MAYBE 832.15/297.48 MAYBE 832.15/297.48 832.15/297.48 We are left with following problem, upon which TcT provides the 832.15/297.48 certificate MAYBE. 832.15/297.48 832.15/297.48 Strict Trs: 832.15/297.48 { lt(x, 0()) -> false() 832.15/297.48 , lt(0(), s(x)) -> true() 832.15/297.48 , lt(s(x), s(y)) -> lt(x, y) 832.15/297.48 , minus(x, y) -> help(lt(y, x), x, y) 832.15/297.48 , help(true(), x, y) -> s(minus(x, s(y))) 832.15/297.48 , help(false(), x, y) -> 0() } 832.15/297.48 Obligation: 832.15/297.48 runtime complexity 832.15/297.48 Answer: 832.15/297.48 MAYBE 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 832.15/297.48 following reason: 832.15/297.48 832.15/297.48 Computation stopped due to timeout after 297.0 seconds. 832.15/297.48 832.15/297.48 2) 'Best' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 832.15/297.48 seconds)' failed due to the following reason: 832.15/297.48 832.15/297.48 The weightgap principle applies (using the following nonconstant 832.15/297.48 growth matrix-interpretation) 832.15/297.48 832.15/297.48 The following argument positions are usable: 832.15/297.48 Uargs(s) = {1}, Uargs(help) = {1} 832.15/297.48 832.15/297.48 TcT has computed the following matrix interpretation satisfying 832.15/297.48 not(EDA) and not(IDA(1)). 832.15/297.48 832.15/297.48 [lt](x1, x2) = [4] 832.15/297.48 832.15/297.48 [0] = [0] 832.15/297.48 832.15/297.48 [s](x1) = [1] x1 + [0] 832.15/297.48 832.15/297.48 [true] = [1] 832.15/297.48 832.15/297.48 [false] = [1] 832.15/297.48 832.15/297.48 [minus](x1, x2) = [1] x1 + [1] x2 + [0] 832.15/297.48 832.15/297.48 [help](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 832.15/297.48 832.15/297.48 The order satisfies the following ordering constraints: 832.15/297.48 832.15/297.48 [lt(x, 0())] = [4] 832.15/297.48 > [1] 832.15/297.48 = [false()] 832.15/297.48 832.15/297.48 [lt(0(), s(x))] = [4] 832.15/297.48 > [1] 832.15/297.48 = [true()] 832.15/297.48 832.15/297.48 [lt(s(x), s(y))] = [4] 832.15/297.48 >= [4] 832.15/297.48 = [lt(x, y)] 832.15/297.48 832.15/297.48 [minus(x, y)] = [1] x + [1] y + [0] 832.15/297.48 ? [1] x + [1] y + [4] 832.15/297.48 = [help(lt(y, x), x, y)] 832.15/297.48 832.15/297.48 [help(true(), x, y)] = [1] x + [1] y + [1] 832.15/297.48 > [1] x + [1] y + [0] 832.15/297.48 = [s(minus(x, s(y)))] 832.15/297.48 832.15/297.48 [help(false(), x, y)] = [1] x + [1] y + [1] 832.15/297.48 > [0] 832.15/297.48 = [0()] 832.15/297.48 832.15/297.48 832.15/297.48 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 832.15/297.48 832.15/297.48 We are left with following problem, upon which TcT provides the 832.15/297.48 certificate MAYBE. 832.15/297.48 832.15/297.48 Strict Trs: 832.15/297.48 { lt(s(x), s(y)) -> lt(x, y) 832.15/297.48 , minus(x, y) -> help(lt(y, x), x, y) } 832.15/297.48 Weak Trs: 832.15/297.48 { lt(x, 0()) -> false() 832.15/297.48 , lt(0(), s(x)) -> true() 832.15/297.48 , help(true(), x, y) -> s(minus(x, s(y))) 832.15/297.48 , help(false(), x, y) -> 0() } 832.15/297.48 Obligation: 832.15/297.48 runtime complexity 832.15/297.48 Answer: 832.15/297.48 MAYBE 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'empty' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 2) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'empty' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 2) 'Fastest' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'empty' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 2) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 The weightgap principle applies (using the following nonconstant 832.15/297.48 growth matrix-interpretation) 832.15/297.48 832.15/297.48 The following argument positions are usable: 832.15/297.48 Uargs(s) = {1}, Uargs(help) = {1} 832.15/297.48 832.15/297.48 TcT has computed the following matrix interpretation satisfying 832.15/297.48 not(EDA) and not(IDA(1)). 832.15/297.48 832.15/297.48 [lt](x1, x2) = [0 0] x1 + [0] 832.15/297.48 [0 1] [0] 832.15/297.48 832.15/297.48 [0] = [0] 832.15/297.48 [1] 832.15/297.48 832.15/297.48 [s](x1) = [1 0] x1 + [0] 832.15/297.48 [0 0] [0] 832.15/297.48 832.15/297.48 [true] = [0] 832.15/297.48 [1] 832.15/297.48 832.15/297.48 [false] = [0] 832.15/297.48 [0] 832.15/297.48 832.15/297.48 [minus](x1, x2) = [0 4] x2 + [1] 832.15/297.48 [0 0] [4] 832.15/297.48 832.15/297.48 [help](x1, x2, x3) = [1 1] x1 + [0] 832.15/297.48 [0 0] [4] 832.15/297.48 832.15/297.48 The order satisfies the following ordering constraints: 832.15/297.48 832.15/297.48 [lt(x, 0())] = [0 0] x + [0] 832.15/297.48 [0 1] [0] 832.15/297.48 >= [0] 832.15/297.48 [0] 832.15/297.48 = [false()] 832.15/297.48 832.15/297.48 [lt(0(), s(x))] = [0] 832.15/297.48 [1] 832.15/297.48 >= [0] 832.15/297.48 [1] 832.15/297.48 = [true()] 832.15/297.48 832.15/297.48 [lt(s(x), s(y))] = [0] 832.15/297.48 [0] 832.15/297.48 ? [0 0] x + [0] 832.15/297.48 [0 1] [0] 832.15/297.48 = [lt(x, y)] 832.15/297.48 832.15/297.48 [minus(x, y)] = [0 4] y + [1] 832.15/297.48 [0 0] [4] 832.15/297.48 > [0 1] y + [0] 832.15/297.48 [0 0] [4] 832.15/297.48 = [help(lt(y, x), x, y)] 832.15/297.48 832.15/297.48 [help(true(), x, y)] = [1] 832.15/297.48 [4] 832.15/297.48 >= [1] 832.15/297.48 [0] 832.15/297.48 = [s(minus(x, s(y)))] 832.15/297.48 832.15/297.48 [help(false(), x, y)] = [0] 832.15/297.48 [4] 832.15/297.48 >= [0] 832.15/297.48 [1] 832.15/297.48 = [0()] 832.15/297.48 832.15/297.48 832.15/297.48 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 832.15/297.48 832.15/297.48 We are left with following problem, upon which TcT provides the 832.15/297.48 certificate MAYBE. 832.15/297.48 832.15/297.48 Strict Trs: { lt(s(x), s(y)) -> lt(x, y) } 832.15/297.48 Weak Trs: 832.15/297.48 { lt(x, 0()) -> false() 832.15/297.48 , lt(0(), s(x)) -> true() 832.15/297.48 , minus(x, y) -> help(lt(y, x), x, y) 832.15/297.48 , help(true(), x, y) -> s(minus(x, s(y))) 832.15/297.48 , help(false(), x, y) -> 0() } 832.15/297.48 Obligation: 832.15/297.48 runtime complexity 832.15/297.48 Answer: 832.15/297.48 MAYBE 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'empty' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 2) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'empty' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 2) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 832.15/297.48 832.15/297.48 832.15/297.48 2) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'empty' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 2) 'With Problem ...' failed due to the following reason: 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 832.15/297.48 832.15/297.48 832.15/297.48 832.15/297.48 2) 'Best' failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 832.15/297.48 following reason: 832.15/297.48 832.15/297.48 The processor is inapplicable, reason: 832.15/297.48 Processor only applicable for innermost runtime complexity analysis 832.15/297.48 832.15/297.48 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 832.15/297.48 to the following reason: 832.15/297.48 832.15/297.48 The processor is inapplicable, reason: 832.15/297.48 Processor only applicable for innermost runtime complexity analysis 832.15/297.48 832.15/297.48 832.15/297.48 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 832.15/297.48 failed due to the following reason: 832.15/297.48 832.15/297.48 None of the processors succeeded. 832.15/297.48 832.15/297.48 Details of failed attempt(s): 832.15/297.48 ----------------------------- 832.15/297.48 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 832.15/297.48 failed due to the following reason: 832.15/297.48 832.15/297.48 match-boundness of the problem could not be verified. 832.15/297.48 832.15/297.48 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 832.15/297.48 failed due to the following reason: 832.15/297.48 832.15/297.48 match-boundness of the problem could not be verified. 832.15/297.48 832.15/297.48 832.15/297.48 832.15/297.48 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 832.15/297.48 the following reason: 832.15/297.48 832.15/297.48 We add the following weak dependency pairs: 832.15/297.48 832.15/297.48 Strict DPs: 832.15/297.48 { lt^#(x, 0()) -> c_1() 832.15/297.48 , lt^#(0(), s(x)) -> c_2() 832.15/297.48 , lt^#(s(x), s(y)) -> c_3(lt^#(x, y)) 832.15/297.48 , minus^#(x, y) -> c_4(help^#(lt(y, x), x, y)) 832.15/297.48 , help^#(true(), x, y) -> c_5(minus^#(x, s(y))) 832.15/297.48 , help^#(false(), x, y) -> c_6() } 832.15/297.48 832.15/297.48 and mark the set of starting terms. 832.15/297.48 832.15/297.48 We are left with following problem, upon which TcT provides the 832.15/297.48 certificate MAYBE. 832.15/297.48 832.15/297.48 Strict DPs: 832.15/297.48 { lt^#(x, 0()) -> c_1() 832.15/297.48 , lt^#(0(), s(x)) -> c_2() 832.15/297.48 , lt^#(s(x), s(y)) -> c_3(lt^#(x, y)) 832.15/297.48 , minus^#(x, y) -> c_4(help^#(lt(y, x), x, y)) 832.15/297.48 , help^#(true(), x, y) -> c_5(minus^#(x, s(y))) 832.15/297.48 , help^#(false(), x, y) -> c_6() } 832.15/297.48 Strict Trs: 832.15/297.48 { lt(x, 0()) -> false() 832.15/297.48 , lt(0(), s(x)) -> true() 832.15/297.48 , lt(s(x), s(y)) -> lt(x, y) 832.15/297.48 , minus(x, y) -> help(lt(y, x), x, y) 832.15/297.48 , help(true(), x, y) -> s(minus(x, s(y))) 832.15/297.48 , help(false(), x, y) -> 0() } 832.15/297.48 Obligation: 832.15/297.48 runtime complexity 832.15/297.48 Answer: 832.15/297.48 MAYBE 832.15/297.48 832.15/297.48 We estimate the number of application of {1,2,6} by applications of 832.15/297.48 Pre({1,2,6}) = {3,4}. Here rules are labeled as follows: 832.15/297.48 832.15/297.48 DPs: 832.15/297.48 { 1: lt^#(x, 0()) -> c_1() 832.15/297.48 , 2: lt^#(0(), s(x)) -> c_2() 832.15/297.48 , 3: lt^#(s(x), s(y)) -> c_3(lt^#(x, y)) 832.15/297.48 , 4: minus^#(x, y) -> c_4(help^#(lt(y, x), x, y)) 832.15/297.48 , 5: help^#(true(), x, y) -> c_5(minus^#(x, s(y))) 832.15/297.48 , 6: help^#(false(), x, y) -> c_6() } 832.15/297.48 832.15/297.48 We are left with following problem, upon which TcT provides the 832.15/297.48 certificate MAYBE. 832.15/297.48 832.15/297.48 Strict DPs: 832.15/297.48 { lt^#(s(x), s(y)) -> c_3(lt^#(x, y)) 832.15/297.48 , minus^#(x, y) -> c_4(help^#(lt(y, x), x, y)) 832.15/297.48 , help^#(true(), x, y) -> c_5(minus^#(x, s(y))) } 832.15/297.48 Strict Trs: 832.15/297.48 { lt(x, 0()) -> false() 832.15/297.48 , lt(0(), s(x)) -> true() 832.15/297.48 , lt(s(x), s(y)) -> lt(x, y) 832.15/297.48 , minus(x, y) -> help(lt(y, x), x, y) 832.15/297.48 , help(true(), x, y) -> s(minus(x, s(y))) 832.15/297.48 , help(false(), x, y) -> 0() } 832.15/297.48 Weak DPs: 832.15/297.48 { lt^#(x, 0()) -> c_1() 832.15/297.48 , lt^#(0(), s(x)) -> c_2() 832.15/297.48 , help^#(false(), x, y) -> c_6() } 832.15/297.48 Obligation: 832.15/297.48 runtime complexity 832.15/297.48 Answer: 832.15/297.48 MAYBE 832.15/297.48 832.15/297.48 Empty strict component of the problem is NOT empty. 832.15/297.48 832.15/297.48 832.15/297.48 Arrrr.. 832.59/297.68 EOF