MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { min(x, 0()) -> 0() , min(0(), y) -> 0() , min(s(x), s(y)) -> s(min(x, y)) , max(x, 0()) -> x , max(0(), y) -> y , max(s(x), s(y)) -> s(max(x, y)) , -(x, 0()) -> x , -(s(x), s(y)) -> -(x, y) , gcd(x, 0(), 0()) -> x , gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) , gcd(0(), y, 0()) -> y , gcd(0(), 0(), z) -> z , gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) , gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) } 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) '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. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { min^#(x, 0()) -> c_1() , min^#(0(), y) -> c_2() , min^#(s(x), s(y)) -> c_3(min^#(x, y)) , max^#(x, 0()) -> c_4(x) , max^#(0(), y) -> c_5(y) , max^#(s(x), s(y)) -> c_6(max^#(x, y)) , -^#(x, 0()) -> c_7(x) , -^#(s(x), s(y)) -> c_8(-^#(x, y)) , gcd^#(x, 0(), 0()) -> c_9(x) , gcd^#(x, s(y), s(z)) -> c_10(gcd^#(x, -(max(y, z), min(y, z)), s(min(y, z)))) , gcd^#(0(), y, 0()) -> c_11(y) , gcd^#(0(), 0(), z) -> c_12(z) , gcd^#(s(x), y, s(z)) -> c_13(gcd^#(-(max(x, z), min(x, z)), y, s(min(x, z)))) , gcd^#(s(x), s(y), z) -> c_14(gcd^#(-(max(x, y), min(x, y)), s(min(x, y)), z)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { min^#(x, 0()) -> c_1() , min^#(0(), y) -> c_2() , min^#(s(x), s(y)) -> c_3(min^#(x, y)) , max^#(x, 0()) -> c_4(x) , max^#(0(), y) -> c_5(y) , max^#(s(x), s(y)) -> c_6(max^#(x, y)) , -^#(x, 0()) -> c_7(x) , -^#(s(x), s(y)) -> c_8(-^#(x, y)) , gcd^#(x, 0(), 0()) -> c_9(x) , gcd^#(x, s(y), s(z)) -> c_10(gcd^#(x, -(max(y, z), min(y, z)), s(min(y, z)))) , gcd^#(0(), y, 0()) -> c_11(y) , gcd^#(0(), 0(), z) -> c_12(z) , gcd^#(s(x), y, s(z)) -> c_13(gcd^#(-(max(x, z), min(x, z)), y, s(min(x, z)))) , gcd^#(s(x), s(y), z) -> c_14(gcd^#(-(max(x, y), min(x, y)), s(min(x, y)), z)) } Strict Trs: { min(x, 0()) -> 0() , min(0(), y) -> 0() , min(s(x), s(y)) -> s(min(x, y)) , max(x, 0()) -> x , max(0(), y) -> y , max(s(x), s(y)) -> s(max(x, y)) , -(x, 0()) -> x , -(s(x), s(y)) -> -(x, y) , gcd(x, 0(), 0()) -> x , gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) , gcd(0(), y, 0()) -> y , gcd(0(), 0(), z) -> z , gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) , gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2} by applications of Pre({1,2}) = {3,4,5,7,9,11,12}. Here rules are labeled as follows: DPs: { 1: min^#(x, 0()) -> c_1() , 2: min^#(0(), y) -> c_2() , 3: min^#(s(x), s(y)) -> c_3(min^#(x, y)) , 4: max^#(x, 0()) -> c_4(x) , 5: max^#(0(), y) -> c_5(y) , 6: max^#(s(x), s(y)) -> c_6(max^#(x, y)) , 7: -^#(x, 0()) -> c_7(x) , 8: -^#(s(x), s(y)) -> c_8(-^#(x, y)) , 9: gcd^#(x, 0(), 0()) -> c_9(x) , 10: gcd^#(x, s(y), s(z)) -> c_10(gcd^#(x, -(max(y, z), min(y, z)), s(min(y, z)))) , 11: gcd^#(0(), y, 0()) -> c_11(y) , 12: gcd^#(0(), 0(), z) -> c_12(z) , 13: gcd^#(s(x), y, s(z)) -> c_13(gcd^#(-(max(x, z), min(x, z)), y, s(min(x, z)))) , 14: gcd^#(s(x), s(y), z) -> c_14(gcd^#(-(max(x, y), min(x, y)), s(min(x, y)), z)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { min^#(s(x), s(y)) -> c_3(min^#(x, y)) , max^#(x, 0()) -> c_4(x) , max^#(0(), y) -> c_5(y) , max^#(s(x), s(y)) -> c_6(max^#(x, y)) , -^#(x, 0()) -> c_7(x) , -^#(s(x), s(y)) -> c_8(-^#(x, y)) , gcd^#(x, 0(), 0()) -> c_9(x) , gcd^#(x, s(y), s(z)) -> c_10(gcd^#(x, -(max(y, z), min(y, z)), s(min(y, z)))) , gcd^#(0(), y, 0()) -> c_11(y) , gcd^#(0(), 0(), z) -> c_12(z) , gcd^#(s(x), y, s(z)) -> c_13(gcd^#(-(max(x, z), min(x, z)), y, s(min(x, z)))) , gcd^#(s(x), s(y), z) -> c_14(gcd^#(-(max(x, y), min(x, y)), s(min(x, y)), z)) } Strict Trs: { min(x, 0()) -> 0() , min(0(), y) -> 0() , min(s(x), s(y)) -> s(min(x, y)) , max(x, 0()) -> x , max(0(), y) -> y , max(s(x), s(y)) -> s(max(x, y)) , -(x, 0()) -> x , -(s(x), s(y)) -> -(x, y) , gcd(x, 0(), 0()) -> x , gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) , gcd(0(), y, 0()) -> y , gcd(0(), 0(), z) -> z , gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) , gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) } Weak DPs: { min^#(x, 0()) -> c_1() , min^#(0(), y) -> c_2() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..