MAYBE 824.75/297.02 MAYBE 824.75/297.02 824.75/297.02 We are left with following problem, upon which TcT provides the 824.75/297.02 certificate MAYBE. 824.75/297.02 824.75/297.02 Strict Trs: 824.75/297.02 { cond(true(), x, y) -> cond(gr(x, y), y, x) 824.75/297.02 , gr(0(), x) -> false() 824.75/297.02 , gr(s(x), 0()) -> true() 824.75/297.02 , gr(s(x), s(y)) -> gr(x, y) } 824.75/297.02 Obligation: 824.75/297.02 runtime complexity 824.75/297.02 Answer: 824.75/297.02 MAYBE 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 824.75/297.02 following reason: 824.75/297.02 824.75/297.02 Computation stopped due to timeout after 297.0 seconds. 824.75/297.02 824.75/297.02 2) 'Best' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 824.75/297.02 seconds)' failed due to the following reason: 824.75/297.02 824.75/297.02 The weightgap principle applies (using the following nonconstant 824.75/297.02 growth matrix-interpretation) 824.75/297.02 824.75/297.02 The following argument positions are usable: 824.75/297.02 Uargs(cond) = {1} 824.75/297.02 824.75/297.02 TcT has computed the following matrix interpretation satisfying 824.75/297.02 not(EDA) and not(IDA(1)). 824.75/297.02 824.75/297.02 [cond](x1, x2, x3) = [1] x1 + [7] 824.75/297.02 824.75/297.02 [true] = [7] 824.75/297.02 824.75/297.02 [gr](x1, x2) = [7] 824.75/297.02 824.75/297.02 [0] = [7] 824.75/297.02 824.75/297.02 [false] = [6] 824.75/297.02 824.75/297.02 [s](x1) = [1] x1 + [7] 824.75/297.02 824.75/297.02 The order satisfies the following ordering constraints: 824.75/297.02 824.75/297.02 [cond(true(), x, y)] = [14] 824.75/297.02 >= [14] 824.75/297.02 = [cond(gr(x, y), y, x)] 824.75/297.02 824.75/297.02 [gr(0(), x)] = [7] 824.75/297.02 > [6] 824.75/297.02 = [false()] 824.75/297.02 824.75/297.02 [gr(s(x), 0())] = [7] 824.75/297.02 >= [7] 824.75/297.02 = [true()] 824.75/297.02 824.75/297.02 [gr(s(x), s(y))] = [7] 824.75/297.02 >= [7] 824.75/297.02 = [gr(x, y)] 824.75/297.02 824.75/297.02 824.75/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 824.75/297.02 824.75/297.02 We are left with following problem, upon which TcT provides the 824.75/297.02 certificate MAYBE. 824.75/297.02 824.75/297.02 Strict Trs: 824.75/297.02 { cond(true(), x, y) -> cond(gr(x, y), y, x) 824.75/297.02 , gr(s(x), 0()) -> true() 824.75/297.02 , gr(s(x), s(y)) -> gr(x, y) } 824.75/297.02 Weak Trs: { gr(0(), x) -> false() } 824.75/297.02 Obligation: 824.75/297.02 runtime complexity 824.75/297.02 Answer: 824.75/297.02 MAYBE 824.75/297.02 824.75/297.02 The weightgap principle applies (using the following nonconstant 824.75/297.02 growth matrix-interpretation) 824.75/297.02 824.75/297.02 The following argument positions are usable: 824.75/297.02 Uargs(cond) = {1} 824.75/297.02 824.75/297.02 TcT has computed the following matrix interpretation satisfying 824.75/297.02 not(EDA) and not(IDA(1)). 824.75/297.02 824.75/297.02 [cond](x1, x2, x3) = [1] x1 + [7] 824.75/297.02 824.75/297.02 [true] = [3] 824.75/297.02 824.75/297.02 [gr](x1, x2) = [7] 824.75/297.02 824.75/297.02 [0] = [7] 824.75/297.02 824.75/297.02 [false] = [7] 824.75/297.02 824.75/297.02 [s](x1) = [1] x1 + [7] 824.75/297.02 824.75/297.02 The order satisfies the following ordering constraints: 824.75/297.02 824.75/297.02 [cond(true(), x, y)] = [10] 824.75/297.02 ? [14] 824.75/297.02 = [cond(gr(x, y), y, x)] 824.75/297.02 824.75/297.02 [gr(0(), x)] = [7] 824.75/297.02 >= [7] 824.75/297.02 = [false()] 824.75/297.02 824.75/297.02 [gr(s(x), 0())] = [7] 824.75/297.02 > [3] 824.75/297.02 = [true()] 824.75/297.02 824.75/297.02 [gr(s(x), s(y))] = [7] 824.75/297.02 >= [7] 824.75/297.02 = [gr(x, y)] 824.75/297.02 824.75/297.02 824.75/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 824.75/297.02 824.75/297.02 We are left with following problem, upon which TcT provides the 824.75/297.02 certificate MAYBE. 824.75/297.02 824.75/297.02 Strict Trs: 824.75/297.02 { cond(true(), x, y) -> cond(gr(x, y), y, x) 824.75/297.02 , gr(s(x), s(y)) -> gr(x, y) } 824.75/297.02 Weak Trs: 824.75/297.02 { gr(0(), x) -> false() 824.75/297.02 , gr(s(x), 0()) -> true() } 824.75/297.02 Obligation: 824.75/297.02 runtime complexity 824.75/297.02 Answer: 824.75/297.02 MAYBE 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'empty' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 2) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'empty' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 2) 'Fastest' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'empty' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 2) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'empty' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 2) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'empty' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 2) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 824.75/297.02 824.75/297.02 824.75/297.02 2) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'empty' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 2) 'With Problem ...' failed due to the following reason: 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 824.75/297.02 824.75/297.02 824.75/297.02 824.75/297.02 2) 'Best' failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 824.75/297.02 following reason: 824.75/297.02 824.75/297.02 The processor is inapplicable, reason: 824.75/297.02 Processor only applicable for innermost runtime complexity analysis 824.75/297.02 824.75/297.02 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 824.75/297.02 to the following reason: 824.75/297.02 824.75/297.02 The processor is inapplicable, reason: 824.75/297.02 Processor only applicable for innermost runtime complexity analysis 824.75/297.02 824.75/297.02 824.75/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 824.75/297.02 failed due to the following reason: 824.75/297.02 824.75/297.02 None of the processors succeeded. 824.75/297.02 824.75/297.02 Details of failed attempt(s): 824.75/297.02 ----------------------------- 824.75/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 824.75/297.02 failed due to the following reason: 824.75/297.02 824.75/297.02 match-boundness of the problem could not be verified. 824.75/297.02 824.75/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 824.75/297.02 failed due to the following reason: 824.75/297.02 824.75/297.02 match-boundness of the problem could not be verified. 824.75/297.02 824.75/297.02 824.75/297.02 824.75/297.02 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 824.75/297.02 the following reason: 824.75/297.02 824.75/297.02 We add the following weak dependency pairs: 824.75/297.02 824.75/297.02 Strict DPs: 824.75/297.02 { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), y, x)) 824.75/297.02 , gr^#(0(), x) -> c_2() 824.75/297.02 , gr^#(s(x), 0()) -> c_3() 824.75/297.02 , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) } 824.75/297.02 824.75/297.02 and mark the set of starting terms. 824.75/297.02 824.75/297.02 We are left with following problem, upon which TcT provides the 824.75/297.02 certificate MAYBE. 824.75/297.02 824.75/297.02 Strict DPs: 824.75/297.02 { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), y, x)) 824.75/297.02 , gr^#(0(), x) -> c_2() 824.75/297.02 , gr^#(s(x), 0()) -> c_3() 824.75/297.02 , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) } 824.75/297.02 Strict Trs: 824.75/297.02 { cond(true(), x, y) -> cond(gr(x, y), y, x) 824.75/297.02 , gr(0(), x) -> false() 824.75/297.02 , gr(s(x), 0()) -> true() 824.75/297.02 , gr(s(x), s(y)) -> gr(x, y) } 824.75/297.02 Obligation: 824.75/297.02 runtime complexity 824.75/297.02 Answer: 824.75/297.02 MAYBE 824.75/297.02 824.75/297.02 We estimate the number of application of {2,3} by applications of 824.75/297.02 Pre({2,3}) = {4}. Here rules are labeled as follows: 824.75/297.02 824.75/297.02 DPs: 824.75/297.02 { 1: cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), y, x)) 824.75/297.02 , 2: gr^#(0(), x) -> c_2() 824.75/297.02 , 3: gr^#(s(x), 0()) -> c_3() 824.75/297.02 , 4: gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) } 824.75/297.02 824.75/297.02 We are left with following problem, upon which TcT provides the 824.75/297.02 certificate MAYBE. 824.75/297.02 824.75/297.02 Strict DPs: 824.75/297.02 { cond^#(true(), x, y) -> c_1(cond^#(gr(x, y), y, x)) 824.75/297.02 , gr^#(s(x), s(y)) -> c_4(gr^#(x, y)) } 824.75/297.02 Strict Trs: 824.75/297.02 { cond(true(), x, y) -> cond(gr(x, y), y, x) 824.75/297.02 , gr(0(), x) -> false() 824.75/297.02 , gr(s(x), 0()) -> true() 824.75/297.02 , gr(s(x), s(y)) -> gr(x, y) } 824.75/297.02 Weak DPs: 824.75/297.02 { gr^#(0(), x) -> c_2() 824.75/297.02 , gr^#(s(x), 0()) -> c_3() } 824.75/297.02 Obligation: 824.75/297.02 runtime complexity 824.75/297.02 Answer: 824.75/297.02 MAYBE 824.75/297.02 824.75/297.02 Empty strict component of the problem is NOT empty. 824.75/297.02 824.75/297.02 824.75/297.02 Arrrr.. 824.97/297.22 EOF