MAYBE 690.83/297.02 MAYBE 690.83/297.02 690.83/297.02 We are left with following problem, upon which TcT provides the 690.83/297.02 certificate MAYBE. 690.83/297.02 690.83/297.02 Strict Trs: 690.83/297.02 { purge(nil()) -> nil() 690.83/297.02 , purge(.(x, y)) -> .(x, purge(remove(x, y))) 690.83/297.02 , remove(x, nil()) -> nil() 690.83/297.02 , remove(x, .(y, z)) -> 690.83/297.02 if(=(x, y), remove(x, z), .(y, remove(x, z))) } 690.83/297.02 Obligation: 690.83/297.02 innermost runtime complexity 690.83/297.02 Answer: 690.83/297.02 MAYBE 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'Best' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 690.83/297.02 following reason: 690.83/297.02 690.83/297.02 Computation stopped due to timeout after 297.0 seconds. 690.83/297.02 690.83/297.02 2) 'Best' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 690.83/297.02 seconds)' failed due to the following reason: 690.83/297.02 690.83/297.02 The weightgap principle applies (using the following nonconstant 690.83/297.02 growth matrix-interpretation) 690.83/297.02 690.83/297.02 The following argument positions are usable: 690.83/297.02 Uargs(purge) = {1}, Uargs(.) = {2}, Uargs(if) = {2, 3} 690.83/297.02 690.83/297.02 TcT has computed the following matrix interpretation satisfying 690.83/297.02 not(EDA) and not(IDA(1)). 690.83/297.02 690.83/297.02 [purge](x1) = [1] x1 + [0] 690.83/297.02 690.83/297.02 [nil] = [0] 690.83/297.02 690.83/297.02 [.](x1, x2) = [1] x2 + [0] 690.83/297.02 690.83/297.02 [remove](x1, x2) = [1] 690.83/297.02 690.83/297.02 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [3] 690.83/297.02 690.83/297.02 [=](x1, x2) = [7] 690.83/297.02 690.83/297.02 The order satisfies the following ordering constraints: 690.83/297.02 690.83/297.02 [purge(nil())] = [0] 690.83/297.02 >= [0] 690.83/297.02 = [nil()] 690.83/297.02 690.83/297.02 [purge(.(x, y))] = [1] y + [0] 690.83/297.02 ? [1] 690.83/297.02 = [.(x, purge(remove(x, y)))] 690.83/297.02 690.83/297.02 [remove(x, nil())] = [1] 690.83/297.02 > [0] 690.83/297.02 = [nil()] 690.83/297.02 690.83/297.02 [remove(x, .(y, z))] = [1] 690.83/297.02 ? [12] 690.83/297.02 = [if(=(x, y), remove(x, z), .(y, remove(x, z)))] 690.83/297.02 690.83/297.02 690.83/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 690.83/297.02 690.83/297.02 We are left with following problem, upon which TcT provides the 690.83/297.02 certificate MAYBE. 690.83/297.02 690.83/297.02 Strict Trs: 690.83/297.02 { purge(nil()) -> nil() 690.83/297.02 , purge(.(x, y)) -> .(x, purge(remove(x, y))) 690.83/297.02 , remove(x, .(y, z)) -> 690.83/297.02 if(=(x, y), remove(x, z), .(y, remove(x, z))) } 690.83/297.02 Weak Trs: { remove(x, nil()) -> nil() } 690.83/297.02 Obligation: 690.83/297.02 innermost runtime complexity 690.83/297.02 Answer: 690.83/297.02 MAYBE 690.83/297.02 690.83/297.02 The weightgap principle applies (using the following nonconstant 690.83/297.02 growth matrix-interpretation) 690.83/297.02 690.83/297.02 The following argument positions are usable: 690.83/297.02 Uargs(purge) = {1}, Uargs(.) = {2}, Uargs(if) = {2, 3} 690.83/297.02 690.83/297.02 TcT has computed the following matrix interpretation satisfying 690.83/297.02 not(EDA) and not(IDA(1)). 690.83/297.02 690.83/297.02 [purge](x1) = [1] x1 + [4] 690.83/297.02 690.83/297.02 [nil] = [0] 690.83/297.02 690.83/297.02 [.](x1, x2) = [1] x2 + [4] 690.83/297.02 690.83/297.02 [remove](x1, x2) = [0] 690.83/297.02 690.83/297.02 [if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [4] 690.83/297.02 690.83/297.02 [=](x1, x2) = [3] 690.83/297.02 690.83/297.02 The order satisfies the following ordering constraints: 690.83/297.02 690.83/297.02 [purge(nil())] = [4] 690.83/297.02 > [0] 690.83/297.02 = [nil()] 690.83/297.02 690.83/297.02 [purge(.(x, y))] = [1] y + [8] 690.83/297.02 >= [8] 690.83/297.02 = [.(x, purge(remove(x, y)))] 690.83/297.02 690.83/297.02 [remove(x, nil())] = [0] 690.83/297.02 >= [0] 690.83/297.02 = [nil()] 690.83/297.02 690.83/297.02 [remove(x, .(y, z))] = [0] 690.83/297.02 ? [11] 690.83/297.02 = [if(=(x, y), remove(x, z), .(y, remove(x, z)))] 690.83/297.02 690.83/297.02 690.83/297.02 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 690.83/297.02 690.83/297.02 We are left with following problem, upon which TcT provides the 690.83/297.02 certificate MAYBE. 690.83/297.02 690.83/297.02 Strict Trs: 690.83/297.02 { purge(.(x, y)) -> .(x, purge(remove(x, y))) 690.83/297.02 , remove(x, .(y, z)) -> 690.83/297.02 if(=(x, y), remove(x, z), .(y, remove(x, z))) } 690.83/297.02 Weak Trs: 690.83/297.02 { purge(nil()) -> nil() 690.83/297.02 , remove(x, nil()) -> nil() } 690.83/297.02 Obligation: 690.83/297.02 innermost runtime complexity 690.83/297.02 Answer: 690.83/297.02 MAYBE 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'Fastest' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 We use the processor 'matrix interpretation of dimension 2' to 690.83/297.02 orient following rules strictly. 690.83/297.02 690.83/297.02 Trs: { purge(.(x, y)) -> .(x, purge(remove(x, y))) } 690.83/297.02 690.83/297.02 The induced complexity on above rules (modulo remaining rules) is 690.83/297.02 YES(?,O(n^1)) . These rules are moved into the corresponding weak 690.83/297.02 component(s). 690.83/297.02 690.83/297.02 Sub-proof: 690.83/297.02 ---------- 690.83/297.02 The following argument positions are usable: 690.83/297.02 Uargs(purge) = {1}, Uargs(.) = {2}, Uargs(if) = {2, 3} 690.83/297.02 690.83/297.02 TcT has computed the following constructor-based matrix 690.83/297.02 interpretation satisfying not(EDA) and not(IDA(1)). 690.83/297.02 690.83/297.02 [purge](x1) = [2 4] x1 + [4] 690.83/297.02 [0 2] [0] 690.83/297.02 690.83/297.02 [nil] = [0] 690.83/297.02 [0] 690.83/297.02 690.83/297.02 [.](x1, x2) = [1 4] x2 + [0] 690.83/297.02 [0 0] [1] 690.83/297.02 690.83/297.02 [remove](x1, x2) = [0] 690.83/297.02 [0] 690.83/297.02 690.83/297.02 [if](x1, x2, x3) = [1 0] x2 + [1 0] x3 + [0] 690.83/297.02 [0 0] [0 0] [0] 690.83/297.02 690.83/297.02 [=](x1, x2) = [7] 690.83/297.02 [0] 690.83/297.02 690.83/297.02 The order satisfies the following ordering constraints: 690.83/297.02 690.83/297.02 [purge(nil())] = [4] 690.83/297.02 [0] 690.83/297.02 > [0] 690.83/297.02 [0] 690.83/297.02 = [nil()] 690.83/297.02 690.83/297.02 [purge(.(x, y))] = [2 8] y + [8] 690.83/297.02 [0 0] [2] 690.83/297.02 > [4] 690.83/297.02 [1] 690.83/297.02 = [.(x, purge(remove(x, y)))] 690.83/297.02 690.83/297.02 [remove(x, nil())] = [0] 690.83/297.02 [0] 690.83/297.02 >= [0] 690.83/297.02 [0] 690.83/297.02 = [nil()] 690.83/297.02 690.83/297.02 [remove(x, .(y, z))] = [0] 690.83/297.02 [0] 690.83/297.02 >= [0] 690.83/297.02 [0] 690.83/297.02 = [if(=(x, y), remove(x, z), .(y, remove(x, z)))] 690.83/297.02 690.83/297.02 690.83/297.02 We return to the main proof. 690.83/297.02 690.83/297.02 We are left with following problem, upon which TcT provides the 690.83/297.02 certificate MAYBE. 690.83/297.02 690.83/297.02 Strict Trs: 690.83/297.02 { remove(x, .(y, z)) -> 690.83/297.02 if(=(x, y), remove(x, z), .(y, remove(x, z))) } 690.83/297.02 Weak Trs: 690.83/297.02 { purge(nil()) -> nil() 690.83/297.02 , purge(.(x, y)) -> .(x, purge(remove(x, y))) 690.83/297.02 , remove(x, nil()) -> nil() } 690.83/297.02 Obligation: 690.83/297.02 innermost runtime complexity 690.83/297.02 Answer: 690.83/297.02 MAYBE 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 2) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'empty' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 2) 'With Problem ...' failed due to the following reason: 690.83/297.02 690.83/297.02 Empty strict component of the problem is NOT empty. 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 2) 'Best' failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 690.83/297.02 following reason: 690.83/297.02 690.83/297.02 The input cannot be shown compatible 690.83/297.02 690.83/297.02 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 690.83/297.02 to the following reason: 690.83/297.02 690.83/297.02 The input cannot be shown compatible 690.83/297.02 690.83/297.02 690.83/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 690.83/297.02 failed due to the following reason: 690.83/297.02 690.83/297.02 None of the processors succeeded. 690.83/297.02 690.83/297.02 Details of failed attempt(s): 690.83/297.02 ----------------------------- 690.83/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 690.83/297.02 failed due to the following reason: 690.83/297.02 690.83/297.02 match-boundness of the problem could not be verified. 690.83/297.02 690.83/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 690.83/297.02 failed due to the following reason: 690.83/297.02 690.83/297.02 match-boundness of the problem could not be verified. 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 690.83/297.02 Arrrr.. 691.05/297.20 EOF