 MAYBE 429.04/256.22 429.04/256.22 We use the processor 'matrix interpretation of dimension 1' to 429.04/256.22 orient following rules strictly. 429.04/256.22 429.04/256.22 Trs: { mark(g(X)) -> a__g(mark(X)) } 429.04/256.22 429.04/256.22 The induced complexity on above rules (modulo remaining rules) is 429.04/256.22 YES(?,O(n^1)) . These rules are moved into the corresponding weak 429.04/256.22 component(s). 429.04/256.22 429.04/256.22 Sub-proof: 429.04/256.22 ---------- 429.04/256.22 The following argument positions are usable: 429.04/256.22 Uargs(g) = {1}, Uargs(a__g) = {1} 429.04/256.22 429.04/256.22 TcT has computed the following constructor-based matrix 429.04/256.22 interpretation satisfying not(EDA). 429.04/256.22 429.04/256.22 [a__f](x1, x2, x3) = [0] 429.04/256.22 429.04/256.22 [g](x1) = [1] x1 + [4] 429.04/256.22 429.04/256.22 [a__g](x1) = [1] x1 + [4] 429.04/256.22 429.04/256.22 [b] = [4] 429.04/256.22 429.04/256.22 [c] = [0] 429.04/256.22 429.04/256.22 [a__b] = [4] 429.04/256.22 429.04/256.22 [mark](x1) = [2] x1 + [0] 429.04/256.22 429.04/256.22 [f](x1, x2, x3) = [0] 429.04/256.22 429.04/256.22 The order satisfies the following ordering constraints: 429.04/256.22 429.04/256.22 [a__f(X1, X2, X3)] = [0] 429.04/256.22 >= [0] 429.04/256.22 = [f(X1, X2, X3)] 429.04/256.22 429.04/256.22 [a__f(X, g(X), Y)] = [0] 429.04/256.22 >= [0] 429.04/256.22 = [a__f(Y, Y, Y)] 429.04/256.22 429.04/256.22 [a__g(X)] = [1] X + [4] 429.04/256.22 >= [1] X + [4] 429.04/256.22 = [g(X)] 429.04/256.22 429.04/256.22 [a__g(b())] = [8] 429.04/256.22 > [0] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [a__b()] = [4] 429.04/256.22 >= [4] 429.04/256.22 = [b()] 429.04/256.22 429.04/256.22 [a__b()] = [4] 429.04/256.22 > [0] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(g(X))] = [2] X + [8] 429.04/256.22 > [2] X + [4] 429.04/256.22 = [a__g(mark(X))] 429.04/256.22 429.04/256.22 [mark(b())] = [8] 429.04/256.22 > [4] 429.04/256.22 = [a__b()] 429.04/256.22 429.04/256.22 [mark(c())] = [0] 429.04/256.22 >= [0] 429.04/256.22 = [c()] 429.04/256.22 429.04/256.22 [mark(f(X1, X2, X3))] = [0] 429.04/256.22 >= [0] 429.04/256.22 = [a__f(X1, X2, X3)] 429.04/256.22 429.04/256.22 429.04/256.22 We return to the main proof. 429.04/256.22 429.04/256.22 We are left with following problem, upon which TcT provides the 429.04/256.22 certificate MAYBE. 429.04/256.22 429.04/256.22 Strict Trs: { a__f(X, g(X), Y) -> a__f(Y, Y, Y) } 429.04/256.22 Weak Trs: 429.04/256.22 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.22 , a__g(X) -> g(X) 429.04/256.22 , a__g(b()) -> c() 429.04/256.22 , a__b() -> b() 429.04/256.22 , a__b() -> c() 429.04/256.22 , mark(g(X)) -> a__g(mark(X)) 429.04/256.22 , mark(b()) -> a__b() 429.04/256.22 , mark(c()) -> c() 429.04/256.22 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.22 Obligation: 429.04/256.22 runtime complexity 429.04/256.23 Answer: 429.04/256.23 MAYBE 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'empty' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 2) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'empty' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 2) 'Fastest' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'empty' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 2) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'empty' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 2) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'empty' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 2) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 429.04/256.23 429.04/256.23 429.04/256.23 2) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'empty' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 2) 'With Problem ...' failed due to the following reason: 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 429.04/256.23 429.04/256.23 429.04/256.23 429.04/256.23 2) 'Best' failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 429.04/256.23 to the following reason: 429.04/256.23 429.04/256.23 The processor is inapplicable, reason: 429.04/256.23 Processor only applicable for innermost runtime complexity analysis 429.04/256.23 429.04/256.23 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 429.04/256.23 following reason: 429.04/256.23 429.04/256.23 The processor is inapplicable, reason: 429.04/256.23 Processor only applicable for innermost runtime complexity analysis 429.04/256.23 429.04/256.23 429.04/256.23 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 429.04/256.23 failed due to the following reason: 429.04/256.23 429.04/256.23 None of the processors succeeded. 429.04/256.23 429.04/256.23 Details of failed attempt(s): 429.04/256.23 ----------------------------- 429.04/256.23 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 429.04/256.23 failed due to the following reason: 429.04/256.23 429.04/256.23 match-boundness of the problem could not be verified. 429.04/256.23 429.04/256.23 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 429.04/256.23 failed due to the following reason: 429.04/256.23 429.04/256.23 match-boundness of the problem could not be verified. 429.04/256.23 429.04/256.23 429.04/256.23 429.04/256.23 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 429.04/256.23 the following reason: 429.04/256.23 429.04/256.23 We add the following weak dependency pairs: 429.04/256.23 429.04/256.23 Strict DPs: 429.04/256.23 { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) 429.04/256.23 , a__f^#(X, g(X), Y) -> c_2(a__f^#(Y, Y, Y)) 429.04/256.23 , a__g^#(X) -> c_3(X) 429.04/256.23 , a__g^#(b()) -> c_4() 429.04/256.23 , a__b^#() -> c_5() 429.04/256.23 , a__b^#() -> c_6() 429.04/256.23 , mark^#(g(X)) -> c_7(a__g^#(mark(X))) 429.04/256.23 , mark^#(b()) -> c_8(a__b^#()) 429.04/256.23 , mark^#(c()) -> c_9() 429.04/256.23 , mark^#(f(X1, X2, X3)) -> c_10(a__f^#(X1, X2, X3)) } 429.04/256.23 429.04/256.23 and mark the set of starting terms. 429.04/256.23 429.04/256.23 We are left with following problem, upon which TcT provides the 429.04/256.23 certificate MAYBE. 429.04/256.23 429.04/256.23 Strict DPs: 429.04/256.23 { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) 429.04/256.23 , a__f^#(X, g(X), Y) -> c_2(a__f^#(Y, Y, Y)) 429.04/256.23 , a__g^#(X) -> c_3(X) 429.04/256.23 , a__g^#(b()) -> c_4() 429.04/256.23 , a__b^#() -> c_5() 429.04/256.23 , a__b^#() -> c_6() 429.04/256.23 , mark^#(g(X)) -> c_7(a__g^#(mark(X))) 429.04/256.23 , mark^#(b()) -> c_8(a__b^#()) 429.04/256.23 , mark^#(c()) -> c_9() 429.04/256.23 , mark^#(f(X1, X2, X3)) -> c_10(a__f^#(X1, X2, X3)) } 429.04/256.23 Strict Trs: 429.04/256.23 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.23 , a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.23 , a__g(X) -> g(X) 429.04/256.23 , a__g(b()) -> c() 429.04/256.23 , a__b() -> b() 429.04/256.23 , a__b() -> c() 429.04/256.23 , mark(g(X)) -> a__g(mark(X)) 429.04/256.23 , mark(b()) -> a__b() 429.04/256.23 , mark(c()) -> c() 429.04/256.23 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.23 Obligation: 429.04/256.23 runtime complexity 429.04/256.23 Answer: 429.04/256.23 MAYBE 429.04/256.23 429.04/256.23 We estimate the number of application of {4,5,6,9} by applications 429.04/256.23 of Pre({4,5,6,9}) = {1,3,7,8}. Here rules are labeled as follows: 429.04/256.23 429.04/256.23 DPs: 429.04/256.23 { 1: a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) 429.04/256.23 , 2: a__f^#(X, g(X), Y) -> c_2(a__f^#(Y, Y, Y)) 429.04/256.23 , 3: a__g^#(X) -> c_3(X) 429.04/256.23 , 4: a__g^#(b()) -> c_4() 429.04/256.23 , 5: a__b^#() -> c_5() 429.04/256.23 , 6: a__b^#() -> c_6() 429.04/256.23 , 7: mark^#(g(X)) -> c_7(a__g^#(mark(X))) 429.04/256.23 , 8: mark^#(b()) -> c_8(a__b^#()) 429.04/256.23 , 9: mark^#(c()) -> c_9() 429.04/256.23 , 10: mark^#(f(X1, X2, X3)) -> c_10(a__f^#(X1, X2, X3)) } 429.04/256.23 429.04/256.23 We are left with following problem, upon which TcT provides the 429.04/256.23 certificate MAYBE. 429.04/256.23 429.04/256.23 Strict DPs: 429.04/256.23 { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) 429.04/256.23 , a__f^#(X, g(X), Y) -> c_2(a__f^#(Y, Y, Y)) 429.04/256.23 , a__g^#(X) -> c_3(X) 429.04/256.23 , mark^#(g(X)) -> c_7(a__g^#(mark(X))) 429.04/256.23 , mark^#(b()) -> c_8(a__b^#()) 429.04/256.23 , mark^#(f(X1, X2, X3)) -> c_10(a__f^#(X1, X2, X3)) } 429.04/256.23 Strict Trs: 429.04/256.23 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.23 , a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.23 , a__g(X) -> g(X) 429.04/256.23 , a__g(b()) -> c() 429.04/256.23 , a__b() -> b() 429.04/256.23 , a__b() -> c() 429.04/256.23 , mark(g(X)) -> a__g(mark(X)) 429.04/256.23 , mark(b()) -> a__b() 429.04/256.23 , mark(c()) -> c() 429.04/256.23 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.23 Weak DPs: 429.04/256.23 { a__g^#(b()) -> c_4() 429.04/256.23 , a__b^#() -> c_5() 429.04/256.23 , a__b^#() -> c_6() 429.04/256.23 , mark^#(c()) -> c_9() } 429.04/256.23 Obligation: 429.04/256.23 runtime complexity 429.04/256.23 Answer: 429.04/256.23 MAYBE 429.04/256.23 429.04/256.23 We estimate the number of application of {5} by applications of 429.04/256.23 Pre({5}) = {1,3}. Here rules are labeled as follows: 429.04/256.23 429.04/256.23 DPs: 429.04/256.23 { 1: a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) 429.04/256.23 , 2: a__f^#(X, g(X), Y) -> c_2(a__f^#(Y, Y, Y)) 429.04/256.23 , 3: a__g^#(X) -> c_3(X) 429.04/256.23 , 4: mark^#(g(X)) -> c_7(a__g^#(mark(X))) 429.04/256.23 , 5: mark^#(b()) -> c_8(a__b^#()) 429.04/256.23 , 6: mark^#(f(X1, X2, X3)) -> c_10(a__f^#(X1, X2, X3)) 429.04/256.23 , 7: a__g^#(b()) -> c_4() 429.04/256.23 , 8: a__b^#() -> c_5() 429.04/256.23 , 9: a__b^#() -> c_6() 429.04/256.23 , 10: mark^#(c()) -> c_9() } 429.04/256.23 429.04/256.23 We are left with following problem, upon which TcT provides the 429.04/256.23 certificate MAYBE. 429.04/256.23 429.04/256.23 Strict DPs: 429.04/256.23 { a__f^#(X1, X2, X3) -> c_1(X1, X2, X3) 429.04/256.23 , a__f^#(X, g(X), Y) -> c_2(a__f^#(Y, Y, Y)) 429.04/256.23 , a__g^#(X) -> c_3(X) 429.04/256.23 , mark^#(g(X)) -> c_7(a__g^#(mark(X))) 429.04/256.23 , mark^#(f(X1, X2, X3)) -> c_10(a__f^#(X1, X2, X3)) } 429.04/256.23 Strict Trs: 429.04/256.23 { a__f(X1, X2, X3) -> f(X1, X2, X3) 429.04/256.23 , a__f(X, g(X), Y) -> a__f(Y, Y, Y) 429.04/256.23 , a__g(X) -> g(X) 429.04/256.23 , a__g(b()) -> c() 429.04/256.23 , a__b() -> b() 429.04/256.23 , a__b() -> c() 429.04/256.23 , mark(g(X)) -> a__g(mark(X)) 429.04/256.23 , mark(b()) -> a__b() 429.04/256.23 , mark(c()) -> c() 429.04/256.23 , mark(f(X1, X2, X3)) -> a__f(X1, X2, X3) } 429.04/256.23 Weak DPs: 429.04/256.23 { a__g^#(b()) -> c_4() 429.04/256.23 , a__b^#() -> c_5() 429.04/256.23 , a__b^#() -> c_6() 429.04/256.23 , mark^#(b()) -> c_8(a__b^#()) 429.04/256.23 , mark^#(c()) -> c_9() } 429.04/256.23 Obligation: 429.04/256.23 runtime complexity 429.04/256.23 Answer: 429.04/256.23 MAYBE 429.04/256.23 429.04/256.23 Empty strict component of the problem is NOT empty. 429.04/256.23 429.04/256.23 429.04/256.23 Arrrr.. 429.35/256.54 EOF