MAYBE 962.29/297.04 MAYBE 962.29/297.04 962.29/297.04 We are left with following problem, upon which TcT provides the 962.29/297.04 certificate MAYBE. 962.29/297.04 962.29/297.04 Strict Trs: 962.29/297.04 { f(s(x)) -> f(id_inc(c(x, x))) 962.29/297.04 , f(c(s(x), y)) -> g(c(x, y)) 962.29/297.04 , id_inc(s(x)) -> s(id_inc(x)) 962.29/297.04 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 962.29/297.04 , id_inc(0()) -> s(0()) 962.29/297.04 , id_inc(0()) -> 0() 962.29/297.04 , g(c(x, x)) -> f(x) 962.29/297.04 , g(c(x, s(y))) -> g(c(y, x)) 962.29/297.04 , g(c(s(x), y)) -> g(c(y, x)) } 962.29/297.04 Obligation: 962.29/297.04 runtime complexity 962.29/297.04 Answer: 962.29/297.04 MAYBE 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 962.29/297.04 following reason: 962.29/297.04 962.29/297.04 Computation stopped due to timeout after 297.0 seconds. 962.29/297.04 962.29/297.04 2) 'Best' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 962.29/297.04 seconds)' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'empty' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 2) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'empty' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 2) 'Fastest' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'empty' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 2) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 962.29/297.04 2) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'empty' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 2) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'empty' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 2) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'empty' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 2) 'With Problem ...' failed due to the following reason: 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 962.29/297.04 962.29/297.04 962.29/297.04 962.29/297.04 962.29/297.04 962.29/297.04 2) 'Best' failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 962.29/297.04 following reason: 962.29/297.04 962.29/297.04 The processor is inapplicable, reason: 962.29/297.04 Processor only applicable for innermost runtime complexity analysis 962.29/297.04 962.29/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 962.29/297.04 to the following reason: 962.29/297.04 962.29/297.04 The processor is inapplicable, reason: 962.29/297.04 Processor only applicable for innermost runtime complexity analysis 962.29/297.04 962.29/297.04 962.29/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 962.29/297.04 failed due to the following reason: 962.29/297.04 962.29/297.04 None of the processors succeeded. 962.29/297.04 962.29/297.04 Details of failed attempt(s): 962.29/297.04 ----------------------------- 962.29/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 962.29/297.04 failed due to the following reason: 962.29/297.04 962.29/297.04 match-boundness of the problem could not be verified. 962.29/297.04 962.29/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 962.29/297.04 failed due to the following reason: 962.29/297.04 962.29/297.04 match-boundness of the problem could not be verified. 962.29/297.04 962.29/297.04 962.29/297.04 962.29/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 962.29/297.04 the following reason: 962.29/297.04 962.29/297.04 We add the following weak dependency pairs: 962.29/297.04 962.29/297.04 Strict DPs: 962.29/297.04 { f^#(s(x)) -> c_1(f^#(id_inc(c(x, x)))) 962.29/297.04 , f^#(c(s(x), y)) -> c_2(g^#(c(x, y))) 962.29/297.04 , g^#(c(x, x)) -> c_7(f^#(x)) 962.29/297.04 , g^#(c(x, s(y))) -> c_8(g^#(c(y, x))) 962.29/297.04 , g^#(c(s(x), y)) -> c_9(g^#(c(y, x))) 962.29/297.04 , id_inc^#(s(x)) -> c_3(id_inc^#(x)) 962.29/297.04 , id_inc^#(c(x, y)) -> c_4(id_inc^#(x), id_inc^#(y)) 962.29/297.04 , id_inc^#(0()) -> c_5() 962.29/297.04 , id_inc^#(0()) -> c_6() } 962.29/297.04 962.29/297.04 and mark the set of starting terms. 962.29/297.04 962.29/297.04 We are left with following problem, upon which TcT provides the 962.29/297.04 certificate MAYBE. 962.29/297.04 962.29/297.04 Strict DPs: 962.29/297.04 { f^#(s(x)) -> c_1(f^#(id_inc(c(x, x)))) 962.29/297.04 , f^#(c(s(x), y)) -> c_2(g^#(c(x, y))) 962.29/297.04 , g^#(c(x, x)) -> c_7(f^#(x)) 962.29/297.04 , g^#(c(x, s(y))) -> c_8(g^#(c(y, x))) 962.29/297.04 , g^#(c(s(x), y)) -> c_9(g^#(c(y, x))) 962.29/297.04 , id_inc^#(s(x)) -> c_3(id_inc^#(x)) 962.29/297.04 , id_inc^#(c(x, y)) -> c_4(id_inc^#(x), id_inc^#(y)) 962.29/297.04 , id_inc^#(0()) -> c_5() 962.29/297.04 , id_inc^#(0()) -> c_6() } 962.29/297.04 Strict Trs: 962.29/297.04 { f(s(x)) -> f(id_inc(c(x, x))) 962.29/297.04 , f(c(s(x), y)) -> g(c(x, y)) 962.29/297.04 , id_inc(s(x)) -> s(id_inc(x)) 962.29/297.04 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 962.29/297.04 , id_inc(0()) -> s(0()) 962.29/297.04 , id_inc(0()) -> 0() 962.29/297.04 , g(c(x, x)) -> f(x) 962.29/297.04 , g(c(x, s(y))) -> g(c(y, x)) 962.29/297.04 , g(c(s(x), y)) -> g(c(y, x)) } 962.29/297.04 Obligation: 962.29/297.04 runtime complexity 962.29/297.04 Answer: 962.29/297.04 MAYBE 962.29/297.04 962.29/297.04 We estimate the number of application of {8,9} by applications of 962.29/297.04 Pre({8,9}) = {6,7}. Here rules are labeled as follows: 962.29/297.04 962.29/297.04 DPs: 962.29/297.04 { 1: f^#(s(x)) -> c_1(f^#(id_inc(c(x, x)))) 962.29/297.04 , 2: f^#(c(s(x), y)) -> c_2(g^#(c(x, y))) 962.29/297.04 , 3: g^#(c(x, x)) -> c_7(f^#(x)) 962.29/297.04 , 4: g^#(c(x, s(y))) -> c_8(g^#(c(y, x))) 962.29/297.04 , 5: g^#(c(s(x), y)) -> c_9(g^#(c(y, x))) 962.29/297.04 , 6: id_inc^#(s(x)) -> c_3(id_inc^#(x)) 962.29/297.04 , 7: id_inc^#(c(x, y)) -> c_4(id_inc^#(x), id_inc^#(y)) 962.29/297.04 , 8: id_inc^#(0()) -> c_5() 962.29/297.04 , 9: id_inc^#(0()) -> c_6() } 962.29/297.04 962.29/297.04 We are left with following problem, upon which TcT provides the 962.29/297.04 certificate MAYBE. 962.29/297.04 962.29/297.04 Strict DPs: 962.29/297.04 { f^#(s(x)) -> c_1(f^#(id_inc(c(x, x)))) 962.29/297.04 , f^#(c(s(x), y)) -> c_2(g^#(c(x, y))) 962.29/297.04 , g^#(c(x, x)) -> c_7(f^#(x)) 962.29/297.04 , g^#(c(x, s(y))) -> c_8(g^#(c(y, x))) 962.29/297.04 , g^#(c(s(x), y)) -> c_9(g^#(c(y, x))) 962.29/297.04 , id_inc^#(s(x)) -> c_3(id_inc^#(x)) 962.29/297.04 , id_inc^#(c(x, y)) -> c_4(id_inc^#(x), id_inc^#(y)) } 962.29/297.04 Strict Trs: 962.29/297.04 { f(s(x)) -> f(id_inc(c(x, x))) 962.29/297.04 , f(c(s(x), y)) -> g(c(x, y)) 962.29/297.04 , id_inc(s(x)) -> s(id_inc(x)) 962.29/297.04 , id_inc(c(x, y)) -> c(id_inc(x), id_inc(y)) 962.29/297.04 , id_inc(0()) -> s(0()) 962.29/297.04 , id_inc(0()) -> 0() 962.29/297.04 , g(c(x, x)) -> f(x) 962.29/297.04 , g(c(x, s(y))) -> g(c(y, x)) 962.29/297.04 , g(c(s(x), y)) -> g(c(y, x)) } 962.29/297.04 Weak DPs: 962.29/297.04 { id_inc^#(0()) -> c_5() 962.29/297.04 , id_inc^#(0()) -> c_6() } 962.29/297.04 Obligation: 962.29/297.04 runtime complexity 962.29/297.04 Answer: 962.29/297.04 MAYBE 962.29/297.04 962.29/297.04 Empty strict component of the problem is NOT empty. 962.29/297.04 962.29/297.04 962.29/297.04 Arrrr.. 963.28/297.91 EOF