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