MAYBE 190.96/117.38 MAYBE 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate MAYBE. 190.96/117.38 190.96/117.38 Strict Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 MAYBE 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'Best' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 190.96/117.38 following reason: 190.96/117.38 190.96/117.38 We add the following dependency tuples: 190.96/117.38 190.96/117.38 Strict DPs: 190.96/117.38 { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) 190.96/117.38 , not^#(or(x, y)) -> c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) 190.96/117.38 , and^#(x, or(y, z)) -> c_3(and^#(x, y), and^#(x, z)) } 190.96/117.38 190.96/117.38 and mark the set of starting terms. 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate MAYBE. 190.96/117.38 190.96/117.38 Strict DPs: 190.96/117.38 { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) 190.96/117.38 , not^#(or(x, y)) -> c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) 190.96/117.38 , and^#(x, or(y, z)) -> c_3(and^#(x, y), and^#(x, z)) } 190.96/117.38 Weak Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 MAYBE 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 We decompose the input problem according to the dependency graph 190.96/117.38 into the upper component 190.96/117.38 190.96/117.38 { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) 190.96/117.38 , not^#(or(x, y)) -> 190.96/117.38 c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) } 190.96/117.38 190.96/117.38 and lower component 190.96/117.38 190.96/117.38 { and^#(x, or(y, z)) -> c_3(and^#(x, y), and^#(x, z)) } 190.96/117.38 190.96/117.38 Further, following extension rules are added to the lower 190.96/117.38 component. 190.96/117.38 190.96/117.38 { not^#(and(x, y)) -> not^#(x) 190.96/117.38 , not^#(and(x, y)) -> not^#(y) 190.96/117.38 , not^#(or(x, y)) -> not^#(x) 190.96/117.38 , not^#(or(x, y)) -> not^#(y) 190.96/117.38 , not^#(or(x, y)) -> and^#(not(x), not(y)) } 190.96/117.38 190.96/117.38 TcT solves the upper component with certificate YES(O(1),O(n^1)). 190.96/117.38 190.96/117.38 Sub-proof: 190.96/117.38 ---------- 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate YES(O(1),O(n^1)). 190.96/117.38 190.96/117.38 Strict DPs: 190.96/117.38 { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) 190.96/117.38 , not^#(or(x, y)) -> 190.96/117.38 c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) } 190.96/117.38 Weak Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 YES(O(1),O(n^1)) 190.96/117.38 190.96/117.38 We use the processor 'matrix interpretation of dimension 1' to 190.96/117.38 orient following rules strictly. 190.96/117.38 190.96/117.38 DPs: 190.96/117.38 { 2: not^#(or(x, y)) -> 190.96/117.38 c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) } 190.96/117.38 190.96/117.38 Sub-proof: 190.96/117.38 ---------- 190.96/117.38 The following argument positions are usable: 190.96/117.38 Uargs(c_1) = {1, 2}, Uargs(c_2) = {1, 2, 3} 190.96/117.38 190.96/117.38 TcT has computed the following constructor-based matrix 190.96/117.38 interpretation satisfying not(EDA). 190.96/117.38 190.96/117.38 [not](x1) = [0] 190.96/117.38 190.96/117.38 [and](x1, x2) = [4] x1 + [1] x2 + [0] 190.96/117.38 190.96/117.38 [or](x1, x2) = [1] x1 + [1] x2 + [1] 190.96/117.38 190.96/117.38 [not^#](x1) = [2] x1 + [0] 190.96/117.38 190.96/117.38 [c_1](x1, x2) = [1] x1 + [1] x2 + [0] 190.96/117.38 190.96/117.38 [c_2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [1] 190.96/117.38 190.96/117.38 [and^#](x1, x2) = [0] 190.96/117.38 190.96/117.38 The order satisfies the following ordering constraints: 190.96/117.38 190.96/117.38 [not(and(x, y))] = [0] 190.96/117.38 ? [1] 190.96/117.38 = [or(not(x), not(y))] 190.96/117.38 190.96/117.38 [not(or(x, y))] = [0] 190.96/117.38 >= [0] 190.96/117.38 = [and(not(x), not(y))] 190.96/117.38 190.96/117.38 [and(x, or(y, z))] = [4] x + [1] y + [1] z + [1] 190.96/117.38 ? [8] x + [1] y + [1] z + [1] 190.96/117.38 = [or(and(x, y), and(x, z))] 190.96/117.38 190.96/117.38 [not^#(and(x, y))] = [8] x + [2] y + [0] 190.96/117.38 >= [2] x + [2] y + [0] 190.96/117.38 = [c_1(not^#(x), not^#(y))] 190.96/117.38 190.96/117.38 [not^#(or(x, y))] = [2] x + [2] y + [2] 190.96/117.38 > [2] x + [2] y + [1] 190.96/117.38 = [c_2(and^#(not(x), not(y)), not^#(x), not^#(y))] 190.96/117.38 190.96/117.38 190.96/117.38 The strictly oriented rules are moved into the weak component. 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate YES(O(1),O(n^1)). 190.96/117.38 190.96/117.38 Strict DPs: { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) } 190.96/117.38 Weak DPs: 190.96/117.38 { not^#(or(x, y)) -> 190.96/117.38 c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) } 190.96/117.38 Weak Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 YES(O(1),O(n^1)) 190.96/117.38 190.96/117.38 We use the processor 'matrix interpretation of dimension 1' to 190.96/117.38 orient following rules strictly. 190.96/117.38 190.96/117.38 DPs: 190.96/117.38 { 1: not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) } 190.96/117.38 190.96/117.38 Sub-proof: 190.96/117.38 ---------- 190.96/117.38 The following argument positions are usable: 190.96/117.38 Uargs(c_1) = {1, 2}, Uargs(c_2) = {1, 2, 3} 190.96/117.38 190.96/117.38 TcT has computed the following constructor-based matrix 190.96/117.38 interpretation satisfying not(EDA). 190.96/117.38 190.96/117.38 [not](x1) = [1] 190.96/117.38 190.96/117.38 [and](x1, x2) = [4] x1 + [1] x2 + [4] 190.96/117.38 190.96/117.38 [or](x1, x2) = [1] x1 + [1] x2 + [0] 190.96/117.38 190.96/117.38 [not^#](x1) = [2] x1 + [0] 190.96/117.38 190.96/117.38 [c_1](x1, x2) = [4] x1 + [1] x2 + [1] 190.96/117.38 190.96/117.38 [c_2](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0] 190.96/117.38 190.96/117.38 [and^#](x1, x2) = [0] 190.96/117.38 190.96/117.38 The order satisfies the following ordering constraints: 190.96/117.38 190.96/117.38 [not(and(x, y))] = [1] 190.96/117.38 ? [2] 190.96/117.38 = [or(not(x), not(y))] 190.96/117.38 190.96/117.38 [not(or(x, y))] = [1] 190.96/117.38 ? [9] 190.96/117.38 = [and(not(x), not(y))] 190.96/117.38 190.96/117.38 [and(x, or(y, z))] = [4] x + [1] y + [1] z + [4] 190.96/117.38 ? [8] x + [1] y + [1] z + [8] 190.96/117.38 = [or(and(x, y), and(x, z))] 190.96/117.38 190.96/117.38 [not^#(and(x, y))] = [8] x + [2] y + [8] 190.96/117.38 > [8] x + [2] y + [1] 190.96/117.38 = [c_1(not^#(x), not^#(y))] 190.96/117.38 190.96/117.38 [not^#(or(x, y))] = [2] x + [2] y + [0] 190.96/117.38 >= [2] x + [2] y + [0] 190.96/117.38 = [c_2(and^#(not(x), not(y)), not^#(x), not^#(y))] 190.96/117.38 190.96/117.38 190.96/117.38 The strictly oriented rules are moved into the weak component. 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate YES(O(1),O(1)). 190.96/117.38 190.96/117.38 Weak DPs: 190.96/117.38 { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) 190.96/117.38 , not^#(or(x, y)) -> 190.96/117.38 c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) } 190.96/117.38 Weak Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 YES(O(1),O(1)) 190.96/117.38 190.96/117.38 The following weak DPs constitute a sub-graph of the DG that is 190.96/117.38 closed under successors. The DPs are removed. 190.96/117.38 190.96/117.38 { not^#(and(x, y)) -> c_1(not^#(x), not^#(y)) 190.96/117.38 , not^#(or(x, y)) -> 190.96/117.38 c_2(and^#(not(x), not(y)), not^#(x), not^#(y)) } 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate YES(O(1),O(1)). 190.96/117.38 190.96/117.38 Weak Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 YES(O(1),O(1)) 190.96/117.38 190.96/117.38 No rule is usable, rules are removed from the input problem. 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate YES(O(1),O(1)). 190.96/117.38 190.96/117.38 Rules: Empty 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 YES(O(1),O(1)) 190.96/117.38 190.96/117.38 Empty rules are trivially bounded 190.96/117.38 190.96/117.38 We return to the main proof. 190.96/117.38 190.96/117.38 We are left with following problem, upon which TcT provides the 190.96/117.38 certificate MAYBE. 190.96/117.38 190.96/117.38 Strict DPs: { and^#(x, or(y, z)) -> c_3(and^#(x, y), and^#(x, z)) } 190.96/117.38 Weak DPs: 190.96/117.38 { not^#(and(x, y)) -> not^#(x) 190.96/117.38 , not^#(and(x, y)) -> not^#(y) 190.96/117.38 , not^#(or(x, y)) -> not^#(x) 190.96/117.38 , not^#(or(x, y)) -> not^#(y) 190.96/117.38 , not^#(or(x, y)) -> and^#(not(x), not(y)) } 190.96/117.38 Weak Trs: 190.96/117.38 { not(and(x, y)) -> or(not(x), not(y)) 190.96/117.38 , not(or(x, y)) -> and(not(x), not(y)) 190.96/117.38 , and(x, or(y, z)) -> or(and(x, y), and(x, z)) } 190.96/117.38 Obligation: 190.96/117.38 innermost runtime complexity 190.96/117.38 Answer: 190.96/117.38 MAYBE 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'Fastest' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'Polynomial Path Order (PS)' failed due to the following reason: 190.96/117.38 190.96/117.38 The input cannot be shown compatible 190.96/117.38 190.96/117.38 190.96/117.38 2) 'Polynomial Path Order (PS)' failed due to the following reason: 190.96/117.38 190.96/117.38 The input cannot be shown compatible 190.96/117.38 190.96/117.38 3) 'Fastest (timeout of 24 seconds)' failed due to the following 190.96/117.38 reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 190.96/117.38 failed due to the following reason: 190.96/117.38 190.96/117.38 match-boundness of the problem could not be verified. 190.96/117.38 190.96/117.38 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 190.96/117.38 failed due to the following reason: 190.96/117.38 190.96/117.38 match-boundness of the problem could not be verified. 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 2) 'Best' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 190.96/117.38 seconds)' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'Fastest' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'empty' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 2) 'With Problem ...' failed due to the following reason: 190.96/117.38 190.96/117.38 Empty strict component of the problem is NOT empty. 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 2) 'Best' failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 190.96/117.38 following reason: 190.96/117.38 190.96/117.38 The input cannot be shown compatible 190.96/117.38 190.96/117.38 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 190.96/117.38 to the following reason: 190.96/117.38 190.96/117.38 The input cannot be shown compatible 190.96/117.38 190.96/117.38 190.96/117.38 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 190.96/117.38 failed due to the following reason: 190.96/117.38 190.96/117.38 None of the processors succeeded. 190.96/117.38 190.96/117.38 Details of failed attempt(s): 190.96/117.38 ----------------------------- 190.96/117.38 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 190.96/117.38 failed due to the following reason: 190.96/117.38 190.96/117.38 match-boundness of the problem could not be verified. 190.96/117.38 190.96/117.38 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 190.96/117.38 failed due to the following reason: 190.96/117.38 190.96/117.38 match-boundness of the problem could not be verified. 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 190.96/117.38 Arrrr.. 191.11/117.47 EOF