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)) , +(x, 0()) -> x , +(x, s(y)) -> s(+(x, y)) } 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: 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(s) = {1}, Uargs(+) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fib](x1) = [0] [0] = [4] [s](x1) = [1] x1 + [0] [+](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {fib, +} The order satisfies the following ordering constraints: [fib(0())] = [0] ? [4] = [0()] [fib(s(0()))] = [0] ? [4] = [s(0())] [fib(s(s(x)))] = [0] >= [0] = [+(fib(s(x)), fib(x))] [+(x, 0())] = [1] x + [4] > [1] x + [0] = [x] [+(x, s(y))] = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = [s(+(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: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , fib(s(s(x))) -> +(fib(s(x)), fib(x)) , +(x, s(y)) -> s(+(x, y)) } Weak Trs: { +(x, 0()) -> x } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(+) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fib](x1) = [4] [0] = [3] [s](x1) = [1] x1 + [0] [+](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {fib, +} The order satisfies the following ordering constraints: [fib(0())] = [4] > [3] = [0()] [fib(s(0()))] = [4] > [3] = [s(0())] [fib(s(s(x)))] = [4] ? [8] = [+(fib(s(x)), fib(x))] [+(x, 0())] = [1] x + [3] > [1] x + [0] = [x] [+(x, s(y))] = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = [s(+(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: { fib(s(s(x))) -> +(fib(s(x)), fib(x)) , +(x, s(y)) -> s(+(x, y)) } Weak Trs: { fib(0()) -> 0() , fib(s(0())) -> s(0()) , +(x, 0()) -> 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) '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 input cannot be shown compatible 2) 'Polynomial Path Order (PS) (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 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. Arrrr..