MAYBE 1053.49/297.03 MAYBE 1053.49/297.03 1053.49/297.03 We are left with following problem, upon which TcT provides the 1053.49/297.03 certificate MAYBE. 1053.49/297.03 1053.49/297.03 Strict Trs: 1053.49/297.03 { active(f(x, y, z)) -> f(x, y, active(z)) 1053.49/297.03 , active(f(b(), c(), x)) -> mark(f(x, x, x)) 1053.49/297.03 , active(d()) -> mark(c()) 1053.49/297.03 , active(d()) -> m(b()) 1053.49/297.03 , f(x, y, mark(z)) -> mark(f(x, y, z)) 1053.49/297.03 , f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z)) 1053.49/297.03 , proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z)) 1053.49/297.03 , proper(b()) -> ok(b()) 1053.49/297.03 , proper(c()) -> ok(c()) 1053.49/297.03 , proper(d()) -> ok(d()) 1053.49/297.03 , top(mark(x)) -> top(proper(x)) 1053.49/297.03 , top(ok(x)) -> top(active(x)) } 1053.49/297.03 Obligation: 1053.49/297.03 runtime complexity 1053.49/297.03 Answer: 1053.49/297.03 MAYBE 1053.49/297.03 1053.49/297.03 None of the processors succeeded. 1053.49/297.03 1053.49/297.03 Details of failed attempt(s): 1053.49/297.03 ----------------------------- 1053.49/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1053.49/297.03 following reason: 1053.49/297.03 1053.49/297.03 Computation stopped due to timeout after 297.0 seconds. 1053.49/297.03 1053.49/297.03 2) 'Best' failed due to the following reason: 1053.49/297.03 1053.49/297.03 None of the processors succeeded. 1053.49/297.03 1053.49/297.03 Details of failed attempt(s): 1053.49/297.03 ----------------------------- 1053.49/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1053.49/297.03 seconds)' failed due to the following reason: 1053.49/297.03 1053.49/297.03 Computation stopped due to timeout after 148.0 seconds. 1053.49/297.03 1053.49/297.03 2) 'Best' failed due to the following reason: 1053.49/297.03 1053.49/297.03 None of the processors succeeded. 1053.49/297.03 1053.49/297.03 Details of failed attempt(s): 1053.49/297.03 ----------------------------- 1053.49/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1053.49/297.03 to the following reason: 1053.49/297.03 1053.49/297.03 The processor is inapplicable, reason: 1053.49/297.03 Processor only applicable for innermost runtime complexity analysis 1053.49/297.03 1053.49/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1053.49/297.03 following reason: 1053.49/297.03 1053.49/297.03 The processor is inapplicable, reason: 1053.49/297.03 Processor only applicable for innermost runtime complexity analysis 1053.49/297.03 1053.49/297.03 1053.49/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1053.49/297.03 failed due to the following reason: 1053.49/297.03 1053.49/297.03 None of the processors succeeded. 1053.49/297.03 1053.49/297.03 Details of failed attempt(s): 1053.49/297.03 ----------------------------- 1053.49/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1053.49/297.03 failed due to the following reason: 1053.49/297.03 1053.49/297.03 match-boundness of the problem could not be verified. 1053.49/297.03 1053.49/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1053.49/297.03 failed due to the following reason: 1053.49/297.03 1053.49/297.03 match-boundness of the problem could not be verified. 1053.49/297.03 1053.49/297.03 1053.49/297.03 1053.49/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1053.49/297.03 the following reason: 1053.49/297.03 1053.49/297.03 We add the following weak dependency pairs: 1053.49/297.03 1053.49/297.03 Strict DPs: 1053.49/297.03 { active^#(f(x, y, z)) -> c_1(f^#(x, y, active(z))) 1053.49/297.03 , active^#(f(b(), c(), x)) -> c_2(f^#(x, x, x)) 1053.49/297.03 , active^#(d()) -> c_3() 1053.49/297.03 , active^#(d()) -> c_4() 1053.49/297.03 , f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) 1053.49/297.03 , f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) 1053.49/297.03 , proper^#(f(x, y, z)) -> c_7(f^#(proper(x), proper(y), proper(z))) 1053.49/297.03 , proper^#(b()) -> c_8() 1053.49/297.03 , proper^#(c()) -> c_9() 1053.49/297.03 , proper^#(d()) -> c_10() 1053.49/297.03 , top^#(mark(x)) -> c_11(top^#(proper(x))) 1053.49/297.03 , top^#(ok(x)) -> c_12(top^#(active(x))) } 1053.49/297.03 1053.49/297.03 and mark the set of starting terms. 1053.49/297.03 1053.49/297.03 We are left with following problem, upon which TcT provides the 1053.49/297.03 certificate MAYBE. 1053.49/297.03 1053.49/297.03 Strict DPs: 1053.49/297.03 { active^#(f(x, y, z)) -> c_1(f^#(x, y, active(z))) 1053.49/297.03 , active^#(f(b(), c(), x)) -> c_2(f^#(x, x, x)) 1053.49/297.03 , active^#(d()) -> c_3() 1053.49/297.03 , active^#(d()) -> c_4() 1053.49/297.03 , f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) 1053.49/297.03 , f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) 1053.49/297.03 , proper^#(f(x, y, z)) -> c_7(f^#(proper(x), proper(y), proper(z))) 1053.49/297.03 , proper^#(b()) -> c_8() 1053.49/297.03 , proper^#(c()) -> c_9() 1053.49/297.03 , proper^#(d()) -> c_10() 1053.49/297.03 , top^#(mark(x)) -> c_11(top^#(proper(x))) 1053.49/297.03 , top^#(ok(x)) -> c_12(top^#(active(x))) } 1053.49/297.03 Strict Trs: 1053.49/297.03 { active(f(x, y, z)) -> f(x, y, active(z)) 1053.49/297.03 , active(f(b(), c(), x)) -> mark(f(x, x, x)) 1053.49/297.03 , active(d()) -> mark(c()) 1053.49/297.03 , active(d()) -> m(b()) 1053.49/297.03 , f(x, y, mark(z)) -> mark(f(x, y, z)) 1053.49/297.03 , f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z)) 1053.49/297.03 , proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z)) 1053.49/297.03 , proper(b()) -> ok(b()) 1053.49/297.03 , proper(c()) -> ok(c()) 1053.49/297.03 , proper(d()) -> ok(d()) 1053.49/297.03 , top(mark(x)) -> top(proper(x)) 1053.49/297.03 , top(ok(x)) -> top(active(x)) } 1053.49/297.03 Obligation: 1053.49/297.03 runtime complexity 1053.49/297.03 Answer: 1053.49/297.03 MAYBE 1053.49/297.03 1053.49/297.03 Consider the dependency graph: 1053.49/297.03 1053.49/297.03 1: active^#(f(x, y, z)) -> c_1(f^#(x, y, active(z))) 1053.49/297.03 -->_1 f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) :6 1053.49/297.03 -->_1 f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) :5 1053.49/297.03 1053.49/297.03 2: active^#(f(b(), c(), x)) -> c_2(f^#(x, x, x)) 1053.49/297.03 -->_1 f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) :6 1053.49/297.03 -->_1 f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) :5 1053.49/297.03 1053.49/297.03 3: active^#(d()) -> c_3() 1053.49/297.03 1053.49/297.03 4: active^#(d()) -> c_4() 1053.49/297.03 1053.49/297.03 5: f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) 1053.49/297.03 -->_1 f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) :6 1053.49/297.03 -->_1 f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) :5 1053.49/297.03 1053.49/297.03 6: f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) 1053.49/297.03 -->_1 f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) :6 1053.49/297.03 -->_1 f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) :5 1053.49/297.03 1053.49/297.03 7: proper^#(f(x, y, z)) -> 1053.49/297.03 c_7(f^#(proper(x), proper(y), proper(z))) 1053.49/297.03 -->_1 f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) :6 1053.49/297.03 -->_1 f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) :5 1053.49/297.03 1053.49/297.03 8: proper^#(b()) -> c_8() 1053.49/297.03 1053.49/297.03 9: proper^#(c()) -> c_9() 1053.49/297.03 1053.49/297.03 10: proper^#(d()) -> c_10() 1053.49/297.03 1053.49/297.03 11: top^#(mark(x)) -> c_11(top^#(proper(x))) 1053.49/297.03 -->_1 top^#(ok(x)) -> c_12(top^#(active(x))) :12 1053.49/297.03 -->_1 top^#(mark(x)) -> c_11(top^#(proper(x))) :11 1053.49/297.03 1053.49/297.03 12: top^#(ok(x)) -> c_12(top^#(active(x))) 1053.49/297.03 -->_1 top^#(ok(x)) -> c_12(top^#(active(x))) :12 1053.49/297.03 -->_1 top^#(mark(x)) -> c_11(top^#(proper(x))) :11 1053.49/297.03 1053.49/297.03 1053.49/297.03 Only the nodes {3,4,5,6,8,9,10,11,12} are reachable from nodes 1053.49/297.03 {3,4,5,6,8,9,10,11,12} that start derivation from marked basic 1053.49/297.03 terms. The nodes not reachable are removed from the problem. 1053.49/297.03 1053.49/297.03 We are left with following problem, upon which TcT provides the 1053.49/297.03 certificate MAYBE. 1053.49/297.03 1053.49/297.03 Strict DPs: 1053.49/297.03 { active^#(d()) -> c_3() 1053.49/297.03 , active^#(d()) -> c_4() 1053.49/297.03 , f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) 1053.49/297.03 , f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) 1053.49/297.03 , proper^#(b()) -> c_8() 1053.49/297.03 , proper^#(c()) -> c_9() 1053.49/297.03 , proper^#(d()) -> c_10() 1053.49/297.03 , top^#(mark(x)) -> c_11(top^#(proper(x))) 1053.49/297.03 , top^#(ok(x)) -> c_12(top^#(active(x))) } 1053.49/297.03 Strict Trs: 1053.49/297.03 { active(f(x, y, z)) -> f(x, y, active(z)) 1053.49/297.03 , active(f(b(), c(), x)) -> mark(f(x, x, x)) 1053.49/297.03 , active(d()) -> mark(c()) 1053.49/297.03 , active(d()) -> m(b()) 1053.49/297.03 , f(x, y, mark(z)) -> mark(f(x, y, z)) 1053.49/297.03 , f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z)) 1053.49/297.03 , proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z)) 1053.49/297.03 , proper(b()) -> ok(b()) 1053.49/297.03 , proper(c()) -> ok(c()) 1053.49/297.03 , proper(d()) -> ok(d()) 1053.49/297.03 , top(mark(x)) -> top(proper(x)) 1053.49/297.03 , top(ok(x)) -> top(active(x)) } 1053.49/297.03 Obligation: 1053.49/297.03 runtime complexity 1053.49/297.03 Answer: 1053.49/297.03 MAYBE 1053.49/297.03 1053.49/297.03 We estimate the number of application of {1,2,5,6,7} by 1053.49/297.03 applications of Pre({1,2,5,6,7}) = {}. Here rules are labeled as 1053.49/297.03 follows: 1053.49/297.03 1053.49/297.03 DPs: 1053.49/297.03 { 1: active^#(d()) -> c_3() 1053.49/297.03 , 2: active^#(d()) -> c_4() 1053.49/297.03 , 3: f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) 1053.49/297.03 , 4: f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) 1053.49/297.03 , 5: proper^#(b()) -> c_8() 1053.49/297.03 , 6: proper^#(c()) -> c_9() 1053.49/297.03 , 7: proper^#(d()) -> c_10() 1053.49/297.03 , 8: top^#(mark(x)) -> c_11(top^#(proper(x))) 1053.49/297.03 , 9: top^#(ok(x)) -> c_12(top^#(active(x))) } 1053.49/297.03 1053.49/297.03 We are left with following problem, upon which TcT provides the 1053.49/297.03 certificate MAYBE. 1053.49/297.03 1053.49/297.03 Strict DPs: 1053.49/297.03 { f^#(x, y, mark(z)) -> c_5(f^#(x, y, z)) 1053.49/297.03 , f^#(ok(x), ok(y), ok(z)) -> c_6(f^#(x, y, z)) 1053.49/297.03 , top^#(mark(x)) -> c_11(top^#(proper(x))) 1053.49/297.03 , top^#(ok(x)) -> c_12(top^#(active(x))) } 1053.49/297.03 Strict Trs: 1053.49/297.03 { active(f(x, y, z)) -> f(x, y, active(z)) 1053.49/297.03 , active(f(b(), c(), x)) -> mark(f(x, x, x)) 1053.49/297.03 , active(d()) -> mark(c()) 1053.49/297.03 , active(d()) -> m(b()) 1053.49/297.03 , f(x, y, mark(z)) -> mark(f(x, y, z)) 1053.49/297.03 , f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z)) 1053.49/297.03 , proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z)) 1053.49/297.03 , proper(b()) -> ok(b()) 1053.49/297.03 , proper(c()) -> ok(c()) 1053.49/297.03 , proper(d()) -> ok(d()) 1053.49/297.03 , top(mark(x)) -> top(proper(x)) 1053.49/297.03 , top(ok(x)) -> top(active(x)) } 1053.49/297.03 Weak DPs: 1053.49/297.03 { active^#(d()) -> c_3() 1053.49/297.03 , active^#(d()) -> c_4() 1053.49/297.03 , proper^#(b()) -> c_8() 1053.49/297.03 , proper^#(c()) -> c_9() 1053.49/297.03 , proper^#(d()) -> c_10() } 1053.49/297.03 Obligation: 1053.49/297.03 runtime complexity 1053.49/297.03 Answer: 1053.49/297.03 MAYBE 1053.49/297.03 1053.49/297.03 Empty strict component of the problem is NOT empty. 1053.49/297.03 1053.49/297.03 1053.49/297.03 Arrrr.. 1053.73/297.23 EOF