MAYBE 737.97/297.12 MAYBE 737.97/297.12 737.97/297.12 We are left with following problem, upon which TcT provides the 737.97/297.12 certificate MAYBE. 737.97/297.12 737.97/297.12 Strict Trs: 737.97/297.12 { ge(x, 0()) -> true() 737.97/297.12 , ge(0(), s(y)) -> false() 737.97/297.12 , ge(s(x), s(y)) -> ge(x, y) 737.97/297.12 , minus(x, 0()) -> x 737.97/297.12 , minus(0(), y) -> 0() 737.97/297.12 , minus(s(x), s(y)) -> minus(x, y) 737.97/297.12 , id_inc(x) -> x 737.97/297.12 , id_inc(x) -> s(x) 737.97/297.12 , div(x, y) -> if(ge(y, s(0())), ge(x, y), x, y) 737.97/297.12 , if(true(), true(), x, y) -> id_inc(div(minus(x, y), y)) 737.97/297.12 , if(true(), false(), x, y) -> 0() 737.97/297.12 , if(false(), b, x, y) -> div_by_zero() } 737.97/297.12 Obligation: 737.97/297.12 runtime complexity 737.97/297.12 Answer: 737.97/297.12 MAYBE 737.97/297.12 737.97/297.12 None of the processors succeeded. 737.97/297.12 737.97/297.12 Details of failed attempt(s): 737.97/297.12 ----------------------------- 737.97/297.12 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 737.97/297.12 following reason: 737.97/297.12 737.97/297.12 Computation stopped due to timeout after 297.0 seconds. 737.97/297.12 737.97/297.12 2) 'Best' failed due to the following reason: 737.97/297.12 737.97/297.12 None of the processors succeeded. 737.97/297.12 737.97/297.12 Details of failed attempt(s): 737.97/297.12 ----------------------------- 737.97/297.12 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 737.97/297.12 seconds)' failed due to the following reason: 737.97/297.12 737.97/297.12 Computation stopped due to timeout after 148.0 seconds. 737.97/297.12 737.97/297.12 2) 'Best' failed due to the following reason: 737.97/297.12 737.97/297.12 None of the processors succeeded. 737.97/297.12 737.97/297.12 Details of failed attempt(s): 737.97/297.12 ----------------------------- 737.97/297.12 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 737.97/297.12 following reason: 737.97/297.12 737.97/297.12 The processor is inapplicable, reason: 737.97/297.12 Processor only applicable for innermost runtime complexity analysis 737.97/297.12 737.97/297.12 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 737.97/297.12 to the following reason: 737.97/297.12 737.97/297.12 The processor is inapplicable, reason: 737.97/297.12 Processor only applicable for innermost runtime complexity analysis 737.97/297.12 737.97/297.12 737.97/297.12 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 737.97/297.12 failed due to the following reason: 737.97/297.12 737.97/297.12 None of the processors succeeded. 737.97/297.12 737.97/297.12 Details of failed attempt(s): 737.97/297.12 ----------------------------- 737.97/297.12 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 737.97/297.12 failed due to the following reason: 737.97/297.12 737.97/297.12 match-boundness of the problem could not be verified. 737.97/297.12 737.97/297.12 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 737.97/297.12 failed due to the following reason: 737.97/297.12 737.97/297.12 match-boundness of the problem could not be verified. 737.97/297.12 737.97/297.12 737.97/297.12 737.97/297.12 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 737.97/297.12 the following reason: 737.97/297.12 737.97/297.12 We add the following weak dependency pairs: 737.97/297.12 737.97/297.12 Strict DPs: 737.97/297.12 { ge^#(x, 0()) -> c_1() 737.97/297.12 , ge^#(0(), s(y)) -> c_2() 737.97/297.12 , ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 737.97/297.12 , minus^#(x, 0()) -> c_4(x) 737.97/297.12 , minus^#(0(), y) -> c_5() 737.97/297.12 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 737.97/297.12 , id_inc^#(x) -> c_7(x) 737.97/297.12 , id_inc^#(x) -> c_8(x) 737.97/297.12 , div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y)) 737.97/297.12 , if^#(true(), true(), x, y) -> c_10(id_inc^#(div(minus(x, y), y))) 737.97/297.12 , if^#(true(), false(), x, y) -> c_11() 737.97/297.12 , if^#(false(), b, x, y) -> c_12() } 737.97/297.12 737.97/297.12 and mark the set of starting terms. 737.97/297.12 737.97/297.12 We are left with following problem, upon which TcT provides the 737.97/297.12 certificate MAYBE. 737.97/297.12 737.97/297.12 Strict DPs: 737.97/297.12 { ge^#(x, 0()) -> c_1() 737.97/297.12 , ge^#(0(), s(y)) -> c_2() 737.97/297.12 , ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 737.97/297.12 , minus^#(x, 0()) -> c_4(x) 737.97/297.12 , minus^#(0(), y) -> c_5() 737.97/297.12 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 737.97/297.12 , id_inc^#(x) -> c_7(x) 737.97/297.12 , id_inc^#(x) -> c_8(x) 737.97/297.12 , div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y)) 737.97/297.12 , if^#(true(), true(), x, y) -> c_10(id_inc^#(div(minus(x, y), y))) 737.97/297.12 , if^#(true(), false(), x, y) -> c_11() 737.97/297.12 , if^#(false(), b, x, y) -> c_12() } 737.97/297.12 Strict Trs: 737.97/297.12 { ge(x, 0()) -> true() 737.97/297.12 , ge(0(), s(y)) -> false() 737.97/297.12 , ge(s(x), s(y)) -> ge(x, y) 737.97/297.12 , minus(x, 0()) -> x 737.97/297.12 , minus(0(), y) -> 0() 737.97/297.12 , minus(s(x), s(y)) -> minus(x, y) 737.97/297.12 , id_inc(x) -> x 737.97/297.12 , id_inc(x) -> s(x) 737.97/297.12 , div(x, y) -> if(ge(y, s(0())), ge(x, y), x, y) 737.97/297.12 , if(true(), true(), x, y) -> id_inc(div(minus(x, y), y)) 737.97/297.12 , if(true(), false(), x, y) -> 0() 737.97/297.12 , if(false(), b, x, y) -> div_by_zero() } 737.97/297.12 Obligation: 737.97/297.12 runtime complexity 737.97/297.12 Answer: 737.97/297.12 MAYBE 737.97/297.12 737.97/297.12 We estimate the number of application of {1,2,5,11,12} by 737.97/297.12 applications of Pre({1,2,5,11,12}) = {3,4,6,7,8,9}. Here rules are 737.97/297.12 labeled as follows: 737.97/297.12 737.97/297.12 DPs: 737.97/297.12 { 1: ge^#(x, 0()) -> c_1() 737.97/297.12 , 2: ge^#(0(), s(y)) -> c_2() 737.97/297.12 , 3: ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 737.97/297.12 , 4: minus^#(x, 0()) -> c_4(x) 737.97/297.12 , 5: minus^#(0(), y) -> c_5() 737.97/297.12 , 6: minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 737.97/297.12 , 7: id_inc^#(x) -> c_7(x) 737.97/297.12 , 8: id_inc^#(x) -> c_8(x) 737.97/297.12 , 9: div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y)) 737.97/297.12 , 10: if^#(true(), true(), x, y) -> 737.97/297.12 c_10(id_inc^#(div(minus(x, y), y))) 737.97/297.12 , 11: if^#(true(), false(), x, y) -> c_11() 737.97/297.12 , 12: if^#(false(), b, x, y) -> c_12() } 737.97/297.12 737.97/297.12 We are left with following problem, upon which TcT provides the 737.97/297.12 certificate MAYBE. 737.97/297.12 737.97/297.12 Strict DPs: 737.97/297.12 { ge^#(s(x), s(y)) -> c_3(ge^#(x, y)) 737.97/297.12 , minus^#(x, 0()) -> c_4(x) 737.97/297.12 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 737.97/297.12 , id_inc^#(x) -> c_7(x) 737.97/297.12 , id_inc^#(x) -> c_8(x) 737.97/297.12 , div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y)) 737.97/297.12 , if^#(true(), true(), x, y) -> 737.97/297.12 c_10(id_inc^#(div(minus(x, y), y))) } 737.97/297.12 Strict Trs: 737.97/297.12 { ge(x, 0()) -> true() 737.97/297.12 , ge(0(), s(y)) -> false() 737.97/297.12 , ge(s(x), s(y)) -> ge(x, y) 737.97/297.12 , minus(x, 0()) -> x 737.97/297.12 , minus(0(), y) -> 0() 737.97/297.12 , minus(s(x), s(y)) -> minus(x, y) 737.97/297.12 , id_inc(x) -> x 737.97/297.12 , id_inc(x) -> s(x) 737.97/297.12 , div(x, y) -> if(ge(y, s(0())), ge(x, y), x, y) 737.97/297.12 , if(true(), true(), x, y) -> id_inc(div(minus(x, y), y)) 737.97/297.12 , if(true(), false(), x, y) -> 0() 737.97/297.12 , if(false(), b, x, y) -> div_by_zero() } 737.97/297.12 Weak DPs: 737.97/297.12 { ge^#(x, 0()) -> c_1() 737.97/297.12 , ge^#(0(), s(y)) -> c_2() 737.97/297.12 , minus^#(0(), y) -> c_5() 737.97/297.12 , if^#(true(), false(), x, y) -> c_11() 737.97/297.12 , if^#(false(), b, x, y) -> c_12() } 737.97/297.12 Obligation: 737.97/297.12 runtime complexity 737.97/297.12 Answer: 737.97/297.12 MAYBE 737.97/297.12 737.97/297.12 Empty strict component of the problem is NOT empty. 737.97/297.12 737.97/297.12 737.97/297.12 Arrrr.. 738.17/297.31 EOF