MAYBE 743.37/297.04 MAYBE 743.37/297.04 743.37/297.04 We are left with following problem, upon which TcT provides the 743.37/297.04 certificate MAYBE. 743.37/297.04 743.37/297.04 Strict Trs: 743.37/297.04 { min(x, 0()) -> 0() 743.37/297.04 , min(0(), y) -> 0() 743.37/297.04 , min(s(x), s(y)) -> s(min(x, y)) 743.37/297.04 , max(x, 0()) -> x 743.37/297.04 , max(0(), y) -> y 743.37/297.04 , max(s(x), s(y)) -> s(max(x, y)) 743.37/297.04 , minus(x, 0()) -> x 743.37/297.04 , minus(s(x), s(y)) -> s(minus(x, any(y))) 743.37/297.04 , any(x) -> x 743.37/297.04 , any(s(x)) -> s(s(any(x))) 743.37/297.04 , gcd(s(x), s(y)) -> 743.37/297.04 gcd(minus(max(x, y), min(x, y)), s(min(x, y))) } 743.37/297.04 Obligation: 743.37/297.04 runtime complexity 743.37/297.04 Answer: 743.37/297.04 MAYBE 743.37/297.04 743.37/297.04 None of the processors succeeded. 743.37/297.04 743.37/297.04 Details of failed attempt(s): 743.37/297.04 ----------------------------- 743.37/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 743.37/297.04 following reason: 743.37/297.04 743.37/297.04 Computation stopped due to timeout after 297.0 seconds. 743.37/297.04 743.37/297.04 2) 'Best' failed due to the following reason: 743.37/297.04 743.37/297.04 None of the processors succeeded. 743.37/297.04 743.37/297.04 Details of failed attempt(s): 743.37/297.04 ----------------------------- 743.37/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 743.37/297.04 seconds)' failed due to the following reason: 743.37/297.04 743.37/297.04 Computation stopped due to timeout after 148.0 seconds. 743.37/297.04 743.37/297.04 2) 'Best' failed due to the following reason: 743.37/297.04 743.37/297.04 None of the processors succeeded. 743.37/297.04 743.37/297.04 Details of failed attempt(s): 743.37/297.04 ----------------------------- 743.37/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 743.37/297.04 following reason: 743.37/297.04 743.37/297.04 The processor is inapplicable, reason: 743.37/297.04 Processor only applicable for innermost runtime complexity analysis 743.37/297.04 743.37/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 743.37/297.04 to the following reason: 743.37/297.04 743.37/297.04 The processor is inapplicable, reason: 743.37/297.04 Processor only applicable for innermost runtime complexity analysis 743.37/297.04 743.37/297.04 743.37/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 743.37/297.04 failed due to the following reason: 743.37/297.04 743.37/297.04 None of the processors succeeded. 743.37/297.04 743.37/297.04 Details of failed attempt(s): 743.37/297.04 ----------------------------- 743.37/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 743.37/297.04 failed due to the following reason: 743.37/297.04 743.37/297.04 match-boundness of the problem could not be verified. 743.37/297.04 743.37/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 743.37/297.04 failed due to the following reason: 743.37/297.04 743.37/297.04 match-boundness of the problem could not be verified. 743.37/297.04 743.37/297.04 743.37/297.04 743.37/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 743.37/297.04 the following reason: 743.37/297.04 743.37/297.04 We add the following weak dependency pairs: 743.37/297.04 743.37/297.04 Strict DPs: 743.37/297.04 { min^#(x, 0()) -> c_1() 743.37/297.04 , min^#(0(), y) -> c_2() 743.37/297.04 , min^#(s(x), s(y)) -> c_3(min^#(x, y)) 743.37/297.04 , max^#(x, 0()) -> c_4(x) 743.37/297.04 , max^#(0(), y) -> c_5(y) 743.37/297.04 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 743.37/297.04 , minus^#(x, 0()) -> c_7(x) 743.37/297.04 , minus^#(s(x), s(y)) -> c_8(minus^#(x, any(y))) 743.37/297.04 , any^#(x) -> c_9(x) 743.37/297.04 , any^#(s(x)) -> c_10(any^#(x)) 743.37/297.04 , gcd^#(s(x), s(y)) -> 743.37/297.04 c_11(gcd^#(minus(max(x, y), min(x, y)), s(min(x, y)))) } 743.37/297.04 743.37/297.04 and mark the set of starting terms. 743.37/297.04 743.37/297.04 We are left with following problem, upon which TcT provides the 743.37/297.04 certificate MAYBE. 743.37/297.04 743.37/297.04 Strict DPs: 743.37/297.04 { min^#(x, 0()) -> c_1() 743.37/297.04 , min^#(0(), y) -> c_2() 743.37/297.04 , min^#(s(x), s(y)) -> c_3(min^#(x, y)) 743.37/297.04 , max^#(x, 0()) -> c_4(x) 743.37/297.04 , max^#(0(), y) -> c_5(y) 743.37/297.04 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 743.37/297.04 , minus^#(x, 0()) -> c_7(x) 743.37/297.04 , minus^#(s(x), s(y)) -> c_8(minus^#(x, any(y))) 743.37/297.04 , any^#(x) -> c_9(x) 743.37/297.04 , any^#(s(x)) -> c_10(any^#(x)) 743.37/297.04 , gcd^#(s(x), s(y)) -> 743.37/297.04 c_11(gcd^#(minus(max(x, y), min(x, y)), s(min(x, y)))) } 743.37/297.04 Strict Trs: 743.37/297.04 { min(x, 0()) -> 0() 743.37/297.04 , min(0(), y) -> 0() 743.37/297.04 , min(s(x), s(y)) -> s(min(x, y)) 743.37/297.04 , max(x, 0()) -> x 743.37/297.04 , max(0(), y) -> y 743.37/297.04 , max(s(x), s(y)) -> s(max(x, y)) 743.37/297.04 , minus(x, 0()) -> x 743.37/297.04 , minus(s(x), s(y)) -> s(minus(x, any(y))) 743.37/297.04 , any(x) -> x 743.37/297.04 , any(s(x)) -> s(s(any(x))) 743.37/297.04 , gcd(s(x), s(y)) -> 743.37/297.04 gcd(minus(max(x, y), min(x, y)), s(min(x, y))) } 743.37/297.04 Obligation: 743.37/297.04 runtime complexity 743.37/297.04 Answer: 743.37/297.04 MAYBE 743.37/297.04 743.37/297.04 We estimate the number of application of {1,2} by applications of 743.37/297.04 Pre({1,2}) = {3,4,5,7,9}. Here rules are labeled as follows: 743.37/297.04 743.37/297.04 DPs: 743.37/297.04 { 1: min^#(x, 0()) -> c_1() 743.37/297.04 , 2: min^#(0(), y) -> c_2() 743.37/297.04 , 3: min^#(s(x), s(y)) -> c_3(min^#(x, y)) 743.37/297.04 , 4: max^#(x, 0()) -> c_4(x) 743.37/297.04 , 5: max^#(0(), y) -> c_5(y) 743.37/297.04 , 6: max^#(s(x), s(y)) -> c_6(max^#(x, y)) 743.37/297.04 , 7: minus^#(x, 0()) -> c_7(x) 743.37/297.04 , 8: minus^#(s(x), s(y)) -> c_8(minus^#(x, any(y))) 743.37/297.04 , 9: any^#(x) -> c_9(x) 743.37/297.04 , 10: any^#(s(x)) -> c_10(any^#(x)) 743.37/297.04 , 11: gcd^#(s(x), s(y)) -> 743.37/297.04 c_11(gcd^#(minus(max(x, y), min(x, y)), s(min(x, y)))) } 743.37/297.04 743.37/297.04 We are left with following problem, upon which TcT provides the 743.37/297.04 certificate MAYBE. 743.37/297.04 743.37/297.04 Strict DPs: 743.37/297.04 { min^#(s(x), s(y)) -> c_3(min^#(x, y)) 743.37/297.04 , max^#(x, 0()) -> c_4(x) 743.37/297.04 , max^#(0(), y) -> c_5(y) 743.37/297.04 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 743.37/297.04 , minus^#(x, 0()) -> c_7(x) 743.37/297.04 , minus^#(s(x), s(y)) -> c_8(minus^#(x, any(y))) 743.37/297.04 , any^#(x) -> c_9(x) 743.37/297.04 , any^#(s(x)) -> c_10(any^#(x)) 743.37/297.04 , gcd^#(s(x), s(y)) -> 743.37/297.04 c_11(gcd^#(minus(max(x, y), min(x, y)), s(min(x, y)))) } 743.37/297.04 Strict Trs: 743.37/297.04 { min(x, 0()) -> 0() 743.37/297.04 , min(0(), y) -> 0() 743.37/297.04 , min(s(x), s(y)) -> s(min(x, y)) 743.37/297.04 , max(x, 0()) -> x 743.37/297.04 , max(0(), y) -> y 743.37/297.04 , max(s(x), s(y)) -> s(max(x, y)) 743.37/297.04 , minus(x, 0()) -> x 743.37/297.04 , minus(s(x), s(y)) -> s(minus(x, any(y))) 743.37/297.04 , any(x) -> x 743.37/297.04 , any(s(x)) -> s(s(any(x))) 743.37/297.04 , gcd(s(x), s(y)) -> 743.37/297.04 gcd(minus(max(x, y), min(x, y)), s(min(x, y))) } 743.37/297.04 Weak DPs: 743.37/297.04 { min^#(x, 0()) -> c_1() 743.37/297.04 , min^#(0(), y) -> c_2() } 743.37/297.04 Obligation: 743.37/297.04 runtime complexity 743.37/297.04 Answer: 743.37/297.04 MAYBE 743.37/297.04 743.37/297.04 Empty strict component of the problem is NOT empty. 743.37/297.04 743.37/297.04 743.37/297.04 Arrrr.. 743.68/297.32 EOF