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)) , minus(x, 0()) -> x , minus(s(x), s(y)) -> s(minus(x, y)) , gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y))) , transform(x) -> s(s(x)) , transform(s(x)) -> s(s(transform(x))) , transform(cons(x, y)) -> y , transform(cons(x, y)) -> cons(cons(x, x), x) , cons(x, y) -> y , cons(x, cons(y, s(z))) -> cons(y, x) , cons(cons(x, z), s(y)) -> transform(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: { 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)) , minus^#(x, 0()) -> c_7(x) , minus^#(s(x), s(y)) -> c_8(minus^#(x, y)) , gcd^#(s(x), s(y)) -> c_9(gcd^#(minus(max(x, y), min(x, transform(y))), s(min(x, y)))) , transform^#(x) -> c_10(x) , transform^#(s(x)) -> c_11(transform^#(x)) , transform^#(cons(x, y)) -> c_12(y) , transform^#(cons(x, y)) -> c_13(cons^#(cons(x, x), x)) , cons^#(x, y) -> c_14(y) , cons^#(x, cons(y, s(z))) -> c_15(cons^#(y, x)) , cons^#(cons(x, z), s(y)) -> c_16(transform^#(x)) } 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)) , minus^#(x, 0()) -> c_7(x) , minus^#(s(x), s(y)) -> c_8(minus^#(x, y)) , gcd^#(s(x), s(y)) -> c_9(gcd^#(minus(max(x, y), min(x, transform(y))), s(min(x, y)))) , transform^#(x) -> c_10(x) , transform^#(s(x)) -> c_11(transform^#(x)) , transform^#(cons(x, y)) -> c_12(y) , transform^#(cons(x, y)) -> c_13(cons^#(cons(x, x), x)) , cons^#(x, y) -> c_14(y) , cons^#(x, cons(y, s(z))) -> c_15(cons^#(y, x)) , cons^#(cons(x, z), s(y)) -> c_16(transform^#(x)) } 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)) , minus(x, 0()) -> x , minus(s(x), s(y)) -> s(minus(x, y)) , gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y))) , transform(x) -> s(s(x)) , transform(s(x)) -> s(s(transform(x))) , transform(cons(x, y)) -> y , transform(cons(x, y)) -> cons(cons(x, x), x) , cons(x, y) -> y , cons(x, cons(y, s(z))) -> cons(y, x) , cons(cons(x, z), s(y)) -> transform(x) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2} by applications of Pre({1,2}) = {3,4,5,7,10,12,14}. 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: minus^#(x, 0()) -> c_7(x) , 8: minus^#(s(x), s(y)) -> c_8(minus^#(x, y)) , 9: gcd^#(s(x), s(y)) -> c_9(gcd^#(minus(max(x, y), min(x, transform(y))), s(min(x, y)))) , 10: transform^#(x) -> c_10(x) , 11: transform^#(s(x)) -> c_11(transform^#(x)) , 12: transform^#(cons(x, y)) -> c_12(y) , 13: transform^#(cons(x, y)) -> c_13(cons^#(cons(x, x), x)) , 14: cons^#(x, y) -> c_14(y) , 15: cons^#(x, cons(y, s(z))) -> c_15(cons^#(y, x)) , 16: cons^#(cons(x, z), s(y)) -> c_16(transform^#(x)) } 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)) , minus^#(x, 0()) -> c_7(x) , minus^#(s(x), s(y)) -> c_8(minus^#(x, y)) , gcd^#(s(x), s(y)) -> c_9(gcd^#(minus(max(x, y), min(x, transform(y))), s(min(x, y)))) , transform^#(x) -> c_10(x) , transform^#(s(x)) -> c_11(transform^#(x)) , transform^#(cons(x, y)) -> c_12(y) , transform^#(cons(x, y)) -> c_13(cons^#(cons(x, x), x)) , cons^#(x, y) -> c_14(y) , cons^#(x, cons(y, s(z))) -> c_15(cons^#(y, x)) , cons^#(cons(x, z), s(y)) -> c_16(transform^#(x)) } 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)) , minus(x, 0()) -> x , minus(s(x), s(y)) -> s(minus(x, y)) , gcd(s(x), s(y)) -> gcd(minus(max(x, y), min(x, transform(y))), s(min(x, y))) , transform(x) -> s(s(x)) , transform(s(x)) -> s(s(transform(x))) , transform(cons(x, y)) -> y , transform(cons(x, y)) -> cons(cons(x, x), x) , cons(x, y) -> y , cons(x, cons(y, s(z))) -> cons(y, x) , cons(cons(x, z), s(y)) -> transform(x) } 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..