MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { bin(x, 0()) -> s(0()) , bin(0(), s(y)) -> 0() , bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y)) } 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(+) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [bin](x1, x2) = [3] [0] = [2] [s](x1) = [1] x1 + [4] [+](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {bin} The order satisfies the following ordering constraints: [bin(x, 0())] = [3] ? [6] = [s(0())] [bin(0(), s(y))] = [3] > [2] = [0()] [bin(s(x), s(y))] = [3] ? [13] = [+(bin(x, s(y)), bin(x, y))] 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: { bin(x, 0()) -> s(0()) , bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y)) } Weak Trs: { bin(0(), s(y)) -> 0() } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(+) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [bin](x1, x2) = [3] [0] = [2] [s](x1) = [1] x1 + [0] [+](x1, x2) = [1] x1 + [1] x2 + [7] The following symbols are considered usable {bin} The order satisfies the following ordering constraints: [bin(x, 0())] = [3] > [2] = [s(0())] [bin(0(), s(y))] = [3] > [2] = [0()] [bin(s(x), s(y))] = [3] ? [13] = [+(bin(x, s(y)), bin(x, y))] 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: { bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y)) } Weak Trs: { bin(x, 0()) -> s(0()) , bin(0(), s(y)) -> 0() } 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) '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) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { bin^#(x, 0()) -> c_1() , bin^#(0(), s(y)) -> c_2() , bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { bin^#(x, 0()) -> c_1() , bin^#(0(), s(y)) -> c_2() , bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) } Strict Trs: { bin(x, 0()) -> s(0()) , bin(0(), s(y)) -> 0() , bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y)) } 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: bin^#(x, 0()) -> c_1() , 2: bin^#(0(), s(y)) -> c_2() , 3: bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { bin^#(s(x), s(y)) -> c_3(bin^#(x, s(y)), bin^#(x, y)) } Strict Trs: { bin(x, 0()) -> s(0()) , bin(0(), s(y)) -> 0() , bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y)) } Weak DPs: { bin^#(x, 0()) -> c_1() , bin^#(0(), s(y)) -> c_2() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..