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