MAYBE 183.18/92.17 MAYBE 183.18/92.17 183.18/92.17 We are left with following problem, upon which TcT provides the 183.18/92.17 certificate MAYBE. 183.18/92.17 183.18/92.17 Strict Trs: 183.18/92.17 { p(p(s(x))) -> p(x) 183.18/92.17 , p(0()) -> s(s(0())) 183.18/92.17 , p(s(x)) -> x 183.18/92.17 , le(p(s(x)), x) -> le(x, x) 183.18/92.17 , le(0(), y) -> true() 183.18/92.17 , le(s(x), 0()) -> false() 183.18/92.17 , le(s(x), s(y)) -> le(x, y) 183.18/92.17 , minus(x, y) -> if(le(x, y), x, y) 183.18/92.17 , if(true(), x, y) -> 0() 183.18/92.17 , if(false(), x, y) -> s(minus(p(x), y)) } 183.18/92.17 Obligation: 183.18/92.17 runtime complexity 183.18/92.17 Answer: 183.18/92.17 MAYBE 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'Best' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 183.18/92.17 seconds)' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'empty' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 2) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'empty' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 2) 'Fastest' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'empty' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 2) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 183.18/92.17 2) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'empty' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 2) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'empty' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 2) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'empty' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 2) 'With Problem ...' failed due to the following reason: 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 183.18/92.17 183.18/92.17 183.18/92.17 183.18/92.17 183.18/92.17 183.18/92.17 2) 'Best' failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 183.18/92.17 following reason: 183.18/92.17 183.18/92.17 The processor is inapplicable, reason: 183.18/92.17 Processor only applicable for innermost runtime complexity analysis 183.18/92.17 183.18/92.17 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 183.18/92.17 to the following reason: 183.18/92.17 183.18/92.17 The processor is inapplicable, reason: 183.18/92.17 Processor only applicable for innermost runtime complexity analysis 183.18/92.17 183.18/92.17 183.18/92.17 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 183.18/92.17 failed due to the following reason: 183.18/92.17 183.18/92.17 None of the processors succeeded. 183.18/92.17 183.18/92.17 Details of failed attempt(s): 183.18/92.17 ----------------------------- 183.18/92.17 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 183.18/92.17 failed due to the following reason: 183.18/92.17 183.18/92.17 match-boundness of the problem could not be verified. 183.18/92.17 183.18/92.17 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 183.18/92.17 failed due to the following reason: 183.18/92.17 183.18/92.17 match-boundness of the problem could not be verified. 183.18/92.17 183.18/92.17 183.18/92.17 183.18/92.17 2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 183.18/92.17 the following reason: 183.18/92.17 183.18/92.17 We add the following weak dependency pairs: 183.18/92.17 183.18/92.17 Strict DPs: 183.18/92.17 { p^#(p(s(x))) -> c_1(p^#(x)) 183.18/92.17 , p^#(0()) -> c_2() 183.18/92.17 , p^#(s(x)) -> c_3(x) 183.18/92.17 , le^#(p(s(x)), x) -> c_4(le^#(x, x)) 183.18/92.17 , le^#(0(), y) -> c_5() 183.18/92.17 , le^#(s(x), 0()) -> c_6() 183.18/92.17 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 183.18/92.17 , minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) 183.18/92.17 , if^#(true(), x, y) -> c_9() 183.18/92.17 , if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } 183.18/92.17 183.18/92.17 and mark the set of starting terms. 183.18/92.17 183.18/92.17 We are left with following problem, upon which TcT provides the 183.18/92.17 certificate MAYBE. 183.18/92.17 183.18/92.17 Strict DPs: 183.18/92.17 { p^#(p(s(x))) -> c_1(p^#(x)) 183.18/92.17 , p^#(0()) -> c_2() 183.18/92.17 , p^#(s(x)) -> c_3(x) 183.18/92.17 , le^#(p(s(x)), x) -> c_4(le^#(x, x)) 183.18/92.17 , le^#(0(), y) -> c_5() 183.18/92.17 , le^#(s(x), 0()) -> c_6() 183.18/92.17 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 183.18/92.17 , minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) 183.18/92.17 , if^#(true(), x, y) -> c_9() 183.18/92.17 , if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } 183.18/92.17 Strict Trs: 183.18/92.17 { p(p(s(x))) -> p(x) 183.18/92.17 , p(0()) -> s(s(0())) 183.18/92.17 , p(s(x)) -> x 183.18/92.17 , le(p(s(x)), x) -> le(x, x) 183.18/92.17 , le(0(), y) -> true() 183.18/92.17 , le(s(x), 0()) -> false() 183.18/92.17 , le(s(x), s(y)) -> le(x, y) 183.18/92.17 , minus(x, y) -> if(le(x, y), x, y) 183.18/92.17 , if(true(), x, y) -> 0() 183.18/92.17 , if(false(), x, y) -> s(minus(p(x), y)) } 183.18/92.17 Obligation: 183.18/92.17 runtime complexity 183.18/92.17 Answer: 183.18/92.17 MAYBE 183.18/92.17 183.18/92.17 We estimate the number of application of {2,5,6,9} by applications 183.18/92.17 of Pre({2,5,6,9}) = {1,3,4,7,8}. Here rules are labeled as follows: 183.18/92.17 183.18/92.17 DPs: 183.18/92.17 { 1: p^#(p(s(x))) -> c_1(p^#(x)) 183.18/92.17 , 2: p^#(0()) -> c_2() 183.18/92.17 , 3: p^#(s(x)) -> c_3(x) 183.18/92.17 , 4: le^#(p(s(x)), x) -> c_4(le^#(x, x)) 183.18/92.17 , 5: le^#(0(), y) -> c_5() 183.18/92.17 , 6: le^#(s(x), 0()) -> c_6() 183.18/92.17 , 7: le^#(s(x), s(y)) -> c_7(le^#(x, y)) 183.18/92.17 , 8: minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) 183.18/92.17 , 9: if^#(true(), x, y) -> c_9() 183.18/92.17 , 10: if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } 183.18/92.17 183.18/92.17 We are left with following problem, upon which TcT provides the 183.18/92.17 certificate MAYBE. 183.18/92.17 183.18/92.17 Strict DPs: 183.18/92.17 { p^#(p(s(x))) -> c_1(p^#(x)) 183.18/92.17 , p^#(s(x)) -> c_3(x) 183.18/92.17 , le^#(p(s(x)), x) -> c_4(le^#(x, x)) 183.18/92.17 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 183.18/92.17 , minus^#(x, y) -> c_8(if^#(le(x, y), x, y)) 183.18/92.17 , if^#(false(), x, y) -> c_10(minus^#(p(x), y)) } 183.18/92.17 Strict Trs: 183.18/92.17 { p(p(s(x))) -> p(x) 183.18/92.17 , p(0()) -> s(s(0())) 183.18/92.17 , p(s(x)) -> x 183.18/92.17 , le(p(s(x)), x) -> le(x, x) 183.18/92.17 , le(0(), y) -> true() 183.18/92.17 , le(s(x), 0()) -> false() 183.18/92.17 , le(s(x), s(y)) -> le(x, y) 183.18/92.17 , minus(x, y) -> if(le(x, y), x, y) 183.18/92.17 , if(true(), x, y) -> 0() 183.18/92.17 , if(false(), x, y) -> s(minus(p(x), y)) } 183.18/92.17 Weak DPs: 183.18/92.17 { p^#(0()) -> c_2() 183.18/92.17 , le^#(0(), y) -> c_5() 183.18/92.17 , le^#(s(x), 0()) -> c_6() 183.18/92.17 , if^#(true(), x, y) -> c_9() } 183.18/92.17 Obligation: 183.18/92.17 runtime complexity 183.18/92.17 Answer: 183.18/92.17 MAYBE 183.18/92.17 183.18/92.17 Empty strict component of the problem is NOT empty. 183.18/92.17 183.18/92.17 183.18/92.17 Arrrr.. 183.44/92.38 EOF