MAYBE 597.19/262.61 MAYBE 597.19/262.61 597.19/262.61 We are left with following problem, upon which TcT provides the 597.19/262.61 certificate MAYBE. 597.19/262.61 597.19/262.61 Strict Trs: 597.19/262.61 { f(x, empty()) -> x 597.19/262.61 , f(empty(), cons(a, k)) -> f(cons(a, k), k) 597.19/262.61 , f(cons(a, k), y) -> f(y, k) } 597.19/262.61 Obligation: 597.19/262.61 runtime complexity 597.19/262.61 Answer: 597.19/262.61 MAYBE 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 597.19/262.61 following reason: 597.19/262.61 597.19/262.61 We add the following weak dependency pairs: 597.19/262.61 597.19/262.61 Strict DPs: 597.19/262.61 { f^#(x, empty()) -> c_1(x) 597.19/262.61 , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k)) 597.19/262.61 , f^#(cons(a, k), y) -> c_3(f^#(y, k)) } 597.19/262.61 597.19/262.61 and mark the set of starting terms. 597.19/262.61 597.19/262.61 We are left with following problem, upon which TcT provides the 597.19/262.61 certificate MAYBE. 597.19/262.61 597.19/262.61 Strict DPs: 597.19/262.61 { f^#(x, empty()) -> c_1(x) 597.19/262.61 , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k)) 597.19/262.61 , f^#(cons(a, k), y) -> c_3(f^#(y, k)) } 597.19/262.61 Strict Trs: 597.19/262.61 { f(x, empty()) -> x 597.19/262.61 , f(empty(), cons(a, k)) -> f(cons(a, k), k) 597.19/262.61 , f(cons(a, k), y) -> f(y, k) } 597.19/262.61 Obligation: 597.19/262.61 runtime complexity 597.19/262.61 Answer: 597.19/262.61 MAYBE 597.19/262.61 597.19/262.61 No rule is usable, rules are removed from the input problem. 597.19/262.61 597.19/262.61 We are left with following problem, upon which TcT provides the 597.19/262.61 certificate MAYBE. 597.19/262.61 597.19/262.61 Strict DPs: 597.19/262.61 { f^#(x, empty()) -> c_1(x) 597.19/262.61 , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k)) 597.19/262.61 , f^#(cons(a, k), y) -> c_3(f^#(y, k)) } 597.19/262.61 Obligation: 597.19/262.61 runtime complexity 597.19/262.61 Answer: 597.19/262.61 MAYBE 597.19/262.61 597.19/262.61 The weightgap principle applies (using the following constant 597.19/262.61 growth matrix-interpretation) 597.19/262.61 597.19/262.61 The following argument positions are usable: 597.19/262.61 Uargs(c_2) = {1}, Uargs(c_3) = {1} 597.19/262.61 597.19/262.61 TcT has computed the following constructor-restricted matrix 597.19/262.61 interpretation. 597.19/262.61 597.19/262.61 [empty] = [0] 597.19/262.61 [0] 597.19/262.61 597.19/262.61 [cons](x1, x2) = [1 0] x1 + [0] 597.19/262.61 [0 0] [0] 597.19/262.61 597.19/262.61 [f^#](x1, x2) = [1] 597.19/262.61 [0] 597.19/262.61 597.19/262.61 [c_1](x1) = [0] 597.19/262.61 [0] 597.19/262.61 597.19/262.61 [c_2](x1) = [1 0] x1 + [0] 597.19/262.61 [0 1] [0] 597.19/262.61 597.19/262.61 [c_3](x1) = [1 0] x1 + [1] 597.19/262.61 [0 1] [0] 597.19/262.61 597.19/262.61 The order satisfies the following ordering constraints: 597.19/262.61 597.19/262.61 [f^#(x, empty())] = [1] 597.19/262.61 [0] 597.19/262.61 > [0] 597.19/262.61 [0] 597.19/262.61 = [c_1(x)] 597.19/262.61 597.19/262.61 [f^#(empty(), cons(a, k))] = [1] 597.19/262.61 [0] 597.19/262.61 >= [1] 597.19/262.61 [0] 597.19/262.61 = [c_2(f^#(cons(a, k), k))] 597.19/262.61 597.19/262.61 [f^#(cons(a, k), y)] = [1] 597.19/262.61 [0] 597.19/262.61 ? [2] 597.19/262.61 [0] 597.19/262.61 = [c_3(f^#(y, k))] 597.19/262.61 597.19/262.61 597.19/262.61 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 597.19/262.61 597.19/262.61 We are left with following problem, upon which TcT provides the 597.19/262.61 certificate MAYBE. 597.19/262.61 597.19/262.61 Strict DPs: 597.19/262.61 { f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k)) 597.19/262.61 , f^#(cons(a, k), y) -> c_3(f^#(y, k)) } 597.19/262.61 Weak DPs: { f^#(x, empty()) -> c_1(x) } 597.19/262.61 Obligation: 597.19/262.61 runtime complexity 597.19/262.61 Answer: 597.19/262.61 MAYBE 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'Inspecting Problem...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'Fastest' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'Polynomial Path Order (PS)' failed due to the following reason: 597.19/262.61 597.19/262.61 The processor is inapplicable, reason: 597.19/262.61 Processor only applicable for innermost runtime complexity analysis 597.19/262.61 597.19/262.61 597.19/262.61 2) 'Fastest (timeout of 24 seconds)' failed due to the following 597.19/262.61 reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 597.19/262.61 failed due to the following reason: 597.19/262.61 597.19/262.61 match-boundness of the problem could not be verified. 597.19/262.61 597.19/262.61 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 597.19/262.61 failed due to the following reason: 597.19/262.61 597.19/262.61 match-boundness of the problem could not be verified. 597.19/262.61 597.19/262.61 597.19/262.61 3) 'Polynomial Path Order (PS)' failed due to the following reason: 597.19/262.61 597.19/262.61 The processor is inapplicable, reason: 597.19/262.61 Processor only applicable for innermost runtime complexity analysis 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 2) 'Best' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 597.19/262.61 seconds)' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'Fastest' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 2) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'empty' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 2) 'With Problem ...' failed due to the following reason: 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 2) 'Best' failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 597.19/262.61 following reason: 597.19/262.61 597.19/262.61 The processor is inapplicable, reason: 597.19/262.61 Processor only applicable for innermost runtime complexity analysis 597.19/262.61 597.19/262.61 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 597.19/262.61 to the following reason: 597.19/262.61 597.19/262.61 The processor is inapplicable, reason: 597.19/262.61 Processor only applicable for innermost runtime complexity analysis 597.19/262.61 597.19/262.61 597.19/262.61 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 597.19/262.61 failed due to the following reason: 597.19/262.61 597.19/262.61 None of the processors succeeded. 597.19/262.61 597.19/262.61 Details of failed attempt(s): 597.19/262.61 ----------------------------- 597.19/262.61 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 597.19/262.61 failed due to the following reason: 597.19/262.61 597.19/262.61 match-boundness of the problem could not be verified. 597.19/262.61 597.19/262.61 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 597.19/262.61 failed due to the following reason: 597.19/262.61 597.19/262.61 match-boundness of the problem could not be verified. 597.19/262.61 597.19/262.61 597.19/262.61 597.19/262.61 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 597.19/262.61 the following reason: 597.19/262.61 597.19/262.61 We add the following weak dependency pairs: 597.19/262.61 597.19/262.61 Strict DPs: 597.19/262.61 { f^#(x, empty()) -> c_1(x) 597.19/262.61 , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k)) 597.19/262.61 , f^#(cons(a, k), y) -> c_3(f^#(y, k)) } 597.19/262.61 597.19/262.61 and mark the set of starting terms. 597.19/262.61 597.19/262.61 We are left with following problem, upon which TcT provides the 597.19/262.61 certificate MAYBE. 597.19/262.61 597.19/262.61 Strict DPs: 597.19/262.61 { f^#(x, empty()) -> c_1(x) 597.19/262.61 , f^#(empty(), cons(a, k)) -> c_2(f^#(cons(a, k), k)) 597.19/262.61 , f^#(cons(a, k), y) -> c_3(f^#(y, k)) } 597.19/262.61 Strict Trs: 597.19/262.61 { f(x, empty()) -> x 597.19/262.61 , f(empty(), cons(a, k)) -> f(cons(a, k), k) 597.19/262.61 , f(cons(a, k), y) -> f(y, k) } 597.19/262.61 Obligation: 597.19/262.61 runtime complexity 597.19/262.61 Answer: 597.19/262.61 MAYBE 597.19/262.61 597.19/262.61 Empty strict component of the problem is NOT empty. 597.19/262.61 597.19/262.61 597.19/262.61 Arrrr.. 597.33/262.78 EOF