MAYBE 254.84/131.16 MAYBE 254.84/131.16 254.84/131.16 We are left with following problem, upon which TcT provides the 254.84/131.16 certificate MAYBE. 254.84/131.16 254.84/131.16 Strict Trs: 254.84/131.16 { minus(0(), y) -> 0() 254.84/131.16 , minus(s(x), y) -> if(gt(s(x), y), x, y) 254.84/131.16 , if(true(), x, y) -> s(minus(x, y)) 254.84/131.16 , if(false(), x, y) -> 0() 254.84/131.16 , gt(0(), y) -> false() 254.84/131.16 , gt(s(x), 0()) -> true() 254.84/131.16 , gt(s(x), s(y)) -> gt(x, y) 254.84/131.16 , mod(x, 0()) -> 0() 254.84/131.16 , mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) 254.84/131.16 , if1(true(), x, y) -> x 254.84/131.16 , if1(false(), x, y) -> mod(minus(x, y), y) 254.84/131.16 , lt(x, 0()) -> false() 254.84/131.16 , lt(0(), s(x)) -> true() 254.84/131.16 , lt(s(x), s(y)) -> lt(x, y) } 254.84/131.16 Obligation: 254.84/131.16 runtime complexity 254.84/131.16 Answer: 254.84/131.16 MAYBE 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'Best' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 254.84/131.16 seconds)' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'empty' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 2) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'empty' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 2) 'Fastest' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'empty' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 2) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 254.84/131.16 2) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'empty' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 2) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'empty' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 2) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'empty' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 2) 'With Problem ...' failed due to the following reason: 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 254.84/131.16 254.84/131.16 254.84/131.16 254.84/131.16 254.84/131.16 254.84/131.16 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 254.84/131.16 failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 254.84/131.16 failed due to the following reason: 254.84/131.16 254.84/131.16 match-boundness of the problem could not be verified. 254.84/131.16 254.84/131.16 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 254.84/131.16 failed due to the following reason: 254.84/131.16 254.84/131.16 match-boundness of the problem could not be verified. 254.84/131.16 254.84/131.16 254.84/131.16 3) 'Best' failed due to the following reason: 254.84/131.16 254.84/131.16 None of the processors succeeded. 254.84/131.16 254.84/131.16 Details of failed attempt(s): 254.84/131.16 ----------------------------- 254.84/131.16 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 254.84/131.16 following reason: 254.84/131.16 254.84/131.16 The processor is inapplicable, reason: 254.84/131.16 Processor only applicable for innermost runtime complexity analysis 254.84/131.16 254.84/131.16 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 254.84/131.16 to the following reason: 254.84/131.16 254.84/131.16 The processor is inapplicable, reason: 254.84/131.16 Processor only applicable for innermost runtime complexity analysis 254.84/131.16 254.84/131.16 254.84/131.16 254.84/131.16 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 254.84/131.16 the following reason: 254.84/131.16 254.84/131.16 We add the following weak dependency pairs: 254.84/131.16 254.84/131.16 Strict DPs: 254.84/131.16 { minus^#(0(), y) -> c_1() 254.84/131.16 , minus^#(s(x), y) -> c_2(if^#(gt(s(x), y), x, y)) 254.84/131.16 , if^#(true(), x, y) -> c_3(minus^#(x, y)) 254.84/131.16 , if^#(false(), x, y) -> c_4() 254.84/131.16 , gt^#(0(), y) -> c_5() 254.84/131.16 , gt^#(s(x), 0()) -> c_6() 254.84/131.16 , gt^#(s(x), s(y)) -> c_7(gt^#(x, y)) 254.84/131.16 , mod^#(x, 0()) -> c_8() 254.84/131.16 , mod^#(x, s(y)) -> c_9(if1^#(lt(x, s(y)), x, s(y))) 254.84/131.16 , if1^#(true(), x, y) -> c_10(x) 254.84/131.16 , if1^#(false(), x, y) -> c_11(mod^#(minus(x, y), y)) 254.84/131.16 , lt^#(x, 0()) -> c_12() 254.84/131.16 , lt^#(0(), s(x)) -> c_13() 254.84/131.16 , lt^#(s(x), s(y)) -> c_14(lt^#(x, y)) } 254.84/131.16 254.84/131.16 and mark the set of starting terms. 254.84/131.16 254.84/131.16 We are left with following problem, upon which TcT provides the 254.84/131.16 certificate MAYBE. 254.84/131.16 254.84/131.16 Strict DPs: 254.84/131.16 { minus^#(0(), y) -> c_1() 254.84/131.16 , minus^#(s(x), y) -> c_2(if^#(gt(s(x), y), x, y)) 254.84/131.16 , if^#(true(), x, y) -> c_3(minus^#(x, y)) 254.84/131.16 , if^#(false(), x, y) -> c_4() 254.84/131.16 , gt^#(0(), y) -> c_5() 254.84/131.16 , gt^#(s(x), 0()) -> c_6() 254.84/131.16 , gt^#(s(x), s(y)) -> c_7(gt^#(x, y)) 254.84/131.16 , mod^#(x, 0()) -> c_8() 254.84/131.16 , mod^#(x, s(y)) -> c_9(if1^#(lt(x, s(y)), x, s(y))) 254.84/131.16 , if1^#(true(), x, y) -> c_10(x) 254.84/131.16 , if1^#(false(), x, y) -> c_11(mod^#(minus(x, y), y)) 254.84/131.16 , lt^#(x, 0()) -> c_12() 254.84/131.16 , lt^#(0(), s(x)) -> c_13() 254.84/131.16 , lt^#(s(x), s(y)) -> c_14(lt^#(x, y)) } 254.84/131.16 Strict Trs: 254.84/131.16 { minus(0(), y) -> 0() 254.84/131.16 , minus(s(x), y) -> if(gt(s(x), y), x, y) 254.84/131.16 , if(true(), x, y) -> s(minus(x, y)) 254.84/131.16 , if(false(), x, y) -> 0() 254.84/131.16 , gt(0(), y) -> false() 254.84/131.16 , gt(s(x), 0()) -> true() 254.84/131.16 , gt(s(x), s(y)) -> gt(x, y) 254.84/131.16 , mod(x, 0()) -> 0() 254.84/131.16 , mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) 254.84/131.16 , if1(true(), x, y) -> x 254.84/131.16 , if1(false(), x, y) -> mod(minus(x, y), y) 254.84/131.16 , lt(x, 0()) -> false() 254.84/131.16 , lt(0(), s(x)) -> true() 254.84/131.16 , lt(s(x), s(y)) -> lt(x, y) } 254.84/131.16 Obligation: 254.84/131.16 runtime complexity 254.84/131.16 Answer: 254.84/131.16 MAYBE 254.84/131.16 254.84/131.16 We estimate the number of application of {1,4,5,6,8,12,13} by 254.84/131.16 applications of Pre({1,4,5,6,8,12,13}) = {2,3,7,10,11,14}. Here 254.84/131.16 rules are labeled as follows: 254.84/131.16 254.84/131.16 DPs: 254.84/131.16 { 1: minus^#(0(), y) -> c_1() 254.84/131.16 , 2: minus^#(s(x), y) -> c_2(if^#(gt(s(x), y), x, y)) 254.84/131.16 , 3: if^#(true(), x, y) -> c_3(minus^#(x, y)) 254.84/131.16 , 4: if^#(false(), x, y) -> c_4() 254.84/131.16 , 5: gt^#(0(), y) -> c_5() 254.84/131.16 , 6: gt^#(s(x), 0()) -> c_6() 254.84/131.16 , 7: gt^#(s(x), s(y)) -> c_7(gt^#(x, y)) 254.84/131.16 , 8: mod^#(x, 0()) -> c_8() 254.84/131.16 , 9: mod^#(x, s(y)) -> c_9(if1^#(lt(x, s(y)), x, s(y))) 254.84/131.16 , 10: if1^#(true(), x, y) -> c_10(x) 254.84/131.16 , 11: if1^#(false(), x, y) -> c_11(mod^#(minus(x, y), y)) 254.84/131.16 , 12: lt^#(x, 0()) -> c_12() 254.84/131.16 , 13: lt^#(0(), s(x)) -> c_13() 254.84/131.16 , 14: lt^#(s(x), s(y)) -> c_14(lt^#(x, y)) } 254.84/131.16 254.84/131.16 We are left with following problem, upon which TcT provides the 254.84/131.16 certificate MAYBE. 254.84/131.16 254.84/131.16 Strict DPs: 254.84/131.16 { minus^#(s(x), y) -> c_2(if^#(gt(s(x), y), x, y)) 254.84/131.16 , if^#(true(), x, y) -> c_3(minus^#(x, y)) 254.84/131.16 , gt^#(s(x), s(y)) -> c_7(gt^#(x, y)) 254.84/131.16 , mod^#(x, s(y)) -> c_9(if1^#(lt(x, s(y)), x, s(y))) 254.84/131.16 , if1^#(true(), x, y) -> c_10(x) 254.84/131.16 , if1^#(false(), x, y) -> c_11(mod^#(minus(x, y), y)) 254.84/131.16 , lt^#(s(x), s(y)) -> c_14(lt^#(x, y)) } 254.84/131.16 Strict Trs: 254.84/131.16 { minus(0(), y) -> 0() 254.84/131.16 , minus(s(x), y) -> if(gt(s(x), y), x, y) 254.84/131.16 , if(true(), x, y) -> s(minus(x, y)) 254.84/131.16 , if(false(), x, y) -> 0() 254.84/131.16 , gt(0(), y) -> false() 254.84/131.16 , gt(s(x), 0()) -> true() 254.84/131.16 , gt(s(x), s(y)) -> gt(x, y) 254.84/131.16 , mod(x, 0()) -> 0() 254.84/131.16 , mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) 254.84/131.16 , if1(true(), x, y) -> x 254.84/131.16 , if1(false(), x, y) -> mod(minus(x, y), y) 254.84/131.16 , lt(x, 0()) -> false() 254.84/131.16 , lt(0(), s(x)) -> true() 254.84/131.16 , lt(s(x), s(y)) -> lt(x, y) } 254.84/131.16 Weak DPs: 254.84/131.16 { minus^#(0(), y) -> c_1() 254.84/131.16 , if^#(false(), x, y) -> c_4() 254.84/131.16 , gt^#(0(), y) -> c_5() 254.84/131.16 , gt^#(s(x), 0()) -> c_6() 254.84/131.16 , mod^#(x, 0()) -> c_8() 254.84/131.16 , lt^#(x, 0()) -> c_12() 254.84/131.16 , lt^#(0(), s(x)) -> c_13() } 254.84/131.16 Obligation: 254.84/131.16 runtime complexity 254.84/131.16 Answer: 254.84/131.16 MAYBE 254.84/131.16 254.84/131.16 Empty strict component of the problem is NOT empty. 254.84/131.16 254.84/131.16 254.84/131.16 Arrrr.. 255.08/131.30 EOF