MAYBE 719.64/297.03 MAYBE 719.64/297.03 719.64/297.03 We are left with following problem, upon which TcT provides the 719.64/297.03 certificate MAYBE. 719.64/297.03 719.64/297.03 Strict Trs: 719.64/297.03 { ge(x, 0()) -> true() 719.64/297.03 , ge(0(), s(y)) -> false() 719.64/297.03 , ge(s(x), s(y)) -> ge(x, y) 719.64/297.03 , minus(x, 0()) -> x 719.64/297.03 , minus(0(), y) -> 0() 719.64/297.03 , minus(s(x), s(y)) -> minus(x, y) 719.64/297.03 , id_inc(x) -> x 719.64/297.03 , id_inc(x) -> s(x) 719.64/297.03 , quot(x, y) -> div(x, y, 0()) 719.64/297.03 , div(x, y, z) -> if(ge(y, s(0())), ge(x, y), x, y, z) 719.64/297.03 , if(true(), true(), x, y, z) -> div(minus(x, y), y, id_inc(z)) 719.64/297.03 , if(true(), false(), x, y, z) -> z 719.64/297.03 , if(false(), b, x, y, z) -> div_by_zero() } 719.64/297.03 Obligation: 719.64/297.03 runtime complexity 719.64/297.03 Answer: 719.64/297.03 MAYBE 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 719.64/297.03 following reason: 719.64/297.03 719.64/297.03 Computation stopped due to timeout after 297.0 seconds. 719.64/297.03 719.64/297.03 2) 'Best' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 719.64/297.03 seconds)' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'empty' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 2) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'empty' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 2) 'Fastest' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'empty' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 2) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 719.64/297.03 2) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'empty' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 2) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'empty' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 2) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'empty' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 2) 'With Problem ...' failed due to the following reason: 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 719.64/297.03 719.64/297.03 719.64/297.03 719.64/297.03 719.64/297.03 719.64/297.03 2) 'Best' failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 719.64/297.03 to the following reason: 719.64/297.03 719.64/297.03 The processor is inapplicable, reason: 719.64/297.03 Processor only applicable for innermost runtime complexity analysis 719.64/297.03 719.64/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 719.64/297.03 following reason: 719.64/297.03 719.64/297.03 The processor is inapplicable, reason: 719.64/297.03 Processor only applicable for innermost runtime complexity analysis 719.64/297.03 719.64/297.03 719.64/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 719.64/297.03 failed due to the following reason: 719.64/297.03 719.64/297.03 None of the processors succeeded. 719.64/297.03 719.64/297.03 Details of failed attempt(s): 719.64/297.03 ----------------------------- 719.64/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 719.64/297.03 failed due to the following reason: 719.64/297.03 719.64/297.03 match-boundness of the problem could not be verified. 719.64/297.03 719.64/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 719.64/297.03 failed due to the following reason: 719.64/297.03 719.64/297.03 match-boundness of the problem could not be verified. 719.64/297.03 719.64/297.03 719.64/297.03 719.64/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 719.64/297.03 the following reason: 719.64/297.03 719.64/297.03 We add the following weak dependency pairs: 719.64/297.03 719.64/297.03 Strict DPs: 719.64/297.03 { ge^#(x, 0()) -> c_1() 719.64/297.03 , ge^#(0(), s(y)) -> c_2() 719.64/297.03 , ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 719.64/297.03 , minus^#(x, 0()) -> c_4(x) 719.64/297.03 , minus^#(0(), y) -> c_5() 719.64/297.03 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 719.64/297.03 , id_inc^#(x) -> c_7(x) 719.64/297.03 , id_inc^#(x) -> c_8(x) 719.64/297.03 , quot^#(x, y) -> c_9(div^#(x, y, 0())) 719.64/297.03 , div^#(x, y, z) -> c_10(if^#(ge(y, s(0())), ge(x, y), x, y, z)) 719.64/297.03 , if^#(true(), true(), x, y, z) -> 719.64/297.03 c_11(div^#(minus(x, y), y, id_inc(z))) 719.64/297.03 , if^#(true(), false(), x, y, z) -> c_12(z) 719.64/297.03 , if^#(false(), b, x, y, z) -> c_13() } 719.64/297.03 719.64/297.03 and mark the set of starting terms. 719.64/297.03 719.64/297.03 We are left with following problem, upon which TcT provides the 719.64/297.03 certificate MAYBE. 719.64/297.03 719.64/297.03 Strict DPs: 719.64/297.03 { ge^#(x, 0()) -> c_1() 719.64/297.03 , ge^#(0(), s(y)) -> c_2() 719.64/297.03 , ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 719.64/297.03 , minus^#(x, 0()) -> c_4(x) 719.64/297.03 , minus^#(0(), y) -> c_5() 719.64/297.03 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 719.64/297.03 , id_inc^#(x) -> c_7(x) 719.64/297.03 , id_inc^#(x) -> c_8(x) 719.64/297.03 , quot^#(x, y) -> c_9(div^#(x, y, 0())) 719.64/297.03 , div^#(x, y, z) -> c_10(if^#(ge(y, s(0())), ge(x, y), x, y, z)) 719.64/297.03 , if^#(true(), true(), x, y, z) -> 719.64/297.03 c_11(div^#(minus(x, y), y, id_inc(z))) 719.64/297.03 , if^#(true(), false(), x, y, z) -> c_12(z) 719.64/297.03 , if^#(false(), b, x, y, z) -> c_13() } 719.64/297.03 Strict Trs: 719.64/297.03 { ge(x, 0()) -> true() 719.64/297.03 , ge(0(), s(y)) -> false() 719.64/297.03 , ge(s(x), s(y)) -> ge(x, y) 719.64/297.03 , minus(x, 0()) -> x 719.64/297.03 , minus(0(), y) -> 0() 719.64/297.03 , minus(s(x), s(y)) -> minus(x, y) 719.64/297.03 , id_inc(x) -> x 719.64/297.03 , id_inc(x) -> s(x) 719.64/297.03 , quot(x, y) -> div(x, y, 0()) 719.64/297.03 , div(x, y, z) -> if(ge(y, s(0())), ge(x, y), x, y, z) 719.64/297.03 , if(true(), true(), x, y, z) -> div(minus(x, y), y, id_inc(z)) 719.64/297.03 , if(true(), false(), x, y, z) -> z 719.64/297.03 , if(false(), b, x, y, z) -> div_by_zero() } 719.64/297.03 Obligation: 719.64/297.03 runtime complexity 719.64/297.03 Answer: 719.64/297.03 MAYBE 719.64/297.03 719.64/297.03 We estimate the number of application of {1,2,5,13} by applications 719.64/297.03 of Pre({1,2,5,13}) = {3,4,6,7,8,10,12}. Here rules are labeled as 719.64/297.03 follows: 719.64/297.03 719.64/297.03 DPs: 719.64/297.03 { 1: ge^#(x, 0()) -> c_1() 719.64/297.03 , 2: ge^#(0(), s(y)) -> c_2() 719.64/297.03 , 3: ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 719.64/297.03 , 4: minus^#(x, 0()) -> c_4(x) 719.64/297.03 , 5: minus^#(0(), y) -> c_5() 719.64/297.03 , 6: minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 719.64/297.03 , 7: id_inc^#(x) -> c_7(x) 719.64/297.03 , 8: id_inc^#(x) -> c_8(x) 719.64/297.03 , 9: quot^#(x, y) -> c_9(div^#(x, y, 0())) 719.64/297.03 , 10: div^#(x, y, z) -> 719.64/297.03 c_10(if^#(ge(y, s(0())), ge(x, y), x, y, z)) 719.64/297.03 , 11: if^#(true(), true(), x, y, z) -> 719.64/297.03 c_11(div^#(minus(x, y), y, id_inc(z))) 719.64/297.03 , 12: if^#(true(), false(), x, y, z) -> c_12(z) 719.64/297.03 , 13: if^#(false(), b, x, y, z) -> c_13() } 719.64/297.03 719.64/297.03 We are left with following problem, upon which TcT provides the 719.64/297.03 certificate MAYBE. 719.64/297.03 719.64/297.03 Strict DPs: 719.64/297.03 { ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 719.64/297.03 , minus^#(x, 0()) -> c_4(x) 719.64/297.03 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 719.64/297.03 , id_inc^#(x) -> c_7(x) 719.64/297.03 , id_inc^#(x) -> c_8(x) 719.64/297.03 , quot^#(x, y) -> c_9(div^#(x, y, 0())) 719.64/297.03 , div^#(x, y, z) -> c_10(if^#(ge(y, s(0())), ge(x, y), x, y, z)) 719.64/297.03 , if^#(true(), true(), x, y, z) -> 719.64/297.03 c_11(div^#(minus(x, y), y, id_inc(z))) 719.64/297.03 , if^#(true(), false(), x, y, z) -> c_12(z) } 719.64/297.03 Strict Trs: 719.64/297.03 { ge(x, 0()) -> true() 719.64/297.03 , ge(0(), s(y)) -> false() 719.64/297.03 , ge(s(x), s(y)) -> ge(x, y) 719.64/297.03 , minus(x, 0()) -> x 719.64/297.03 , minus(0(), y) -> 0() 719.64/297.03 , minus(s(x), s(y)) -> minus(x, y) 719.64/297.03 , id_inc(x) -> x 719.64/297.03 , id_inc(x) -> s(x) 719.64/297.03 , quot(x, y) -> div(x, y, 0()) 719.64/297.03 , div(x, y, z) -> if(ge(y, s(0())), ge(x, y), x, y, z) 719.64/297.03 , if(true(), true(), x, y, z) -> div(minus(x, y), y, id_inc(z)) 719.64/297.03 , if(true(), false(), x, y, z) -> z 719.64/297.03 , if(false(), b, x, y, z) -> div_by_zero() } 719.64/297.03 Weak DPs: 719.64/297.03 { ge^#(x, 0()) -> c_1() 719.64/297.03 , ge^#(0(), s(y)) -> c_2() 719.64/297.03 , minus^#(0(), y) -> c_5() 719.64/297.03 , if^#(false(), b, x, y, z) -> c_13() } 719.64/297.03 Obligation: 719.64/297.03 runtime complexity 719.64/297.03 Answer: 719.64/297.03 MAYBE 719.64/297.03 719.64/297.03 Empty strict component of the problem is NOT empty. 719.64/297.03 719.64/297.03 719.64/297.03 Arrrr.. 719.96/297.32 EOF