MAYBE 1055.45/297.03 MAYBE 1055.45/297.03 1055.45/297.03 We are left with following problem, upon which TcT provides the 1055.45/297.03 certificate MAYBE. 1055.45/297.03 1055.45/297.03 Strict Trs: 1055.45/297.03 { minus(s(x), y) -> if(gt(s(x), y), x, y) 1055.45/297.03 , if(true(), x, y) -> s(minus(x, y)) 1055.45/297.03 , if(false(), x, y) -> 0() 1055.45/297.03 , gt(s(x), s(y)) -> gt(x, y) 1055.45/297.03 , gt(s(x), 0()) -> true() 1055.45/297.03 , gt(0(), y) -> false() 1055.45/297.03 , ge(x, 0()) -> true() 1055.45/297.03 , ge(s(x), s(y)) -> ge(x, y) 1055.45/297.03 , ge(0(), s(x)) -> false() 1055.45/297.03 , div(x, y) -> if1(ge(x, y), x, y) 1055.45/297.03 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 1055.45/297.03 , if1(false(), x, y) -> 0() 1055.45/297.03 , if2(true(), x, y) -> s(div(minus(x, y), y)) 1055.45/297.03 , if2(false(), x, y) -> 0() } 1055.45/297.03 Obligation: 1055.45/297.03 runtime complexity 1055.45/297.03 Answer: 1055.45/297.03 MAYBE 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1055.45/297.03 following reason: 1055.45/297.03 1055.45/297.03 Computation stopped due to timeout after 297.0 seconds. 1055.45/297.03 1055.45/297.03 2) 'Best' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1055.45/297.03 seconds)' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'empty' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 2) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'empty' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 2) 'Fastest' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'empty' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 2) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 1055.45/297.03 2) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'empty' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 2) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'empty' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 2) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'empty' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 2) 'With Problem ...' failed due to the following reason: 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 1055.45/297.03 1055.45/297.03 1055.45/297.03 1055.45/297.03 1055.45/297.03 1055.45/297.03 2) 'Best' failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1055.45/297.03 following reason: 1055.45/297.03 1055.45/297.03 The processor is inapplicable, reason: 1055.45/297.03 Processor only applicable for innermost runtime complexity analysis 1055.45/297.03 1055.45/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1055.45/297.03 to the following reason: 1055.45/297.03 1055.45/297.03 The processor is inapplicable, reason: 1055.45/297.03 Processor only applicable for innermost runtime complexity analysis 1055.45/297.03 1055.45/297.03 1055.45/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1055.45/297.03 failed due to the following reason: 1055.45/297.03 1055.45/297.03 None of the processors succeeded. 1055.45/297.03 1055.45/297.03 Details of failed attempt(s): 1055.45/297.03 ----------------------------- 1055.45/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1055.45/297.03 failed due to the following reason: 1055.45/297.03 1055.45/297.03 match-boundness of the problem could not be verified. 1055.45/297.03 1055.45/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1055.45/297.03 failed due to the following reason: 1055.45/297.03 1055.45/297.03 match-boundness of the problem could not be verified. 1055.45/297.03 1055.45/297.03 1055.45/297.03 1055.45/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1055.45/297.03 the following reason: 1055.45/297.03 1055.45/297.03 We add the following weak dependency pairs: 1055.45/297.03 1055.45/297.03 Strict DPs: 1055.45/297.03 { minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y)) 1055.45/297.03 , if^#(true(), x, y) -> c_2(minus^#(x, y)) 1055.45/297.03 , if^#(false(), x, y) -> c_3() 1055.45/297.03 , gt^#(s(x), s(y)) -> c_4(gt^#(x, y)) 1055.45/297.03 , gt^#(s(x), 0()) -> c_5() 1055.45/297.03 , gt^#(0(), y) -> c_6() 1055.45/297.03 , ge^#(x, 0()) -> c_7() 1055.45/297.03 , ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 1055.45/297.03 , ge^#(0(), s(x)) -> c_9() 1055.45/297.03 , div^#(x, y) -> c_10(if1^#(ge(x, y), x, y)) 1055.45/297.03 , if1^#(true(), x, y) -> c_11(if2^#(gt(y, 0()), x, y)) 1055.45/297.03 , if1^#(false(), x, y) -> c_12() 1055.45/297.03 , if2^#(true(), x, y) -> c_13(div^#(minus(x, y), y)) 1055.45/297.03 , if2^#(false(), x, y) -> c_14() } 1055.45/297.03 1055.45/297.03 and mark the set of starting terms. 1055.45/297.03 1055.45/297.03 We are left with following problem, upon which TcT provides the 1055.45/297.03 certificate MAYBE. 1055.45/297.03 1055.45/297.03 Strict DPs: 1055.45/297.03 { minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y)) 1055.45/297.03 , if^#(true(), x, y) -> c_2(minus^#(x, y)) 1055.45/297.03 , if^#(false(), x, y) -> c_3() 1055.45/297.03 , gt^#(s(x), s(y)) -> c_4(gt^#(x, y)) 1055.45/297.03 , gt^#(s(x), 0()) -> c_5() 1055.45/297.03 , gt^#(0(), y) -> c_6() 1055.45/297.03 , ge^#(x, 0()) -> c_7() 1055.45/297.03 , ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 1055.45/297.03 , ge^#(0(), s(x)) -> c_9() 1055.45/297.03 , div^#(x, y) -> c_10(if1^#(ge(x, y), x, y)) 1055.45/297.03 , if1^#(true(), x, y) -> c_11(if2^#(gt(y, 0()), x, y)) 1055.45/297.03 , if1^#(false(), x, y) -> c_12() 1055.45/297.03 , if2^#(true(), x, y) -> c_13(div^#(minus(x, y), y)) 1055.45/297.03 , if2^#(false(), x, y) -> c_14() } 1055.45/297.03 Strict Trs: 1055.45/297.03 { minus(s(x), y) -> if(gt(s(x), y), x, y) 1055.45/297.03 , if(true(), x, y) -> s(minus(x, y)) 1055.45/297.03 , if(false(), x, y) -> 0() 1055.45/297.03 , gt(s(x), s(y)) -> gt(x, y) 1055.45/297.03 , gt(s(x), 0()) -> true() 1055.45/297.03 , gt(0(), y) -> false() 1055.45/297.03 , ge(x, 0()) -> true() 1055.45/297.03 , ge(s(x), s(y)) -> ge(x, y) 1055.45/297.03 , ge(0(), s(x)) -> false() 1055.45/297.03 , div(x, y) -> if1(ge(x, y), x, y) 1055.45/297.03 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 1055.45/297.03 , if1(false(), x, y) -> 0() 1055.45/297.03 , if2(true(), x, y) -> s(div(minus(x, y), y)) 1055.45/297.03 , if2(false(), x, y) -> 0() } 1055.45/297.03 Obligation: 1055.45/297.03 runtime complexity 1055.45/297.03 Answer: 1055.45/297.03 MAYBE 1055.45/297.03 1055.45/297.03 We estimate the number of application of {3,5,6,7,9,12,14} by 1055.45/297.03 applications of Pre({3,5,6,7,9,12,14}) = {1,4,8,10,11}. Here rules 1055.45/297.03 are labeled as follows: 1055.45/297.03 1055.45/297.03 DPs: 1055.45/297.03 { 1: minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y)) 1055.45/297.03 , 2: if^#(true(), x, y) -> c_2(minus^#(x, y)) 1055.45/297.03 , 3: if^#(false(), x, y) -> c_3() 1055.45/297.03 , 4: gt^#(s(x), s(y)) -> c_4(gt^#(x, y)) 1055.45/297.03 , 5: gt^#(s(x), 0()) -> c_5() 1055.45/297.03 , 6: gt^#(0(), y) -> c_6() 1055.45/297.03 , 7: ge^#(x, 0()) -> c_7() 1055.45/297.03 , 8: ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 1055.45/297.03 , 9: ge^#(0(), s(x)) -> c_9() 1055.45/297.03 , 10: div^#(x, y) -> c_10(if1^#(ge(x, y), x, y)) 1055.45/297.03 , 11: if1^#(true(), x, y) -> c_11(if2^#(gt(y, 0()), x, y)) 1055.45/297.03 , 12: if1^#(false(), x, y) -> c_12() 1055.45/297.03 , 13: if2^#(true(), x, y) -> c_13(div^#(minus(x, y), y)) 1055.45/297.03 , 14: if2^#(false(), x, y) -> c_14() } 1055.45/297.03 1055.45/297.03 We are left with following problem, upon which TcT provides the 1055.45/297.03 certificate MAYBE. 1055.45/297.03 1055.45/297.03 Strict DPs: 1055.45/297.03 { minus^#(s(x), y) -> c_1(if^#(gt(s(x), y), x, y)) 1055.45/297.03 , if^#(true(), x, y) -> c_2(minus^#(x, y)) 1055.45/297.03 , gt^#(s(x), s(y)) -> c_4(gt^#(x, y)) 1055.45/297.03 , ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 1055.45/297.03 , div^#(x, y) -> c_10(if1^#(ge(x, y), x, y)) 1055.45/297.03 , if1^#(true(), x, y) -> c_11(if2^#(gt(y, 0()), x, y)) 1055.45/297.03 , if2^#(true(), x, y) -> c_13(div^#(minus(x, y), y)) } 1055.45/297.03 Strict Trs: 1055.45/297.03 { minus(s(x), y) -> if(gt(s(x), y), x, y) 1055.45/297.03 , if(true(), x, y) -> s(minus(x, y)) 1055.45/297.03 , if(false(), x, y) -> 0() 1055.45/297.03 , gt(s(x), s(y)) -> gt(x, y) 1055.45/297.03 , gt(s(x), 0()) -> true() 1055.45/297.03 , gt(0(), y) -> false() 1055.45/297.03 , ge(x, 0()) -> true() 1055.45/297.03 , ge(s(x), s(y)) -> ge(x, y) 1055.45/297.03 , ge(0(), s(x)) -> false() 1055.45/297.03 , div(x, y) -> if1(ge(x, y), x, y) 1055.45/297.03 , if1(true(), x, y) -> if2(gt(y, 0()), x, y) 1055.45/297.03 , if1(false(), x, y) -> 0() 1055.45/297.03 , if2(true(), x, y) -> s(div(minus(x, y), y)) 1055.45/297.03 , if2(false(), x, y) -> 0() } 1055.45/297.03 Weak DPs: 1055.45/297.03 { if^#(false(), x, y) -> c_3() 1055.45/297.03 , gt^#(s(x), 0()) -> c_5() 1055.45/297.03 , gt^#(0(), y) -> c_6() 1055.45/297.03 , ge^#(x, 0()) -> c_7() 1055.45/297.03 , ge^#(0(), s(x)) -> c_9() 1055.45/297.03 , if1^#(false(), x, y) -> c_12() 1055.45/297.03 , if2^#(false(), x, y) -> c_14() } 1055.45/297.03 Obligation: 1055.45/297.03 runtime complexity 1055.45/297.03 Answer: 1055.45/297.03 MAYBE 1055.45/297.03 1055.45/297.03 Empty strict component of the problem is NOT empty. 1055.45/297.03 1055.45/297.03 1055.45/297.03 Arrrr.. 1055.78/297.34 EOF