MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(true(), x, y) -> f(gt(x, y), x, round(s(y))) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(s(0())) , round(0()) -> 0() } 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: 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: 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) '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 2) '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 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) -> c_1(f^#(gt(x, y), x, round(s(y)))) , gt^#(s(u), s(v)) -> c_2(gt^#(u, v)) , gt^#(s(u), 0()) -> c_3() , gt^#(0(), v) -> c_4() , round^#(s(s(x))) -> c_5(round^#(x)) , round^#(s(0())) -> c_6() , round^#(0()) -> c_7() } 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) -> c_1(f^#(gt(x, y), x, round(s(y)))) , gt^#(s(u), s(v)) -> c_2(gt^#(u, v)) , gt^#(s(u), 0()) -> c_3() , gt^#(0(), v) -> c_4() , round^#(s(s(x))) -> c_5(round^#(x)) , round^#(s(0())) -> c_6() , round^#(0()) -> c_7() } Strict Trs: { f(true(), x, y) -> f(gt(x, y), x, round(s(y))) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(s(0())) , round(0()) -> 0() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,4,6,7} by applications of Pre({3,4,6,7}) = {2,5}. Here rules are labeled as follows: DPs: { 1: f^#(true(), x, y) -> c_1(f^#(gt(x, y), x, round(s(y)))) , 2: gt^#(s(u), s(v)) -> c_2(gt^#(u, v)) , 3: gt^#(s(u), 0()) -> c_3() , 4: gt^#(0(), v) -> c_4() , 5: round^#(s(s(x))) -> c_5(round^#(x)) , 6: round^#(s(0())) -> c_6() , 7: round^#(0()) -> c_7() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(true(), x, y) -> c_1(f^#(gt(x, y), x, round(s(y)))) , gt^#(s(u), s(v)) -> c_2(gt^#(u, v)) , round^#(s(s(x))) -> c_5(round^#(x)) } Strict Trs: { f(true(), x, y) -> f(gt(x, y), x, round(s(y))) , gt(s(u), s(v)) -> gt(u, v) , gt(s(u), 0()) -> true() , gt(0(), v) -> false() , round(s(s(x))) -> s(s(round(x))) , round(s(0())) -> s(s(0())) , round(0()) -> 0() } Weak DPs: { gt^#(s(u), 0()) -> c_3() , gt^#(0(), v) -> c_4() , round^#(s(0())) -> c_6() , round^#(0()) -> c_7() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..