MAYBE 898.60/297.13 MAYBE 898.60/297.13 898.60/297.13 We are left with following problem, upon which TcT provides the 898.60/297.13 certificate MAYBE. 898.60/297.13 898.60/297.13 Strict Trs: 898.60/297.13 { minus(x, 0()) -> x 898.60/297.13 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 898.60/297.13 , minus(s(x), s(y)) -> minus(x, y) 898.60/297.13 , quot(0(), s(y)) -> 0() 898.60/297.13 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 898.60/297.13 , plus(0(), y) -> y 898.60/297.13 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 898.60/297.13 , plus(s(x), y) -> s(plus(x, y)) 898.60/297.13 , plus(s(x), s(y)) -> 898.60/297.13 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 898.60/297.13 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , plus(zero(), y) -> y 898.60/297.13 , app(l, nil()) -> l 898.60/297.13 , app(nil(), k) -> k 898.60/297.13 , app(cons(x, l), k) -> cons(x, app(l, k)) 898.60/297.13 , sum(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 sum(app(l, sum(cons(x, cons(y, k))))) 898.60/297.13 , sum(cons(x, nil())) -> cons(x, nil()) 898.60/297.13 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 898.60/297.13 , if(true(), x, y) -> x 898.60/297.13 , if(false(), x, y) -> y 898.60/297.13 , gt(s(x), s(y)) -> gt(x, y) 898.60/297.13 , gt(s(x), zero()) -> true() 898.60/297.13 , gt(zero(), y) -> false() 898.60/297.13 , not(x) -> if(x, false(), true()) 898.60/297.13 , id(x) -> x } 898.60/297.13 Obligation: 898.60/297.13 runtime complexity 898.60/297.13 Answer: 898.60/297.13 MAYBE 898.60/297.13 898.60/297.13 None of the processors succeeded. 898.60/297.13 898.60/297.13 Details of failed attempt(s): 898.60/297.13 ----------------------------- 898.60/297.13 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 898.60/297.13 following reason: 898.60/297.13 898.60/297.13 Computation stopped due to timeout after 297.0 seconds. 898.60/297.13 898.60/297.13 2) 'Best' failed due to the following reason: 898.60/297.13 898.60/297.13 None of the processors succeeded. 898.60/297.13 898.60/297.13 Details of failed attempt(s): 898.60/297.13 ----------------------------- 898.60/297.13 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 898.60/297.13 seconds)' failed due to the following reason: 898.60/297.13 898.60/297.13 Computation stopped due to timeout after 148.0 seconds. 898.60/297.13 898.60/297.13 2) 'Best' failed due to the following reason: 898.60/297.13 898.60/297.13 None of the processors succeeded. 898.60/297.13 898.60/297.13 Details of failed attempt(s): 898.60/297.13 ----------------------------- 898.60/297.13 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 898.60/297.13 following reason: 898.60/297.13 898.60/297.13 The processor is inapplicable, reason: 898.60/297.13 Processor only applicable for innermost runtime complexity analysis 898.60/297.13 898.60/297.13 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 898.60/297.13 to the following reason: 898.60/297.13 898.60/297.13 The processor is inapplicable, reason: 898.60/297.13 Processor only applicable for innermost runtime complexity analysis 898.60/297.13 898.60/297.13 898.60/297.13 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 898.60/297.13 failed due to the following reason: 898.60/297.13 898.60/297.13 None of the processors succeeded. 898.60/297.13 898.60/297.13 Details of failed attempt(s): 898.60/297.13 ----------------------------- 898.60/297.13 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 898.60/297.13 failed due to the following reason: 898.60/297.13 898.60/297.13 match-boundness of the problem could not be verified. 898.60/297.13 898.60/297.13 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 898.60/297.13 failed due to the following reason: 898.60/297.13 898.60/297.13 match-boundness of the problem could not be verified. 898.60/297.13 898.60/297.13 898.60/297.13 898.60/297.13 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 898.60/297.13 the following reason: 898.60/297.13 898.60/297.13 We add the following weak dependency pairs: 898.60/297.13 898.60/297.13 Strict DPs: 898.60/297.13 { minus^#(x, 0()) -> c_1(x) 898.60/297.13 , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 898.60/297.13 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 898.60/297.13 , quot^#(0(), s(y)) -> c_4() 898.60/297.13 , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 898.60/297.13 , plus^#(0(), y) -> c_6(y) 898.60/297.13 , plus^#(s(x), x) -> c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 898.60/297.13 , plus^#(s(x), y) -> c_8(plus^#(x, y)) 898.60/297.13 , plus^#(s(x), s(y)) -> 898.60/297.13 c_9(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 898.60/297.13 , plus^#(id(x), s(y)) -> c_10(plus^#(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , plus^#(zero(), y) -> c_11(y) 898.60/297.13 , app^#(l, nil()) -> c_12(l) 898.60/297.13 , app^#(nil(), k) -> c_13(k) 898.60/297.13 , app^#(cons(x, l), k) -> c_14(x, app^#(l, k)) 898.60/297.13 , sum^#(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 c_15(sum^#(app(l, sum(cons(x, cons(y, k)))))) 898.60/297.13 , sum^#(cons(x, nil())) -> c_16(x) 898.60/297.13 , sum^#(cons(x, cons(y, l))) -> c_17(sum^#(cons(plus(x, y), l))) 898.60/297.13 , if^#(true(), x, y) -> c_18(x) 898.60/297.13 , if^#(false(), x, y) -> c_19(y) 898.60/297.13 , gt^#(s(x), s(y)) -> c_20(gt^#(x, y)) 898.60/297.13 , gt^#(s(x), zero()) -> c_21() 898.60/297.13 , gt^#(zero(), y) -> c_22() 898.60/297.13 , not^#(x) -> c_23(if^#(x, false(), true())) 898.60/297.13 , id^#(x) -> c_24(x) } 898.60/297.13 898.60/297.13 and mark the set of starting terms. 898.60/297.13 898.60/297.13 We are left with following problem, upon which TcT provides the 898.60/297.13 certificate MAYBE. 898.60/297.13 898.60/297.13 Strict DPs: 898.60/297.13 { minus^#(x, 0()) -> c_1(x) 898.60/297.13 , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 898.60/297.13 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 898.60/297.13 , quot^#(0(), s(y)) -> c_4() 898.60/297.13 , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 898.60/297.13 , plus^#(0(), y) -> c_6(y) 898.60/297.13 , plus^#(s(x), x) -> c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 898.60/297.13 , plus^#(s(x), y) -> c_8(plus^#(x, y)) 898.60/297.13 , plus^#(s(x), s(y)) -> 898.60/297.13 c_9(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 898.60/297.13 , plus^#(id(x), s(y)) -> c_10(plus^#(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , plus^#(zero(), y) -> c_11(y) 898.60/297.13 , app^#(l, nil()) -> c_12(l) 898.60/297.13 , app^#(nil(), k) -> c_13(k) 898.60/297.13 , app^#(cons(x, l), k) -> c_14(x, app^#(l, k)) 898.60/297.13 , sum^#(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 c_15(sum^#(app(l, sum(cons(x, cons(y, k)))))) 898.60/297.13 , sum^#(cons(x, nil())) -> c_16(x) 898.60/297.13 , sum^#(cons(x, cons(y, l))) -> c_17(sum^#(cons(plus(x, y), l))) 898.60/297.13 , if^#(true(), x, y) -> c_18(x) 898.60/297.13 , if^#(false(), x, y) -> c_19(y) 898.60/297.13 , gt^#(s(x), s(y)) -> c_20(gt^#(x, y)) 898.60/297.13 , gt^#(s(x), zero()) -> c_21() 898.60/297.13 , gt^#(zero(), y) -> c_22() 898.60/297.13 , not^#(x) -> c_23(if^#(x, false(), true())) 898.60/297.13 , id^#(x) -> c_24(x) } 898.60/297.13 Strict Trs: 898.60/297.13 { minus(x, 0()) -> x 898.60/297.13 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 898.60/297.13 , minus(s(x), s(y)) -> minus(x, y) 898.60/297.13 , quot(0(), s(y)) -> 0() 898.60/297.13 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 898.60/297.13 , plus(0(), y) -> y 898.60/297.13 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 898.60/297.13 , plus(s(x), y) -> s(plus(x, y)) 898.60/297.13 , plus(s(x), s(y)) -> 898.60/297.13 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 898.60/297.13 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , plus(zero(), y) -> y 898.60/297.13 , app(l, nil()) -> l 898.60/297.13 , app(nil(), k) -> k 898.60/297.13 , app(cons(x, l), k) -> cons(x, app(l, k)) 898.60/297.13 , sum(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 sum(app(l, sum(cons(x, cons(y, k))))) 898.60/297.13 , sum(cons(x, nil())) -> cons(x, nil()) 898.60/297.13 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 898.60/297.13 , if(true(), x, y) -> x 898.60/297.13 , if(false(), x, y) -> y 898.60/297.13 , gt(s(x), s(y)) -> gt(x, y) 898.60/297.13 , gt(s(x), zero()) -> true() 898.60/297.13 , gt(zero(), y) -> false() 898.60/297.13 , not(x) -> if(x, false(), true()) 898.60/297.13 , id(x) -> x } 898.60/297.13 Obligation: 898.60/297.13 runtime complexity 898.60/297.13 Answer: 898.60/297.13 MAYBE 898.60/297.13 898.60/297.13 We estimate the number of application of {4,21,22} by applications 898.60/297.13 of Pre({4,21,22}) = {1,5,6,11,12,13,14,16,18,19,20,24}. Here rules 898.60/297.13 are labeled as follows: 898.60/297.13 898.60/297.13 DPs: 898.60/297.13 { 1: minus^#(x, 0()) -> c_1(x) 898.60/297.13 , 2: minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 898.60/297.13 , 3: minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 898.60/297.13 , 4: quot^#(0(), s(y)) -> c_4() 898.60/297.13 , 5: quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 898.60/297.13 , 6: plus^#(0(), y) -> c_6(y) 898.60/297.13 , 7: plus^#(s(x), x) -> 898.60/297.13 c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 898.60/297.13 , 8: plus^#(s(x), y) -> c_8(plus^#(x, y)) 898.60/297.13 , 9: plus^#(s(x), s(y)) -> 898.60/297.13 c_9(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 898.60/297.13 , 10: plus^#(id(x), s(y)) -> 898.60/297.13 c_10(plus^#(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , 11: plus^#(zero(), y) -> c_11(y) 898.60/297.13 , 12: app^#(l, nil()) -> c_12(l) 898.60/297.13 , 13: app^#(nil(), k) -> c_13(k) 898.60/297.13 , 14: app^#(cons(x, l), k) -> c_14(x, app^#(l, k)) 898.60/297.13 , 15: sum^#(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 c_15(sum^#(app(l, sum(cons(x, cons(y, k)))))) 898.60/297.13 , 16: sum^#(cons(x, nil())) -> c_16(x) 898.60/297.13 , 17: sum^#(cons(x, cons(y, l))) -> 898.60/297.13 c_17(sum^#(cons(plus(x, y), l))) 898.60/297.13 , 18: if^#(true(), x, y) -> c_18(x) 898.60/297.13 , 19: if^#(false(), x, y) -> c_19(y) 898.60/297.13 , 20: gt^#(s(x), s(y)) -> c_20(gt^#(x, y)) 898.60/297.13 , 21: gt^#(s(x), zero()) -> c_21() 898.60/297.13 , 22: gt^#(zero(), y) -> c_22() 898.60/297.13 , 23: not^#(x) -> c_23(if^#(x, false(), true())) 898.60/297.13 , 24: id^#(x) -> c_24(x) } 898.60/297.13 898.60/297.13 We are left with following problem, upon which TcT provides the 898.60/297.13 certificate MAYBE. 898.60/297.13 898.60/297.13 Strict DPs: 898.60/297.13 { minus^#(x, 0()) -> c_1(x) 898.60/297.13 , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 898.60/297.13 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 898.60/297.13 , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 898.60/297.13 , plus^#(0(), y) -> c_6(y) 898.60/297.13 , plus^#(s(x), x) -> c_7(plus^#(if(gt(x, x), id(x), id(x)), s(x))) 898.60/297.13 , plus^#(s(x), y) -> c_8(plus^#(x, y)) 898.60/297.13 , plus^#(s(x), s(y)) -> 898.60/297.13 c_9(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))) 898.60/297.13 , plus^#(id(x), s(y)) -> c_10(plus^#(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , plus^#(zero(), y) -> c_11(y) 898.60/297.13 , app^#(l, nil()) -> c_12(l) 898.60/297.13 , app^#(nil(), k) -> c_13(k) 898.60/297.13 , app^#(cons(x, l), k) -> c_14(x, app^#(l, k)) 898.60/297.13 , sum^#(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 c_15(sum^#(app(l, sum(cons(x, cons(y, k)))))) 898.60/297.13 , sum^#(cons(x, nil())) -> c_16(x) 898.60/297.13 , sum^#(cons(x, cons(y, l))) -> c_17(sum^#(cons(plus(x, y), l))) 898.60/297.13 , if^#(true(), x, y) -> c_18(x) 898.60/297.13 , if^#(false(), x, y) -> c_19(y) 898.60/297.13 , gt^#(s(x), s(y)) -> c_20(gt^#(x, y)) 898.60/297.13 , not^#(x) -> c_23(if^#(x, false(), true())) 898.60/297.13 , id^#(x) -> c_24(x) } 898.60/297.13 Strict Trs: 898.60/297.13 { minus(x, 0()) -> x 898.60/297.13 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 898.60/297.13 , minus(s(x), s(y)) -> minus(x, y) 898.60/297.13 , quot(0(), s(y)) -> 0() 898.60/297.13 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 898.60/297.13 , plus(0(), y) -> y 898.60/297.13 , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x)) 898.60/297.13 , plus(s(x), y) -> s(plus(x, y)) 898.60/297.13 , plus(s(x), s(y)) -> 898.60/297.13 s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) 898.60/297.13 , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) 898.60/297.13 , plus(zero(), y) -> y 898.60/297.13 , app(l, nil()) -> l 898.60/297.13 , app(nil(), k) -> k 898.60/297.13 , app(cons(x, l), k) -> cons(x, app(l, k)) 898.60/297.13 , sum(app(l, cons(x, cons(y, k)))) -> 898.60/297.13 sum(app(l, sum(cons(x, cons(y, k))))) 898.60/297.13 , sum(cons(x, nil())) -> cons(x, nil()) 898.60/297.13 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) 898.60/297.13 , if(true(), x, y) -> x 898.60/297.13 , if(false(), x, y) -> y 898.60/297.13 , gt(s(x), s(y)) -> gt(x, y) 898.60/297.13 , gt(s(x), zero()) -> true() 898.60/297.13 , gt(zero(), y) -> false() 898.60/297.13 , not(x) -> if(x, false(), true()) 898.60/297.13 , id(x) -> x } 898.60/297.13 Weak DPs: 898.60/297.13 { quot^#(0(), s(y)) -> c_4() 898.60/297.13 , gt^#(s(x), zero()) -> c_21() 898.60/297.13 , gt^#(zero(), y) -> c_22() } 898.60/297.13 Obligation: 898.60/297.13 runtime complexity 898.60/297.13 Answer: 898.60/297.13 MAYBE 898.60/297.13 898.60/297.13 Empty strict component of the problem is NOT empty. 898.60/297.13 898.60/297.13 898.60/297.13 Arrrr.. 898.74/297.24 EOF