MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) } Obligation: innermost 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) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: We add the following innermost weak dependency pairs: Strict DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) } Strict Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) } Obligation: innermost runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() , fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_3) = {1, 2} TcT has computed the following constructor-restricted matrix interpretation. [0] = [0] [0] [s](x1) = [0] [0] [fib^#](x1) = [1] [0] [c_1] = [0] [0] [c_2] = [0] [0] [c_3](x1, x2) = [1 0] x1 + [1 0] x2 + [1] [0 1] [0 1] [2] The following symbols are considered usable {fib^#} The order satisfies the following ordering constraints: [fib^#(0())] = [1] [0] > [0] [0] = [c_1()] [fib^#(s(0()))] = [1] [0] > [0] [0] = [c_2()] [fib^#(s(s(x)))] = [1] [0] ? [3] [2] = [c_3(fib^#(s(x)), fib^#(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 DPs: { fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) } Weak DPs: { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { fib^#(0()) -> c_1() , fib^#(s(0())) -> c_2() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fib^#(s(s(x))) -> c_3(fib^#(s(x)), fib^#(x)) } Obligation: innermost 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) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 2) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 3) 'Fastest (timeout of 5 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. 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)). [fib](x1) = [7] [0] = [3] [s](x1) = [1] x1 + [3] [+](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {fib} The order satisfies the following ordering constraints: [fib(0())] = [7] > [3] = [0()] [fib(s(0()))] = [7] > [6] = [s(0())] [fib(s(s(x)))] = [7] ? [14] = [+(fib(s(x)), fib(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: { fib(s(s(x))) -> +(fib(s(x)), fib(x)) } Weak Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) } Obligation: innermost 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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 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 minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. Arrrr..