MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(f(x)) -> b() , f(g(a())) -> f(s(g(b()))) , g(x) -> f(g(x)) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {1}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [0] [g](x1) = [1] x1 + [4] [a] = [4] [s](x1) = [1] x1 + [0] [b] = [0] The following symbols are considered usable {f, g} The order satisfies the following ordering constraints: [f(f(x))] = [1] x + [0] >= [0] = [b()] [f(g(a()))] = [8] > [4] = [f(s(g(b())))] [g(x)] = [1] x + [4] >= [1] x + [4] = [f(g(x))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(f(x)) -> b() , g(x) -> f(g(x)) } Weak Trs: { f(g(a())) -> f(s(g(b()))) } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(f) = {1}, Uargs(s) = {1} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [4] [g](x1) = [1] x1 + [0] [a] = [4] [s](x1) = [1] x1 + [0] [b] = [0] The following symbols are considered usable {f, g} The order satisfies the following ordering constraints: [f(f(x))] = [1] x + [8] > [0] = [b()] [f(g(a()))] = [8] > [4] = [f(s(g(b())))] [g(x)] = [1] x + [0] ? [1] x + [4] = [f(g(x))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { g(x) -> f(g(x)) } Weak Trs: { f(f(x)) -> b() , f(g(a())) -> f(s(g(b()))) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { f^#(f(x)) -> c_1() , f^#(g(a())) -> c_2(f^#(s(g(b())))) , g^#(x) -> c_3(f^#(g(x))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(f(x)) -> c_1() , f^#(g(a())) -> c_2(f^#(s(g(b())))) , g^#(x) -> c_3(f^#(g(x))) } Strict Trs: { f(f(x)) -> b() , f(g(a())) -> f(s(g(b()))) , g(x) -> f(g(x)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2} by applications of Pre({1,2}) = {3}. Here rules are labeled as follows: DPs: { 1: f^#(f(x)) -> c_1() , 2: f^#(g(a())) -> c_2(f^#(s(g(b())))) , 3: g^#(x) -> c_3(f^#(g(x))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { g^#(x) -> c_3(f^#(g(x))) } Strict Trs: { f(f(x)) -> b() , f(g(a())) -> f(s(g(b()))) , g(x) -> f(g(x)) } Weak DPs: { f^#(f(x)) -> c_1() , f^#(g(a())) -> c_2(f^#(s(g(b())))) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1} by applications of Pre({1}) = {}. Here rules are labeled as follows: DPs: { 1: g^#(x) -> c_3(f^#(g(x))) , 2: f^#(f(x)) -> c_1() , 3: f^#(g(a())) -> c_2(f^#(s(g(b())))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(f(x)) -> b() , f(g(a())) -> f(s(g(b()))) , g(x) -> f(g(x)) } Weak DPs: { f^#(f(x)) -> c_1() , f^#(g(a())) -> c_2(f^#(s(g(b())))) , g^#(x) -> c_3(f^#(g(x))) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..