MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) , if_quot(true(), x, y) -> s(quot(minus(x, y), y)) , if_quot(false(), x, y) -> 0() } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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: 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: 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 processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) '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 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. 2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { minus^#(x, 0()) -> c_1(x) , minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) , le^#(0(), y) -> c_3() , le^#(s(x), 0()) -> c_4() , le^#(s(x), s(y)) -> c_5(le^#(x, y)) , quot^#(x, s(y)) -> c_6(if_quot^#(le(s(y), x), x, s(y))) , if_quot^#(true(), x, y) -> c_7(quot^#(minus(x, y), y)) , if_quot^#(false(), x, y) -> c_8() } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { minus^#(x, 0()) -> c_1(x) , minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) , le^#(0(), y) -> c_3() , le^#(s(x), 0()) -> c_4() , le^#(s(x), s(y)) -> c_5(le^#(x, y)) , quot^#(x, s(y)) -> c_6(if_quot^#(le(s(y), x), x, s(y))) , if_quot^#(true(), x, y) -> c_7(quot^#(minus(x, y), y)) , if_quot^#(false(), x, y) -> c_8() } Strict Trs: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) , if_quot(true(), x, y) -> s(quot(minus(x, y), y)) , if_quot(false(), x, y) -> 0() } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,4,8} by applications of Pre({3,4,8}) = {1,5,6}. Here rules are labeled as follows: DPs: { 1: minus^#(x, 0()) -> c_1(x) , 2: minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) , 3: le^#(0(), y) -> c_3() , 4: le^#(s(x), 0()) -> c_4() , 5: le^#(s(x), s(y)) -> c_5(le^#(x, y)) , 6: quot^#(x, s(y)) -> c_6(if_quot^#(le(s(y), x), x, s(y))) , 7: if_quot^#(true(), x, y) -> c_7(quot^#(minus(x, y), y)) , 8: if_quot^#(false(), x, y) -> c_8() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { minus^#(x, 0()) -> c_1(x) , minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) , le^#(s(x), s(y)) -> c_5(le^#(x, y)) , quot^#(x, s(y)) -> c_6(if_quot^#(le(s(y), x), x, s(y))) , if_quot^#(true(), x, y) -> c_7(quot^#(minus(x, y), y)) } Strict Trs: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) , if_quot(true(), x, y) -> s(quot(minus(x, y), y)) , if_quot(false(), x, y) -> 0() } Weak DPs: { le^#(0(), y) -> c_3() , le^#(s(x), 0()) -> c_4() , if_quot^#(false(), x, y) -> c_8() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..