MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { minus(0(), x) -> 0() , minus(s(x), 0()) -> s(x) , minus(s(x), s(y)) -> minus(x, y) , mod(x, 0()) -> 0() , mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) , if(true(), x, y) -> x , if(false(), x, y) -> mod(minus(x, y), y) , lt(x, 0()) -> false() , lt(0(), s(x)) -> true() , lt(s(x), s(y)) -> lt(x, y) , gcd(x, 0()) -> x , gcd(0(), s(y)) -> s(y) , gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) } 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: Computation stopped due to timeout after 30.0 seconds. 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: { minus^#(0(), x) -> c_1() , minus^#(s(x), 0()) -> c_2(x) , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) , mod^#(x, 0()) -> c_4() , mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) , if^#(true(), x, y) -> c_6(x) , if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) , lt^#(x, 0()) -> c_8() , lt^#(0(), s(x)) -> c_9() , lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) , gcd^#(x, 0()) -> c_11(x) , gcd^#(0(), s(y)) -> c_12(y) , gcd^#(s(x), s(y)) -> c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { minus^#(0(), x) -> c_1() , minus^#(s(x), 0()) -> c_2(x) , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) , mod^#(x, 0()) -> c_4() , mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) , if^#(true(), x, y) -> c_6(x) , if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) , lt^#(x, 0()) -> c_8() , lt^#(0(), s(x)) -> c_9() , lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) , gcd^#(x, 0()) -> c_11(x) , gcd^#(0(), s(y)) -> c_12(y) , gcd^#(s(x), s(y)) -> c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } Strict Trs: { minus(0(), x) -> 0() , minus(s(x), 0()) -> s(x) , minus(s(x), s(y)) -> minus(x, y) , mod(x, 0()) -> 0() , mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) , if(true(), x, y) -> x , if(false(), x, y) -> mod(minus(x, y), y) , lt(x, 0()) -> false() , lt(0(), s(x)) -> true() , lt(s(x), s(y)) -> lt(x, y) , gcd(x, 0()) -> x , gcd(0(), s(y)) -> s(y) , gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,4,8,9} by applications of Pre({1,4,8,9}) = {2,3,6,7,10,11,12}. Here rules are labeled as follows: DPs: { 1: minus^#(0(), x) -> c_1() , 2: minus^#(s(x), 0()) -> c_2(x) , 3: minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) , 4: mod^#(x, 0()) -> c_4() , 5: mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) , 6: if^#(true(), x, y) -> c_6(x) , 7: if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) , 8: lt^#(x, 0()) -> c_8() , 9: lt^#(0(), s(x)) -> c_9() , 10: lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) , 11: gcd^#(x, 0()) -> c_11(x) , 12: gcd^#(0(), s(y)) -> c_12(y) , 13: gcd^#(s(x), s(y)) -> c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { minus^#(s(x), 0()) -> c_2(x) , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) , mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) , if^#(true(), x, y) -> c_6(x) , if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) , lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) , gcd^#(x, 0()) -> c_11(x) , gcd^#(0(), s(y)) -> c_12(y) , gcd^#(s(x), s(y)) -> c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } Strict Trs: { minus(0(), x) -> 0() , minus(s(x), 0()) -> s(x) , minus(s(x), s(y)) -> minus(x, y) , mod(x, 0()) -> 0() , mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) , if(true(), x, y) -> x , if(false(), x, y) -> mod(minus(x, y), y) , lt(x, 0()) -> false() , lt(0(), s(x)) -> true() , lt(s(x), s(y)) -> lt(x, y) , gcd(x, 0()) -> x , gcd(0(), s(y)) -> s(y) , gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) } Weak DPs: { minus^#(0(), x) -> c_1() , mod^#(x, 0()) -> c_4() , lt^#(x, 0()) -> c_8() , lt^#(0(), s(x)) -> c_9() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..