MAYBE 501.36/148.03 MAYBE 501.36/148.03 501.36/148.03 We are left with following problem, upon which TcT provides the 501.36/148.03 certificate MAYBE. 501.36/148.03 501.36/148.03 Strict Trs: 501.36/148.03 { f(0()) -> true() 501.36/148.03 , f(1()) -> false() 501.36/148.03 , f(s(x)) -> f(x) 501.36/148.03 , if(true(), s(x), s(y)) -> s(x) 501.36/148.03 , if(false(), s(x), s(y)) -> s(y) 501.36/148.03 , g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 501.36/148.03 , g(x, c(y)) -> c(g(x, y)) } 501.36/148.03 Obligation: 501.36/148.03 runtime complexity 501.36/148.03 Answer: 501.36/148.03 MAYBE 501.36/148.03 501.36/148.03 None of the processors succeeded. 501.36/148.03 501.36/148.03 Details of failed attempt(s): 501.36/148.03 ----------------------------- 501.36/148.03 1) 'Best' failed due to the following reason: 501.36/148.03 501.36/148.03 None of the processors succeeded. 501.36/148.03 501.36/148.03 Details of failed attempt(s): 501.36/148.03 ----------------------------- 501.36/148.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 501.36/148.03 seconds)' failed due to the following reason: 501.36/148.03 501.36/148.03 Computation stopped due to timeout after 148.0 seconds. 501.36/148.03 501.36/148.03 2) 'Best' failed due to the following reason: 501.36/148.03 501.36/148.03 None of the processors succeeded. 501.36/148.03 501.36/148.03 Details of failed attempt(s): 501.36/148.03 ----------------------------- 501.36/148.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 501.36/148.03 to the following reason: 501.36/148.03 501.36/148.03 The processor is inapplicable, reason: 501.36/148.03 Processor only applicable for innermost runtime complexity analysis 501.36/148.03 501.36/148.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 501.36/148.03 following reason: 501.36/148.03 501.36/148.03 The processor is inapplicable, reason: 501.36/148.03 Processor only applicable for innermost runtime complexity analysis 501.36/148.03 501.36/148.03 501.36/148.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 501.36/148.03 failed due to the following reason: 501.36/148.03 501.36/148.03 None of the processors succeeded. 501.36/148.03 501.36/148.03 Details of failed attempt(s): 501.36/148.03 ----------------------------- 501.36/148.03 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 501.36/148.03 failed due to the following reason: 501.36/148.03 501.36/148.03 match-boundness of the problem could not be verified. 501.36/148.03 501.36/148.03 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 501.36/148.03 failed due to the following reason: 501.36/148.03 501.36/148.03 match-boundness of the problem could not be verified. 501.36/148.03 501.36/148.03 501.36/148.03 501.36/148.03 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 501.36/148.03 the following reason: 501.36/148.03 501.36/148.03 We add the following weak dependency pairs: 501.36/148.03 501.36/148.03 Strict DPs: 501.36/148.03 { f^#(0()) -> c_1() 501.36/148.03 , f^#(1()) -> c_2() 501.36/148.03 , f^#(s(x)) -> c_3(f^#(x)) 501.36/148.03 , if^#(true(), s(x), s(y)) -> c_4(x) 501.36/148.03 , if^#(false(), s(x), s(y)) -> c_5(y) 501.36/148.03 , g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y)))) 501.36/148.03 , g^#(x, c(y)) -> c_7(g^#(x, y)) } 501.36/148.03 501.36/148.03 and mark the set of starting terms. 501.36/148.03 501.36/148.03 We are left with following problem, upon which TcT provides the 501.36/148.03 certificate MAYBE. 501.36/148.03 501.36/148.03 Strict DPs: 501.36/148.03 { f^#(0()) -> c_1() 501.36/148.03 , f^#(1()) -> c_2() 501.36/148.03 , f^#(s(x)) -> c_3(f^#(x)) 501.36/148.03 , if^#(true(), s(x), s(y)) -> c_4(x) 501.36/148.03 , if^#(false(), s(x), s(y)) -> c_5(y) 501.36/148.03 , g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y)))) 501.36/148.03 , g^#(x, c(y)) -> c_7(g^#(x, y)) } 501.36/148.03 Strict Trs: 501.36/148.03 { f(0()) -> true() 501.36/148.03 , f(1()) -> false() 501.36/148.03 , f(s(x)) -> f(x) 501.36/148.03 , if(true(), s(x), s(y)) -> s(x) 501.36/148.03 , if(false(), s(x), s(y)) -> s(y) 501.36/148.03 , g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 501.36/148.03 , g(x, c(y)) -> c(g(x, y)) } 501.36/148.03 Obligation: 501.36/148.03 runtime complexity 501.36/148.03 Answer: 501.36/148.03 MAYBE 501.36/148.03 501.36/148.03 We estimate the number of application of {1,2,6} by applications of 501.36/148.03 Pre({1,2,6}) = {3,4,5,7}. Here rules are labeled as follows: 501.36/148.03 501.36/148.03 DPs: 501.36/148.03 { 1: f^#(0()) -> c_1() 501.36/148.03 , 2: f^#(1()) -> c_2() 501.36/148.03 , 3: f^#(s(x)) -> c_3(f^#(x)) 501.36/148.03 , 4: if^#(true(), s(x), s(y)) -> c_4(x) 501.36/148.03 , 5: if^#(false(), s(x), s(y)) -> c_5(y) 501.36/148.03 , 6: g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y)))) 501.36/148.03 , 7: g^#(x, c(y)) -> c_7(g^#(x, y)) } 501.36/148.03 501.36/148.03 We are left with following problem, upon which TcT provides the 501.36/148.03 certificate MAYBE. 501.36/148.03 501.36/148.03 Strict DPs: 501.36/148.03 { f^#(s(x)) -> c_3(f^#(x)) 501.36/148.03 , if^#(true(), s(x), s(y)) -> c_4(x) 501.36/148.03 , if^#(false(), s(x), s(y)) -> c_5(y) 501.36/148.03 , g^#(x, c(y)) -> c_7(g^#(x, y)) } 501.36/148.03 Strict Trs: 501.36/148.03 { f(0()) -> true() 501.36/148.03 , f(1()) -> false() 501.36/148.03 , f(s(x)) -> f(x) 501.36/148.03 , if(true(), s(x), s(y)) -> s(x) 501.36/148.03 , if(false(), s(x), s(y)) -> s(y) 501.36/148.03 , g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 501.36/148.03 , g(x, c(y)) -> c(g(x, y)) } 501.36/148.03 Weak DPs: 501.36/148.03 { f^#(0()) -> c_1() 501.36/148.03 , f^#(1()) -> c_2() 501.36/148.03 , g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y)))) } 501.36/148.03 Obligation: 501.36/148.03 runtime complexity 501.36/148.03 Answer: 501.36/148.03 MAYBE 501.36/148.03 501.36/148.03 Empty strict component of the problem is NOT empty. 501.36/148.03 501.36/148.03 501.36/148.03 Arrrr.. 501.81/148.44 EOF