MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , double(s(x)) -> s(s(double(x))) , double(0()) -> 0() , log(s(x)) -> loop(s(x), s(0()), 0()) , log(0()) -> logError() , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) , if(false(), x, y, z) -> loop(x, double(y), s(z)) , if(true(), x, y, z) -> z } 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) '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 minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-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: { le^#(s(x), s(y)) -> c_1(le^#(x, y)) , le^#(s(x), 0()) -> c_2() , le^#(0(), y) -> c_3() , double^#(s(x)) -> c_4(double^#(x)) , double^#(0()) -> c_5() , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) , log^#(0()) -> c_7() , loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) , if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) , if^#(true(), x, y, z) -> c_10(z) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { le^#(s(x), s(y)) -> c_1(le^#(x, y)) , le^#(s(x), 0()) -> c_2() , le^#(0(), y) -> c_3() , double^#(s(x)) -> c_4(double^#(x)) , double^#(0()) -> c_5() , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) , log^#(0()) -> c_7() , loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) , if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) , if^#(true(), x, y, z) -> c_10(z) } Strict Trs: { le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , double(s(x)) -> s(s(double(x))) , double(0()) -> 0() , log(s(x)) -> loop(s(x), s(0()), 0()) , log(0()) -> logError() , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) , if(false(), x, y, z) -> loop(x, double(y), s(z)) , if(true(), x, y, z) -> z } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2,3,5,7} by applications of Pre({2,3,5,7}) = {1,4,10}. Here rules are labeled as follows: DPs: { 1: le^#(s(x), s(y)) -> c_1(le^#(x, y)) , 2: le^#(s(x), 0()) -> c_2() , 3: le^#(0(), y) -> c_3() , 4: double^#(s(x)) -> c_4(double^#(x)) , 5: double^#(0()) -> c_5() , 6: log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) , 7: log^#(0()) -> c_7() , 8: loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) , 9: if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) , 10: if^#(true(), x, y, z) -> c_10(z) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { le^#(s(x), s(y)) -> c_1(le^#(x, y)) , double^#(s(x)) -> c_4(double^#(x)) , log^#(s(x)) -> c_6(loop^#(s(x), s(0()), 0())) , loop^#(x, s(y), z) -> c_8(if^#(le(x, s(y)), x, s(y), z)) , if^#(false(), x, y, z) -> c_9(loop^#(x, double(y), s(z))) , if^#(true(), x, y, z) -> c_10(z) } Strict Trs: { le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , double(s(x)) -> s(s(double(x))) , double(0()) -> 0() , log(s(x)) -> loop(s(x), s(0()), 0()) , log(0()) -> logError() , loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) , if(false(), x, y, z) -> loop(x, double(y), s(z)) , if(true(), x, y, z) -> z } Weak DPs: { le^#(s(x), 0()) -> c_2() , le^#(0(), y) -> c_3() , double^#(0()) -> c_5() , log^#(0()) -> c_7() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..