MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { p(p(s(x))) -> p(x) , p(0()) -> s(s(0())) , p(s(x)) -> x , le(p(s(x)), x) -> le(x, x) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , minus(x, y) -> if(le(x, y), x, y) , if(true(), x, y) -> 0() , if(false(), x, y) -> s(minus(p(x), y)) } 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: 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. 2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { p^#(p(s(x))) -> c_1(p^#(x)) , p^#(0()) -> c_2() , p^#(s(x)) -> c_3(x) , le^#(p(s(x)), x) -> c_4(le^#(x, x)) , le^#(0(), y) -> c_5() , le^#(s(x), 0()) -> c_6() , le^#(s(x), s(y)) -> c_7(le^#(x, y)) , minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) , if^#(true(), x, y) -> c_9() , if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { p^#(p(s(x))) -> c_1(p^#(x)) , p^#(0()) -> c_2() , p^#(s(x)) -> c_3(x) , le^#(p(s(x)), x) -> c_4(le^#(x, x)) , le^#(0(), y) -> c_5() , le^#(s(x), 0()) -> c_6() , le^#(s(x), s(y)) -> c_7(le^#(x, y)) , minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) , if^#(true(), x, y) -> c_9() , if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } Strict Trs: { p(p(s(x))) -> p(x) , p(0()) -> s(s(0())) , p(s(x)) -> x , le(p(s(x)), x) -> le(x, x) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , minus(x, y) -> if(le(x, y), x, y) , if(true(), x, y) -> 0() , if(false(), x, y) -> s(minus(p(x), y)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2,5,6,9} by applications of Pre({2,5,6,9}) = {1,3,4,7,8}. Here rules are labeled as follows: DPs: { 1: p^#(p(s(x))) -> c_1(p^#(x)) , 2: p^#(0()) -> c_2() , 3: p^#(s(x)) -> c_3(x) , 4: le^#(p(s(x)), x) -> c_4(le^#(x, x)) , 5: le^#(0(), y) -> c_5() , 6: le^#(s(x), 0()) -> c_6() , 7: le^#(s(x), s(y)) -> c_7(le^#(x, y)) , 8: minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) , 9: if^#(true(), x, y) -> c_9() , 10: if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { p^#(p(s(x))) -> c_1(p^#(x)) , p^#(s(x)) -> c_3(x) , le^#(p(s(x)), x) -> c_4(le^#(x, x)) , le^#(s(x), s(y)) -> c_7(le^#(x, y)) , minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) , if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } Strict Trs: { p(p(s(x))) -> p(x) , p(0()) -> s(s(0())) , p(s(x)) -> x , le(p(s(x)), x) -> le(x, x) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , minus(x, y) -> if(le(x, y), x, y) , if(true(), x, y) -> 0() , if(false(), x, y) -> s(minus(p(x), y)) } Weak DPs: { p^#(0()) -> c_2() , le^#(0(), y) -> c_5() , le^#(s(x), 0()) -> c_6() , if^#(true(), x, y) -> c_9() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..