MAYBE 689.69/297.05 MAYBE 689.69/297.05 689.69/297.05 We are left with following problem, upon which TcT provides the 689.69/297.05 certificate MAYBE. 689.69/297.05 689.69/297.05 Strict Trs: 689.69/297.05 { le(0(), y) -> true() 689.69/297.05 , le(s(x), 0()) -> false() 689.69/297.05 , le(s(x), s(y)) -> le(x, y) 689.69/297.05 , pred(s(x)) -> x 689.69/297.05 , minus(x, 0()) -> x 689.69/297.05 , minus(x, s(y)) -> pred(minus(x, y)) 689.69/297.05 , gcd(0(), y) -> y 689.69/297.05 , gcd(s(x), 0()) -> s(x) 689.69/297.05 , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 689.69/297.05 , if_gcd(true(), x, y) -> gcd(minus(x, y), y) 689.69/297.05 , if_gcd(false(), x, y) -> gcd(minus(y, x), x) } 689.69/297.05 Obligation: 689.69/297.05 runtime complexity 689.69/297.05 Answer: 689.69/297.05 MAYBE 689.69/297.05 689.69/297.05 None of the processors succeeded. 689.69/297.05 689.69/297.05 Details of failed attempt(s): 689.69/297.05 ----------------------------- 689.69/297.05 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 689.69/297.05 following reason: 689.69/297.05 689.69/297.05 Computation stopped due to timeout after 297.0 seconds. 689.69/297.05 689.69/297.05 2) 'Best' failed due to the following reason: 689.69/297.05 689.69/297.05 None of the processors succeeded. 689.69/297.05 689.69/297.05 Details of failed attempt(s): 689.69/297.05 ----------------------------- 689.69/297.05 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 689.69/297.05 seconds)' failed due to the following reason: 689.69/297.05 689.69/297.05 Computation stopped due to timeout after 148.0 seconds. 689.69/297.05 689.69/297.05 2) 'Best' failed due to the following reason: 689.69/297.05 689.69/297.05 None of the processors succeeded. 689.69/297.05 689.69/297.05 Details of failed attempt(s): 689.69/297.05 ----------------------------- 689.69/297.05 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 689.69/297.05 to the following reason: 689.69/297.05 689.69/297.05 The processor is inapplicable, reason: 689.69/297.05 Processor only applicable for innermost runtime complexity analysis 689.69/297.05 689.69/297.05 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 689.69/297.05 following reason: 689.69/297.05 689.69/297.05 The processor is inapplicable, reason: 689.69/297.05 Processor only applicable for innermost runtime complexity analysis 689.69/297.05 689.69/297.05 689.69/297.05 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 689.69/297.05 failed due to the following reason: 689.69/297.05 689.69/297.05 None of the processors succeeded. 689.69/297.05 689.69/297.05 Details of failed attempt(s): 689.69/297.05 ----------------------------- 689.69/297.05 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 689.69/297.05 failed due to the following reason: 689.69/297.05 689.69/297.05 match-boundness of the problem could not be verified. 689.69/297.05 689.69/297.05 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 689.69/297.05 failed due to the following reason: 689.69/297.05 689.69/297.05 match-boundness of the problem could not be verified. 689.69/297.05 689.69/297.05 689.69/297.05 689.69/297.05 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 689.69/297.05 the following reason: 689.69/297.05 689.69/297.05 We add the following weak dependency pairs: 689.69/297.05 689.69/297.05 Strict DPs: 689.69/297.05 { le^#(0(), y) -> c_1() 689.69/297.05 , le^#(s(x), 0()) -> c_2() 689.69/297.05 , le^#(s(x), s(y)) -> c_3(le^#(x, y)) 689.69/297.05 , pred^#(s(x)) -> c_4(x) 689.69/297.05 , minus^#(x, 0()) -> c_5(x) 689.69/297.05 , minus^#(x, s(y)) -> c_6(pred^#(minus(x, y))) 689.69/297.05 , gcd^#(0(), y) -> c_7(y) 689.69/297.05 , gcd^#(s(x), 0()) -> c_8(x) 689.69/297.05 , gcd^#(s(x), s(y)) -> c_9(if_gcd^#(le(y, x), s(x), s(y))) 689.69/297.05 , if_gcd^#(true(), x, y) -> c_10(gcd^#(minus(x, y), y)) 689.69/297.05 , if_gcd^#(false(), x, y) -> c_11(gcd^#(minus(y, x), x)) } 689.69/297.05 689.69/297.05 and mark the set of starting terms. 689.69/297.05 689.69/297.05 We are left with following problem, upon which TcT provides the 689.69/297.05 certificate MAYBE. 689.69/297.05 689.69/297.05 Strict DPs: 689.69/297.05 { le^#(0(), y) -> c_1() 689.69/297.05 , le^#(s(x), 0()) -> c_2() 689.69/297.05 , le^#(s(x), s(y)) -> c_3(le^#(x, y)) 689.69/297.05 , pred^#(s(x)) -> c_4(x) 689.69/297.05 , minus^#(x, 0()) -> c_5(x) 689.69/297.05 , minus^#(x, s(y)) -> c_6(pred^#(minus(x, y))) 689.69/297.05 , gcd^#(0(), y) -> c_7(y) 689.69/297.05 , gcd^#(s(x), 0()) -> c_8(x) 689.69/297.05 , gcd^#(s(x), s(y)) -> c_9(if_gcd^#(le(y, x), s(x), s(y))) 689.69/297.05 , if_gcd^#(true(), x, y) -> c_10(gcd^#(minus(x, y), y)) 689.69/297.05 , if_gcd^#(false(), x, y) -> c_11(gcd^#(minus(y, x), x)) } 689.69/297.05 Strict Trs: 689.69/297.05 { le(0(), y) -> true() 689.69/297.05 , le(s(x), 0()) -> false() 689.69/297.05 , le(s(x), s(y)) -> le(x, y) 689.69/297.05 , pred(s(x)) -> x 689.69/297.05 , minus(x, 0()) -> x 689.69/297.05 , minus(x, s(y)) -> pred(minus(x, y)) 689.69/297.05 , gcd(0(), y) -> y 689.69/297.05 , gcd(s(x), 0()) -> s(x) 689.69/297.05 , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 689.69/297.05 , if_gcd(true(), x, y) -> gcd(minus(x, y), y) 689.69/297.05 , if_gcd(false(), x, y) -> gcd(minus(y, x), x) } 689.69/297.05 Obligation: 689.69/297.05 runtime complexity 689.69/297.05 Answer: 689.69/297.05 MAYBE 689.69/297.05 689.69/297.05 We estimate the number of application of {1,2} by applications of 689.69/297.05 Pre({1,2}) = {3,4,5,7,8}. Here rules are labeled as follows: 689.69/297.05 689.69/297.05 DPs: 689.69/297.05 { 1: le^#(0(), y) -> c_1() 689.69/297.05 , 2: le^#(s(x), 0()) -> c_2() 689.69/297.05 , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y)) 689.69/297.05 , 4: pred^#(s(x)) -> c_4(x) 689.69/297.05 , 5: minus^#(x, 0()) -> c_5(x) 689.69/297.05 , 6: minus^#(x, s(y)) -> c_6(pred^#(minus(x, y))) 689.69/297.05 , 7: gcd^#(0(), y) -> c_7(y) 689.69/297.05 , 8: gcd^#(s(x), 0()) -> c_8(x) 689.69/297.05 , 9: gcd^#(s(x), s(y)) -> c_9(if_gcd^#(le(y, x), s(x), s(y))) 689.69/297.05 , 10: if_gcd^#(true(), x, y) -> c_10(gcd^#(minus(x, y), y)) 689.69/297.05 , 11: if_gcd^#(false(), x, y) -> c_11(gcd^#(minus(y, x), x)) } 689.69/297.05 689.69/297.05 We are left with following problem, upon which TcT provides the 689.69/297.05 certificate MAYBE. 689.69/297.05 689.69/297.05 Strict DPs: 689.69/297.05 { le^#(s(x), s(y)) -> c_3(le^#(x, y)) 689.69/297.05 , pred^#(s(x)) -> c_4(x) 689.69/297.05 , minus^#(x, 0()) -> c_5(x) 689.69/297.05 , minus^#(x, s(y)) -> c_6(pred^#(minus(x, y))) 689.69/297.05 , gcd^#(0(), y) -> c_7(y) 689.69/297.05 , gcd^#(s(x), 0()) -> c_8(x) 689.69/297.05 , gcd^#(s(x), s(y)) -> c_9(if_gcd^#(le(y, x), s(x), s(y))) 689.69/297.05 , if_gcd^#(true(), x, y) -> c_10(gcd^#(minus(x, y), y)) 689.69/297.05 , if_gcd^#(false(), x, y) -> c_11(gcd^#(minus(y, x), x)) } 689.69/297.05 Strict Trs: 689.69/297.05 { le(0(), y) -> true() 689.69/297.05 , le(s(x), 0()) -> false() 689.69/297.05 , le(s(x), s(y)) -> le(x, y) 689.69/297.05 , pred(s(x)) -> x 689.69/297.05 , minus(x, 0()) -> x 689.69/297.05 , minus(x, s(y)) -> pred(minus(x, y)) 689.69/297.05 , gcd(0(), y) -> y 689.69/297.05 , gcd(s(x), 0()) -> s(x) 689.69/297.05 , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 689.69/297.05 , if_gcd(true(), x, y) -> gcd(minus(x, y), y) 689.69/297.05 , if_gcd(false(), x, y) -> gcd(minus(y, x), x) } 689.69/297.05 Weak DPs: 689.69/297.05 { le^#(0(), y) -> c_1() 689.69/297.05 , le^#(s(x), 0()) -> c_2() } 689.69/297.05 Obligation: 689.69/297.05 runtime complexity 689.69/297.05 Answer: 689.69/297.05 MAYBE 689.69/297.05 689.69/297.05 Empty strict component of the problem is NOT empty. 689.69/297.05 689.69/297.05 689.69/297.05 Arrrr.. 690.01/297.36 EOF