MAYBE 725.57/297.04 MAYBE 725.57/297.04 725.57/297.04 We are left with following problem, upon which TcT provides the 725.57/297.04 certificate MAYBE. 725.57/297.04 725.57/297.04 Strict Trs: 725.57/297.04 { minus(0(), x) -> 0() 725.57/297.04 , minus(s(x), 0()) -> s(x) 725.57/297.04 , minus(s(x), s(y)) -> minus(x, y) 725.57/297.04 , mod(x, 0()) -> 0() 725.57/297.04 , mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) 725.57/297.04 , if(true(), x, y) -> x 725.57/297.04 , if(false(), x, y) -> mod(minus(x, y), y) 725.57/297.04 , lt(x, 0()) -> false() 725.57/297.04 , lt(0(), s(x)) -> true() 725.57/297.04 , lt(s(x), s(y)) -> lt(x, y) 725.57/297.04 , gcd(x, 0()) -> x 725.57/297.04 , gcd(0(), s(y)) -> s(y) 725.57/297.04 , gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) } 725.57/297.04 Obligation: 725.57/297.04 runtime complexity 725.57/297.04 Answer: 725.57/297.04 MAYBE 725.57/297.04 725.57/297.04 None of the processors succeeded. 725.57/297.04 725.57/297.04 Details of failed attempt(s): 725.57/297.04 ----------------------------- 725.57/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 725.57/297.04 following reason: 725.57/297.04 725.57/297.04 Computation stopped due to timeout after 297.0 seconds. 725.57/297.04 725.57/297.04 2) 'Best' failed due to the following reason: 725.57/297.04 725.57/297.04 None of the processors succeeded. 725.57/297.04 725.57/297.04 Details of failed attempt(s): 725.57/297.04 ----------------------------- 725.57/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 725.57/297.04 seconds)' failed due to the following reason: 725.57/297.04 725.57/297.04 Computation stopped due to timeout after 148.0 seconds. 725.57/297.04 725.57/297.04 2) 'Best' failed due to the following reason: 725.57/297.04 725.57/297.04 None of the processors succeeded. 725.57/297.04 725.57/297.04 Details of failed attempt(s): 725.57/297.04 ----------------------------- 725.57/297.04 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 725.57/297.04 to the following reason: 725.57/297.04 725.57/297.04 The processor is inapplicable, reason: 725.57/297.04 Processor only applicable for innermost runtime complexity analysis 725.57/297.04 725.57/297.04 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 725.57/297.04 following reason: 725.57/297.04 725.57/297.04 The processor is inapplicable, reason: 725.57/297.04 Processor only applicable for innermost runtime complexity analysis 725.57/297.04 725.57/297.04 725.57/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 725.57/297.04 failed due to the following reason: 725.57/297.04 725.57/297.04 None of the processors succeeded. 725.57/297.04 725.57/297.04 Details of failed attempt(s): 725.57/297.04 ----------------------------- 725.57/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 725.57/297.04 failed due to the following reason: 725.57/297.04 725.57/297.04 match-boundness of the problem could not be verified. 725.57/297.04 725.57/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 725.57/297.04 failed due to the following reason: 725.57/297.04 725.57/297.04 match-boundness of the problem could not be verified. 725.57/297.04 725.57/297.04 725.57/297.04 725.57/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 725.57/297.04 the following reason: 725.57/297.04 725.57/297.04 We add the following weak dependency pairs: 725.57/297.04 725.57/297.04 Strict DPs: 725.57/297.04 { minus^#(0(), x) -> c_1() 725.57/297.04 , minus^#(s(x), 0()) -> c_2(x) 725.57/297.04 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 725.57/297.04 , mod^#(x, 0()) -> c_4() 725.57/297.04 , mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) 725.57/297.04 , if^#(true(), x, y) -> c_6(x) 725.57/297.04 , if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) 725.57/297.04 , lt^#(x, 0()) -> c_8() 725.57/297.04 , lt^#(0(), s(x)) -> c_9() 725.57/297.04 , lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) 725.57/297.04 , gcd^#(x, 0()) -> c_11(x) 725.57/297.04 , gcd^#(0(), s(y)) -> c_12(y) 725.57/297.04 , gcd^#(s(x), s(y)) -> 725.57/297.04 c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } 725.57/297.04 725.57/297.04 and mark the set of starting terms. 725.57/297.04 725.57/297.04 We are left with following problem, upon which TcT provides the 725.57/297.04 certificate MAYBE. 725.57/297.04 725.57/297.04 Strict DPs: 725.57/297.04 { minus^#(0(), x) -> c_1() 725.57/297.04 , minus^#(s(x), 0()) -> c_2(x) 725.57/297.04 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 725.57/297.04 , mod^#(x, 0()) -> c_4() 725.57/297.04 , mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) 725.57/297.04 , if^#(true(), x, y) -> c_6(x) 725.57/297.04 , if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) 725.57/297.04 , lt^#(x, 0()) -> c_8() 725.57/297.04 , lt^#(0(), s(x)) -> c_9() 725.57/297.04 , lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) 725.57/297.04 , gcd^#(x, 0()) -> c_11(x) 725.57/297.04 , gcd^#(0(), s(y)) -> c_12(y) 725.57/297.04 , gcd^#(s(x), s(y)) -> 725.57/297.04 c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } 725.57/297.04 Strict Trs: 725.57/297.04 { minus(0(), x) -> 0() 725.57/297.04 , minus(s(x), 0()) -> s(x) 725.57/297.04 , minus(s(x), s(y)) -> minus(x, y) 725.57/297.04 , mod(x, 0()) -> 0() 725.57/297.04 , mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) 725.57/297.04 , if(true(), x, y) -> x 725.57/297.04 , if(false(), x, y) -> mod(minus(x, y), y) 725.57/297.04 , lt(x, 0()) -> false() 725.57/297.04 , lt(0(), s(x)) -> true() 725.57/297.04 , lt(s(x), s(y)) -> lt(x, y) 725.57/297.04 , gcd(x, 0()) -> x 725.57/297.04 , gcd(0(), s(y)) -> s(y) 725.57/297.04 , gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) } 725.57/297.04 Obligation: 725.57/297.04 runtime complexity 725.57/297.04 Answer: 725.57/297.04 MAYBE 725.57/297.04 725.57/297.04 We estimate the number of application of {1,4,8,9} by applications 725.57/297.04 of Pre({1,4,8,9}) = {2,3,6,7,10,11,12}. Here rules are labeled as 725.57/297.04 follows: 725.57/297.04 725.57/297.04 DPs: 725.57/297.04 { 1: minus^#(0(), x) -> c_1() 725.57/297.04 , 2: minus^#(s(x), 0()) -> c_2(x) 725.57/297.04 , 3: minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 725.57/297.04 , 4: mod^#(x, 0()) -> c_4() 725.57/297.04 , 5: mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) 725.57/297.04 , 6: if^#(true(), x, y) -> c_6(x) 725.57/297.04 , 7: if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) 725.57/297.04 , 8: lt^#(x, 0()) -> c_8() 725.57/297.04 , 9: lt^#(0(), s(x)) -> c_9() 725.57/297.04 , 10: lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) 725.57/297.04 , 11: gcd^#(x, 0()) -> c_11(x) 725.57/297.04 , 12: gcd^#(0(), s(y)) -> c_12(y) 725.57/297.04 , 13: gcd^#(s(x), s(y)) -> 725.57/297.04 c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } 725.57/297.04 725.57/297.04 We are left with following problem, upon which TcT provides the 725.57/297.04 certificate MAYBE. 725.57/297.04 725.57/297.04 Strict DPs: 725.57/297.04 { minus^#(s(x), 0()) -> c_2(x) 725.57/297.04 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 725.57/297.04 , mod^#(x, s(y)) -> c_5(if^#(lt(x, s(y)), x, s(y))) 725.57/297.04 , if^#(true(), x, y) -> c_6(x) 725.57/297.04 , if^#(false(), x, y) -> c_7(mod^#(minus(x, y), y)) 725.57/297.04 , lt^#(s(x), s(y)) -> c_10(lt^#(x, y)) 725.57/297.04 , gcd^#(x, 0()) -> c_11(x) 725.57/297.04 , gcd^#(0(), s(y)) -> c_12(y) 725.57/297.04 , gcd^#(s(x), s(y)) -> 725.57/297.04 c_13(gcd^#(mod(s(x), s(y)), mod(s(y), s(x)))) } 725.57/297.04 Strict Trs: 725.57/297.04 { minus(0(), x) -> 0() 725.57/297.04 , minus(s(x), 0()) -> s(x) 725.57/297.04 , minus(s(x), s(y)) -> minus(x, y) 725.57/297.04 , mod(x, 0()) -> 0() 725.57/297.04 , mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) 725.57/297.04 , if(true(), x, y) -> x 725.57/297.04 , if(false(), x, y) -> mod(minus(x, y), y) 725.57/297.04 , lt(x, 0()) -> false() 725.57/297.04 , lt(0(), s(x)) -> true() 725.57/297.04 , lt(s(x), s(y)) -> lt(x, y) 725.57/297.04 , gcd(x, 0()) -> x 725.57/297.04 , gcd(0(), s(y)) -> s(y) 725.57/297.04 , gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) } 725.57/297.04 Weak DPs: 725.57/297.04 { minus^#(0(), x) -> c_1() 725.57/297.04 , mod^#(x, 0()) -> c_4() 725.57/297.04 , lt^#(x, 0()) -> c_8() 725.57/297.04 , lt^#(0(), s(x)) -> c_9() } 725.57/297.04 Obligation: 725.57/297.04 runtime complexity 725.57/297.04 Answer: 725.57/297.04 MAYBE 725.57/297.04 725.57/297.04 Empty strict component of the problem is NOT empty. 725.57/297.04 725.57/297.04 725.57/297.04 Arrrr.. 725.89/297.32 EOF