MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(true(), x, y, z) -> g(gt(x, y), x, y, z) , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() } 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: Computation stopped due to timeout after 30.0 seconds. 2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 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^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) , g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) , g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) , gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) , gt^#(s(u), 0()) -> c_5() , gt^#(0(), v) -> c_6() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) , g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) , g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) , gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) , gt^#(s(u), 0()) -> c_5() , gt^#(0(), v) -> c_6() } Strict Trs: { f(true(), x, y, z) -> g(gt(x, y), x, y, z) , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {5,6} by applications of Pre({5,6}) = {4}. Here rules are labeled as follows: DPs: { 1: f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) , 2: g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) , 3: g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) , 4: gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) , 5: gt^#(s(u), 0()) -> c_5() , 6: gt^#(0(), v) -> c_6() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(true(), x, y, z) -> c_1(g^#(gt(x, y), x, y, z)) , g^#(true(), x, y, z) -> c_2(f^#(gt(x, z), x, y, s(z))) , g^#(true(), x, y, z) -> c_3(f^#(gt(x, z), x, s(y), z)) , gt^#(s(u), s(v)) -> c_4(gt^#(u, v)) } Strict Trs: { f(true(), x, y, z) -> g(gt(x, y), x, y, z) , g(true(), x, y, z) -> f(gt(x, z), x, y, s(z)) , g(true(), x, y, z) -> f(gt(x, z), x, s(y), z) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() } Weak DPs: { gt^#(s(u), 0()) -> c_5() , gt^#(0(), v) -> c_6() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..