MAYBE 1143.86/297.28 MAYBE 1143.86/297.28 1143.86/297.28 We are left with following problem, upon which TcT provides the 1143.86/297.28 certificate MAYBE. 1143.86/297.28 1143.86/297.28 Strict Trs: 1143.86/297.28 { qsort(nil()) -> nil() 1143.86/297.28 , qsort(.(x, y)) -> 1143.86/297.28 ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y)))) 1143.86/297.28 , lowers(x, nil()) -> nil() 1143.86/297.28 , lowers(x, .(y, z)) -> 1143.86/297.28 if(<=(y, x), .(y, lowers(x, z)), lowers(x, z)) 1143.86/297.28 , greaters(x, nil()) -> nil() 1143.86/297.28 , greaters(x, .(y, z)) -> 1143.86/297.28 if(<=(y, x), greaters(x, z), .(y, greaters(x, z))) } 1143.86/297.28 Obligation: 1143.86/297.28 runtime complexity 1143.86/297.28 Answer: 1143.86/297.28 MAYBE 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1143.86/297.28 following reason: 1143.86/297.28 1143.86/297.28 Computation stopped due to timeout after 297.0 seconds. 1143.86/297.28 1143.86/297.28 2) 'Best' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1143.86/297.28 seconds)' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'empty' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 2) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'empty' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 2) 'Fastest' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'empty' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 2) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'empty' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 2) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'empty' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 2) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 1143.86/297.28 1143.86/297.28 1143.86/297.28 2) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'empty' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 2) 'With Problem ...' failed due to the following reason: 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 1143.86/297.28 1143.86/297.28 1143.86/297.28 1143.86/297.28 2) 'Best' failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1143.86/297.28 following reason: 1143.86/297.28 1143.86/297.28 The processor is inapplicable, reason: 1143.86/297.28 Processor only applicable for innermost runtime complexity analysis 1143.86/297.28 1143.86/297.28 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1143.86/297.28 to the following reason: 1143.86/297.28 1143.86/297.28 The processor is inapplicable, reason: 1143.86/297.28 Processor only applicable for innermost runtime complexity analysis 1143.86/297.28 1143.86/297.28 1143.86/297.28 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1143.86/297.28 failed due to the following reason: 1143.86/297.28 1143.86/297.28 None of the processors succeeded. 1143.86/297.28 1143.86/297.28 Details of failed attempt(s): 1143.86/297.28 ----------------------------- 1143.86/297.28 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1143.86/297.28 failed due to the following reason: 1143.86/297.28 1143.86/297.28 match-boundness of the problem could not be verified. 1143.86/297.28 1143.86/297.28 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1143.86/297.28 failed due to the following reason: 1143.86/297.28 1143.86/297.28 match-boundness of the problem could not be verified. 1143.86/297.28 1143.86/297.28 1143.86/297.28 1143.86/297.28 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1143.86/297.28 the following reason: 1143.86/297.28 1143.86/297.28 We add the following weak dependency pairs: 1143.86/297.28 1143.86/297.28 Strict DPs: 1143.86/297.28 { qsort^#(nil()) -> c_1() 1143.86/297.28 , qsort^#(.(x, y)) -> 1143.86/297.28 c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y))) 1143.86/297.28 , lowers^#(x, nil()) -> c_3() 1143.86/297.28 , lowers^#(x, .(y, z)) -> 1143.86/297.28 c_4(y, x, y, lowers^#(x, z), lowers^#(x, z)) 1143.86/297.28 , greaters^#(x, nil()) -> c_5() 1143.86/297.28 , greaters^#(x, .(y, z)) -> 1143.86/297.28 c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) } 1143.86/297.28 1143.86/297.28 and mark the set of starting terms. 1143.86/297.28 1143.86/297.28 We are left with following problem, upon which TcT provides the 1143.86/297.28 certificate MAYBE. 1143.86/297.28 1143.86/297.28 Strict DPs: 1143.86/297.28 { qsort^#(nil()) -> c_1() 1143.86/297.28 , qsort^#(.(x, y)) -> 1143.86/297.28 c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y))) 1143.86/297.28 , lowers^#(x, nil()) -> c_3() 1143.86/297.28 , lowers^#(x, .(y, z)) -> 1143.86/297.28 c_4(y, x, y, lowers^#(x, z), lowers^#(x, z)) 1143.86/297.28 , greaters^#(x, nil()) -> c_5() 1143.86/297.28 , greaters^#(x, .(y, z)) -> 1143.86/297.28 c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) } 1143.86/297.28 Strict Trs: 1143.86/297.28 { qsort(nil()) -> nil() 1143.86/297.28 , qsort(.(x, y)) -> 1143.86/297.28 ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y)))) 1143.86/297.28 , lowers(x, nil()) -> nil() 1143.86/297.28 , lowers(x, .(y, z)) -> 1143.86/297.28 if(<=(y, x), .(y, lowers(x, z)), lowers(x, z)) 1143.86/297.28 , greaters(x, nil()) -> nil() 1143.86/297.28 , greaters(x, .(y, z)) -> 1143.86/297.28 if(<=(y, x), greaters(x, z), .(y, greaters(x, z))) } 1143.86/297.28 Obligation: 1143.86/297.28 runtime complexity 1143.86/297.28 Answer: 1143.86/297.28 MAYBE 1143.86/297.28 1143.86/297.28 We estimate the number of application of {1,3,5} by applications of 1143.86/297.28 Pre({1,3,5}) = {2,4,6}. Here rules are labeled as follows: 1143.86/297.28 1143.86/297.28 DPs: 1143.86/297.28 { 1: qsort^#(nil()) -> c_1() 1143.86/297.28 , 2: qsort^#(.(x, y)) -> 1143.86/297.28 c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y))) 1143.86/297.28 , 3: lowers^#(x, nil()) -> c_3() 1143.86/297.28 , 4: lowers^#(x, .(y, z)) -> 1143.86/297.28 c_4(y, x, y, lowers^#(x, z), lowers^#(x, z)) 1143.86/297.28 , 5: greaters^#(x, nil()) -> c_5() 1143.86/297.28 , 6: greaters^#(x, .(y, z)) -> 1143.86/297.28 c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) } 1143.86/297.28 1143.86/297.28 We are left with following problem, upon which TcT provides the 1143.86/297.28 certificate MAYBE. 1143.86/297.28 1143.86/297.28 Strict DPs: 1143.86/297.28 { qsort^#(.(x, y)) -> 1143.86/297.28 c_2(qsort^#(lowers(x, y)), x, qsort^#(greaters(x, y))) 1143.86/297.28 , lowers^#(x, .(y, z)) -> 1143.86/297.28 c_4(y, x, y, lowers^#(x, z), lowers^#(x, z)) 1143.86/297.28 , greaters^#(x, .(y, z)) -> 1143.86/297.28 c_6(y, x, greaters^#(x, z), y, greaters^#(x, z)) } 1143.86/297.28 Strict Trs: 1143.86/297.28 { qsort(nil()) -> nil() 1143.86/297.28 , qsort(.(x, y)) -> 1143.86/297.28 ++(qsort(lowers(x, y)), .(x, qsort(greaters(x, y)))) 1143.86/297.28 , lowers(x, nil()) -> nil() 1143.86/297.28 , lowers(x, .(y, z)) -> 1143.86/297.28 if(<=(y, x), .(y, lowers(x, z)), lowers(x, z)) 1143.86/297.28 , greaters(x, nil()) -> nil() 1143.86/297.28 , greaters(x, .(y, z)) -> 1143.86/297.28 if(<=(y, x), greaters(x, z), .(y, greaters(x, z))) } 1143.86/297.28 Weak DPs: 1143.86/297.28 { qsort^#(nil()) -> c_1() 1143.86/297.28 , lowers^#(x, nil()) -> c_3() 1143.86/297.28 , greaters^#(x, nil()) -> c_5() } 1143.86/297.28 Obligation: 1143.86/297.28 runtime complexity 1143.86/297.28 Answer: 1143.86/297.28 MAYBE 1143.86/297.28 1143.86/297.28 Empty strict component of the problem is NOT empty. 1143.86/297.28 1143.86/297.28 1143.86/297.28 Arrrr.. 1144.59/297.74 EOF