MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> 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: We add the following dependency tuples: Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) , if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) , if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {2,3} by applications of Pre({2,3}) = {1}. Here rules are labeled as follows: DPs: { 1: f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) , 2: if^#(true(), X, Y) -> c_2() , 3: if^#(false(), X, Y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) } Weak DPs: { if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } 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. { if^#(true(), X, Y) -> c_2() , if^#(false(), X, Y) -> c_3() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE Due to missing edges in the dependency-graph, the right-hand sides of following rules could be simplified: { f^#(X) -> c_1(if^#(X, c(), f(true())), f^#(true())) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { f^#(X) -> c_1(f^#(true())) } Weak Trs: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X , if(false(), X, Y) -> Y } 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: { f^#(X) -> c_1(f^#(true())) } 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) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 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) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 2) '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(if) = {3} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [0] [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] [c] = [0] [true] = [0] [false] = [1] The following symbols are considered usable {f, if} The order satisfies the following ordering constraints: [f(X)] = [1] X + [0] >= [1] X + [0] = [if(X, c(), f(true()))] [if(true(), X, Y)] = [1] X + [1] Y + [0] >= [1] X + [0] = [X] [if(false(), X, Y)] = [1] X + [1] Y + [1] > [1] Y + [0] = [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: { f(X) -> if(X, c(), f(true())) , if(true(), X, Y) -> X } Weak Trs: { if(false(), X, Y) -> Y } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(if) = {3} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [f](x1) = [1] x1 + [4] [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] [c] = [0] [true] = [4] [false] = [7] The following symbols are considered usable {f, if} The order satisfies the following ordering constraints: [f(X)] = [1] X + [4] ? [1] X + [8] = [if(X, c(), f(true()))] [if(true(), X, Y)] = [1] X + [1] Y + [4] > [1] X + [0] = [X] [if(false(), X, Y)] = [1] X + [1] Y + [7] > [1] Y + [0] = [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: { f(X) -> if(X, c(), f(true())) } Weak Trs: { if(true(), X, Y) -> X , if(false(), X, Y) -> 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) '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. 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 input cannot be shown compatible 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible Arrrr..