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