MAYBE 834.74/297.03 MAYBE 834.74/297.03 834.74/297.03 We are left with following problem, upon which TcT provides the 834.74/297.03 certificate MAYBE. 834.74/297.03 834.74/297.03 Strict Trs: 834.74/297.03 { minus(x, 0()) -> x 834.74/297.03 , minus(s(x), s(y)) -> minus(x, y) 834.74/297.03 , quot(0(), s(y)) -> 0() 834.74/297.03 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 834.74/297.03 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 834.74/297.03 , plus(s(x), s(y)) -> 834.74/297.03 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 834.74/297.03 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 834.74/297.03 , plus(zero(), y) -> y 834.74/297.03 , if(true(), x, y) -> x 834.74/297.03 , if(false(), x, y) -> y 834.74/297.03 , gt(s(x), s(y)) -> gt(x, y) 834.74/297.03 , gt(s(x), zero()) -> true() 834.74/297.03 , gt(zero(), y) -> false() 834.74/297.03 , not(x) -> if(x, false(), true()) 834.74/297.03 , id(x) -> x } 834.74/297.03 Obligation: 834.74/297.03 runtime complexity 834.74/297.03 Answer: 834.74/297.03 MAYBE 834.74/297.03 834.74/297.03 None of the processors succeeded. 834.74/297.03 834.74/297.03 Details of failed attempt(s): 834.74/297.03 ----------------------------- 834.74/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 834.74/297.03 following reason: 834.74/297.03 834.74/297.03 Computation stopped due to timeout after 297.0 seconds. 834.74/297.03 834.74/297.03 2) 'Best' failed due to the following reason: 834.74/297.03 834.74/297.03 None of the processors succeeded. 834.74/297.04 834.74/297.04 Details of failed attempt(s): 834.74/297.04 ----------------------------- 834.74/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 834.74/297.04 seconds)' failed due to the following reason: 834.74/297.04 834.74/297.04 Computation stopped due to timeout after 148.0 seconds. 834.74/297.04 834.74/297.04 2) 'Best' failed due to the following reason: 834.74/297.04 834.74/297.04 None of the processors succeeded. 834.74/297.04 834.74/297.04 Details of failed attempt(s): 834.74/297.04 ----------------------------- 834.74/297.04 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 834.74/297.04 to the following reason: 834.74/297.04 834.74/297.04 The processor is inapplicable, reason: 834.74/297.04 Processor only applicable for innermost runtime complexity analysis 834.74/297.04 834.74/297.04 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 834.74/297.04 following reason: 834.74/297.04 834.74/297.04 The processor is inapplicable, reason: 834.74/297.04 Processor only applicable for innermost runtime complexity analysis 834.74/297.04 834.74/297.04 834.74/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 834.74/297.04 failed due to the following reason: 834.74/297.04 834.74/297.04 None of the processors succeeded. 834.74/297.04 834.74/297.04 Details of failed attempt(s): 834.74/297.04 ----------------------------- 834.74/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 834.74/297.04 failed due to the following reason: 834.74/297.04 834.74/297.04 match-boundness of the problem could not be verified. 834.74/297.04 834.74/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 834.74/297.04 failed due to the following reason: 834.74/297.04 834.74/297.04 match-boundness of the problem could not be verified. 834.74/297.04 834.74/297.04 834.74/297.04 834.74/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 834.74/297.04 the following reason: 834.74/297.04 834.74/297.04 We add the following weak dependency pairs: 834.74/297.04 834.74/297.04 Strict DPs: 834.74/297.04 { minus^#(x, 0()) -> c_1(x) 834.74/297.04 , minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) 834.74/297.04 , quot^#(0(), s(y)) -> c_3() 834.74/297.04 , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) 834.74/297.04 , plus^#(s(x), x) -> c_5(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 834.74/297.04 , plus^#(s(x), s(y)) -> 834.74/297.04 c_6(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 834.74/297.04 , plus^#(id(x), s(y)) -> c_7(plus^#(x, if(gt(s(y), y), y, s(y)))) 834.74/297.04 , plus^#(zero(), y) -> c_8(y) 834.74/297.04 , if^#(true(), x, y) -> c_9(x) 834.74/297.04 , if^#(false(), x, y) -> c_10(y) 834.74/297.04 , gt^#(s(x), s(y)) -> c_11(gt^#(x, y)) 834.74/297.04 , gt^#(s(x), zero()) -> c_12() 834.74/297.04 , gt^#(zero(), y) -> c_13() 834.74/297.04 , not^#(x) -> c_14(if^#(x, false(), true())) 834.74/297.04 , id^#(x) -> c_15(x) } 834.74/297.04 834.74/297.04 and mark the set of starting terms. 834.74/297.04 834.74/297.04 We are left with following problem, upon which TcT provides the 834.74/297.04 certificate MAYBE. 834.74/297.04 834.74/297.04 Strict DPs: 834.74/297.04 { minus^#(x, 0()) -> c_1(x) 834.74/297.04 , minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) 834.74/297.04 , quot^#(0(), s(y)) -> c_3() 834.74/297.04 , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) 834.74/297.04 , plus^#(s(x), x) -> c_5(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 834.74/297.04 , plus^#(s(x), s(y)) -> 834.74/297.04 c_6(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 834.74/297.04 , plus^#(id(x), s(y)) -> c_7(plus^#(x, if(gt(s(y), y), y, s(y)))) 834.74/297.04 , plus^#(zero(), y) -> c_8(y) 834.74/297.04 , if^#(true(), x, y) -> c_9(x) 834.74/297.04 , if^#(false(), x, y) -> c_10(y) 834.74/297.04 , gt^#(s(x), s(y)) -> c_11(gt^#(x, y)) 834.74/297.04 , gt^#(s(x), zero()) -> c_12() 834.74/297.04 , gt^#(zero(), y) -> c_13() 834.74/297.04 , not^#(x) -> c_14(if^#(x, false(), true())) 834.74/297.04 , id^#(x) -> c_15(x) } 834.74/297.04 Strict Trs: 834.74/297.04 { minus(x, 0()) -> x 834.74/297.04 , minus(s(x), s(y)) -> minus(x, y) 834.74/297.04 , quot(0(), s(y)) -> 0() 834.74/297.04 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 834.74/297.04 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 834.74/297.04 , plus(s(x), s(y)) -> 834.74/297.04 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 834.74/297.04 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 834.74/297.04 , plus(zero(), y) -> y 834.74/297.04 , if(true(), x, y) -> x 834.74/297.04 , if(false(), x, y) -> y 834.74/297.04 , gt(s(x), s(y)) -> gt(x, y) 834.74/297.04 , gt(s(x), zero()) -> true() 834.74/297.04 , gt(zero(), y) -> false() 834.74/297.04 , not(x) -> if(x, false(), true()) 834.74/297.04 , id(x) -> x } 834.74/297.04 Obligation: 834.74/297.04 runtime complexity 834.74/297.04 Answer: 834.74/297.04 MAYBE 834.74/297.04 834.74/297.04 We estimate the number of application of {3,12,13} by applications 834.74/297.04 of Pre({3,12,13}) = {1,4,8,9,10,11,15}. Here rules are labeled as 834.74/297.04 follows: 834.74/297.04 834.74/297.04 DPs: 834.74/297.04 { 1: minus^#(x, 0()) -> c_1(x) 834.74/297.04 , 2: minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) 834.74/297.04 , 3: quot^#(0(), s(y)) -> c_3() 834.74/297.04 , 4: quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) 834.74/297.04 , 5: plus^#(s(x), x) -> 834.74/297.04 c_5(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 834.74/297.04 , 6: plus^#(s(x), s(y)) -> 834.74/297.04 c_6(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 834.74/297.04 , 7: plus^#(id(x), s(y)) -> 834.74/297.04 c_7(plus^#(x, if(gt(s(y), y), y, s(y)))) 834.74/297.04 , 8: plus^#(zero(), y) -> c_8(y) 834.74/297.04 , 9: if^#(true(), x, y) -> c_9(x) 834.74/297.04 , 10: if^#(false(), x, y) -> c_10(y) 834.74/297.04 , 11: gt^#(s(x), s(y)) -> c_11(gt^#(x, y)) 834.74/297.04 , 12: gt^#(s(x), zero()) -> c_12() 834.74/297.04 , 13: gt^#(zero(), y) -> c_13() 834.74/297.04 , 14: not^#(x) -> c_14(if^#(x, false(), true())) 834.74/297.04 , 15: id^#(x) -> c_15(x) } 834.74/297.04 834.74/297.04 We are left with following problem, upon which TcT provides the 834.74/297.04 certificate MAYBE. 834.74/297.04 834.74/297.04 Strict DPs: 834.74/297.04 { minus^#(x, 0()) -> c_1(x) 834.74/297.04 , minus^#(s(x), s(y)) -> c_2(minus^#(x, y)) 834.74/297.04 , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y))) 834.74/297.04 , plus^#(s(x), x) -> c_5(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 834.74/297.04 , plus^#(s(x), s(y)) -> 834.74/297.04 c_6(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 834.74/297.04 , plus^#(id(x), s(y)) -> c_7(plus^#(x, if(gt(s(y), y), y, s(y)))) 834.74/297.04 , plus^#(zero(), y) -> c_8(y) 834.74/297.04 , if^#(true(), x, y) -> c_9(x) 834.74/297.04 , if^#(false(), x, y) -> c_10(y) 834.74/297.04 , gt^#(s(x), s(y)) -> c_11(gt^#(x, y)) 834.74/297.04 , not^#(x) -> c_14(if^#(x, false(), true())) 834.74/297.04 , id^#(x) -> c_15(x) } 834.74/297.04 Strict Trs: 834.74/297.04 { minus(x, 0()) -> x 834.74/297.04 , minus(s(x), s(y)) -> minus(x, y) 834.74/297.04 , quot(0(), s(y)) -> 0() 834.74/297.04 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 834.74/297.04 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 834.74/297.04 , plus(s(x), s(y)) -> 834.74/297.04 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 834.74/297.04 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 834.74/297.04 , plus(zero(), y) -> y 834.74/297.04 , if(true(), x, y) -> x 834.74/297.04 , if(false(), x, y) -> y 834.74/297.04 , gt(s(x), s(y)) -> gt(x, y) 834.74/297.04 , gt(s(x), zero()) -> true() 834.74/297.04 , gt(zero(), y) -> false() 834.74/297.04 , not(x) -> if(x, false(), true()) 834.74/297.04 , id(x) -> x } 834.74/297.04 Weak DPs: 834.74/297.04 { quot^#(0(), s(y)) -> c_3() 834.74/297.04 , gt^#(s(x), zero()) -> c_12() 834.74/297.04 , gt^#(zero(), y) -> c_13() } 834.74/297.04 Obligation: 834.74/297.04 runtime complexity 834.74/297.04 Answer: 834.74/297.04 MAYBE 834.74/297.04 834.74/297.04 Empty strict component of the problem is NOT empty. 834.74/297.04 834.74/297.04 834.74/297.04 Arrrr.. 834.96/297.28 EOF