MAYBE 534.25/297.08 MAYBE 534.25/297.08 534.25/297.08 We are left with following problem, upon which TcT provides the 534.25/297.08 certificate MAYBE. 534.25/297.08 534.25/297.08 Strict Trs: 534.25/297.08 { plus(x, 0()) -> x 534.25/297.08 , plus(0(), y) -> y 534.25/297.08 , plus(s(x), y) -> s(plus(x, y)) 534.25/297.08 , times(0(), y) -> 0() 534.25/297.08 , times(s(x), y) -> plus(y, times(x, y)) 534.25/297.08 , times(s(0()), y) -> y 534.25/297.08 , div(x, y) -> quot(x, y, y) 534.25/297.08 , div(0(), y) -> 0() 534.25/297.08 , div(div(x, y), z) -> div(x, times(y, z)) 534.25/297.08 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 534.25/297.08 , quot(0(), s(y), z) -> 0() 534.25/297.08 , quot(s(x), s(y), z) -> quot(x, y, z) } 534.25/297.08 Obligation: 534.25/297.08 runtime complexity 534.25/297.08 Answer: 534.25/297.08 MAYBE 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 534.25/297.08 following reason: 534.25/297.08 534.25/297.08 Computation stopped due to timeout after 297.0 seconds. 534.25/297.08 534.25/297.08 2) 'Best' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 534.25/297.08 seconds)' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'empty' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 2) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'empty' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 2) 'Fastest' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'empty' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 2) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 534.25/297.08 2) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'empty' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 2) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'empty' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 2) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'empty' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 2) 'With Problem ...' failed due to the following reason: 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 534.25/297.08 534.25/297.08 534.25/297.08 534.25/297.08 534.25/297.08 534.25/297.08 2) 'Best' failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 534.25/297.08 following reason: 534.25/297.08 534.25/297.08 The processor is inapplicable, reason: 534.25/297.08 Processor only applicable for innermost runtime complexity analysis 534.25/297.08 534.25/297.08 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 534.25/297.08 to the following reason: 534.25/297.08 534.25/297.08 The processor is inapplicable, reason: 534.25/297.08 Processor only applicable for innermost runtime complexity analysis 534.25/297.08 534.25/297.08 534.25/297.08 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 534.25/297.08 failed due to the following reason: 534.25/297.08 534.25/297.08 None of the processors succeeded. 534.25/297.08 534.25/297.08 Details of failed attempt(s): 534.25/297.08 ----------------------------- 534.25/297.08 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 534.25/297.08 failed due to the following reason: 534.25/297.08 534.25/297.08 match-boundness of the problem could not be verified. 534.25/297.08 534.25/297.08 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 534.25/297.08 failed due to the following reason: 534.25/297.08 534.25/297.08 match-boundness of the problem could not be verified. 534.25/297.08 534.25/297.08 534.25/297.08 534.25/297.08 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 534.25/297.08 the following reason: 534.25/297.08 534.25/297.08 We add the following weak dependency pairs: 534.25/297.08 534.25/297.08 Strict DPs: 534.25/297.08 { plus^#(x, 0()) -> c_1(x) 534.25/297.08 , plus^#(0(), y) -> c_2(y) 534.25/297.08 , plus^#(s(x), y) -> c_3(plus^#(x, y)) 534.25/297.08 , times^#(0(), y) -> c_4() 534.25/297.08 , times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 534.25/297.08 , times^#(s(0()), y) -> c_6(y) 534.25/297.08 , div^#(x, y) -> c_7(quot^#(x, y, y)) 534.25/297.08 , div^#(0(), y) -> c_8() 534.25/297.08 , div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 534.25/297.08 , quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 534.25/297.08 , quot^#(0(), s(y), z) -> c_11() 534.25/297.08 , quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) } 534.25/297.08 534.25/297.08 and mark the set of starting terms. 534.25/297.08 534.25/297.08 We are left with following problem, upon which TcT provides the 534.25/297.08 certificate MAYBE. 534.25/297.08 534.25/297.08 Strict DPs: 534.25/297.08 { plus^#(x, 0()) -> c_1(x) 534.25/297.08 , plus^#(0(), y) -> c_2(y) 534.25/297.08 , plus^#(s(x), y) -> c_3(plus^#(x, y)) 534.25/297.08 , times^#(0(), y) -> c_4() 534.25/297.08 , times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 534.25/297.08 , times^#(s(0()), y) -> c_6(y) 534.25/297.08 , div^#(x, y) -> c_7(quot^#(x, y, y)) 534.25/297.08 , div^#(0(), y) -> c_8() 534.25/297.08 , div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 534.25/297.08 , quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 534.25/297.08 , quot^#(0(), s(y), z) -> c_11() 534.25/297.08 , quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) } 534.25/297.08 Strict Trs: 534.25/297.08 { plus(x, 0()) -> x 534.25/297.08 , plus(0(), y) -> y 534.25/297.08 , plus(s(x), y) -> s(plus(x, y)) 534.25/297.08 , times(0(), y) -> 0() 534.25/297.08 , times(s(x), y) -> plus(y, times(x, y)) 534.25/297.08 , times(s(0()), y) -> y 534.25/297.08 , div(x, y) -> quot(x, y, y) 534.25/297.08 , div(0(), y) -> 0() 534.25/297.08 , div(div(x, y), z) -> div(x, times(y, z)) 534.25/297.08 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 534.25/297.08 , quot(0(), s(y), z) -> 0() 534.25/297.08 , quot(s(x), s(y), z) -> quot(x, y, z) } 534.25/297.08 Obligation: 534.25/297.08 runtime complexity 534.25/297.08 Answer: 534.25/297.08 MAYBE 534.25/297.08 534.25/297.08 We estimate the number of application of {4,8,11} by applications 534.25/297.08 of Pre({4,8,11}) = {1,2,6,7,9,10,12}. Here rules are labeled as 534.25/297.08 follows: 534.25/297.08 534.25/297.08 DPs: 534.25/297.08 { 1: plus^#(x, 0()) -> c_1(x) 534.25/297.08 , 2: plus^#(0(), y) -> c_2(y) 534.25/297.08 , 3: plus^#(s(x), y) -> c_3(plus^#(x, y)) 534.25/297.08 , 4: times^#(0(), y) -> c_4() 534.25/297.08 , 5: times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 534.25/297.08 , 6: times^#(s(0()), y) -> c_6(y) 534.25/297.08 , 7: div^#(x, y) -> c_7(quot^#(x, y, y)) 534.25/297.08 , 8: div^#(0(), y) -> c_8() 534.25/297.08 , 9: div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 534.25/297.08 , 10: quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 534.25/297.08 , 11: quot^#(0(), s(y), z) -> c_11() 534.25/297.08 , 12: quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) } 534.25/297.08 534.25/297.08 We are left with following problem, upon which TcT provides the 534.25/297.08 certificate MAYBE. 534.25/297.08 534.25/297.08 Strict DPs: 534.25/297.08 { plus^#(x, 0()) -> c_1(x) 534.25/297.08 , plus^#(0(), y) -> c_2(y) 534.25/297.08 , plus^#(s(x), y) -> c_3(plus^#(x, y)) 534.25/297.08 , times^#(s(x), y) -> c_5(plus^#(y, times(x, y))) 534.25/297.08 , times^#(s(0()), y) -> c_6(y) 534.25/297.08 , div^#(x, y) -> c_7(quot^#(x, y, y)) 534.25/297.08 , div^#(div(x, y), z) -> c_9(div^#(x, times(y, z))) 534.25/297.08 , quot^#(x, 0(), s(z)) -> c_10(div^#(x, s(z))) 534.25/297.08 , quot^#(s(x), s(y), z) -> c_12(quot^#(x, y, z)) } 534.25/297.08 Strict Trs: 534.25/297.08 { plus(x, 0()) -> x 534.25/297.08 , plus(0(), y) -> y 534.25/297.08 , plus(s(x), y) -> s(plus(x, y)) 534.25/297.08 , times(0(), y) -> 0() 534.25/297.08 , times(s(x), y) -> plus(y, times(x, y)) 534.25/297.08 , times(s(0()), y) -> y 534.25/297.08 , div(x, y) -> quot(x, y, y) 534.25/297.08 , div(0(), y) -> 0() 534.25/297.08 , div(div(x, y), z) -> div(x, times(y, z)) 534.25/297.08 , quot(x, 0(), s(z)) -> s(div(x, s(z))) 534.25/297.08 , quot(0(), s(y), z) -> 0() 534.25/297.08 , quot(s(x), s(y), z) -> quot(x, y, z) } 534.25/297.08 Weak DPs: 534.25/297.08 { times^#(0(), y) -> c_4() 534.25/297.08 , div^#(0(), y) -> c_8() 534.25/297.08 , quot^#(0(), s(y), z) -> c_11() } 534.25/297.08 Obligation: 534.25/297.08 runtime complexity 534.25/297.08 Answer: 534.25/297.08 MAYBE 534.25/297.08 534.25/297.08 Empty strict component of the problem is NOT empty. 534.25/297.08 534.25/297.08 534.25/297.08 Arrrr.. 534.69/297.41 EOF