MAYBE 814.03/297.04 MAYBE 814.03/297.04 814.03/297.04 We are left with following problem, upon which TcT provides the 814.03/297.04 certificate MAYBE. 814.03/297.04 814.03/297.04 Strict Trs: 814.03/297.04 { minus(x, 0()) -> x 814.03/297.04 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 814.03/297.04 , minus(s(x), s(y)) -> minus(x, y) 814.03/297.04 , quot(0(), s(y)) -> 0() 814.03/297.04 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 814.03/297.04 , plus(0(), y) -> y 814.03/297.04 , plus(s(x), y) -> s(plus(x, y)) 814.03/297.04 , app(l, nil()) -> l 814.03/297.04 , app(nil(), k) -> k 814.03/297.04 , app(cons(x, l), k) -> cons(x, app(l, k)) 814.03/297.04 , sum(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 sum(app(l, sum(cons(x, cons(y, k))))) 814.03/297.04 , sum(cons(x, nil())) -> cons(x, nil()) 814.03/297.04 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) } 814.03/297.04 Obligation: 814.03/297.04 runtime complexity 814.03/297.04 Answer: 814.03/297.04 MAYBE 814.03/297.04 814.03/297.04 None of the processors succeeded. 814.03/297.04 814.03/297.04 Details of failed attempt(s): 814.03/297.04 ----------------------------- 814.03/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 814.03/297.04 following reason: 814.03/297.04 814.03/297.04 Computation stopped due to timeout after 297.0 seconds. 814.03/297.04 814.03/297.04 2) 'Best' failed due to the following reason: 814.03/297.04 814.03/297.04 None of the processors succeeded. 814.03/297.04 814.03/297.04 Details of failed attempt(s): 814.03/297.04 ----------------------------- 814.03/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 814.03/297.04 seconds)' failed due to the following reason: 814.03/297.04 814.03/297.04 Computation stopped due to timeout after 148.0 seconds. 814.03/297.04 814.03/297.04 2) 'Best' failed due to the following reason: 814.03/297.04 814.03/297.04 None of the processors succeeded. 814.03/297.04 814.03/297.04 Details of failed attempt(s): 814.03/297.04 ----------------------------- 814.03/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 814.03/297.04 following reason: 814.03/297.04 814.03/297.04 The processor is inapplicable, reason: 814.03/297.04 Processor only applicable for innermost runtime complexity analysis 814.03/297.04 814.03/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 814.03/297.04 to the following reason: 814.03/297.04 814.03/297.04 The processor is inapplicable, reason: 814.03/297.04 Processor only applicable for innermost runtime complexity analysis 814.03/297.04 814.03/297.04 814.03/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 814.03/297.04 failed due to the following reason: 814.03/297.04 814.03/297.04 None of the processors succeeded. 814.03/297.04 814.03/297.04 Details of failed attempt(s): 814.03/297.04 ----------------------------- 814.03/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 814.03/297.04 failed due to the following reason: 814.03/297.04 814.03/297.04 match-boundness of the problem could not be verified. 814.03/297.04 814.03/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 814.03/297.04 failed due to the following reason: 814.03/297.04 814.03/297.04 match-boundness of the problem could not be verified. 814.03/297.04 814.03/297.04 814.03/297.04 814.03/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 814.03/297.04 the following reason: 814.03/297.04 814.03/297.04 We add the following weak dependency pairs: 814.03/297.04 814.03/297.04 Strict DPs: 814.03/297.04 { minus^#(x, 0()) -> c_1(x) 814.03/297.04 , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 814.03/297.04 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 814.03/297.04 , quot^#(0(), s(y)) -> c_4() 814.03/297.04 , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 814.03/297.04 , plus^#(0(), y) -> c_6(y) 814.03/297.04 , plus^#(s(x), y) -> c_7(plus^#(x, y)) 814.03/297.04 , app^#(l, nil()) -> c_8(l) 814.03/297.04 , app^#(nil(), k) -> c_9(k) 814.03/297.04 , app^#(cons(x, l), k) -> c_10(x, app^#(l, k)) 814.03/297.04 , sum^#(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 c_11(sum^#(app(l, sum(cons(x, cons(y, k)))))) 814.03/297.04 , sum^#(cons(x, nil())) -> c_12(x) 814.03/297.04 , sum^#(cons(x, cons(y, l))) -> c_13(sum^#(cons(plus(x, y), l))) } 814.03/297.04 814.03/297.04 and mark the set of starting terms. 814.03/297.04 814.03/297.04 We are left with following problem, upon which TcT provides the 814.03/297.04 certificate MAYBE. 814.03/297.04 814.03/297.04 Strict DPs: 814.03/297.04 { minus^#(x, 0()) -> c_1(x) 814.03/297.04 , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 814.03/297.04 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 814.03/297.04 , quot^#(0(), s(y)) -> c_4() 814.03/297.04 , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 814.03/297.04 , plus^#(0(), y) -> c_6(y) 814.03/297.04 , plus^#(s(x), y) -> c_7(plus^#(x, y)) 814.03/297.04 , app^#(l, nil()) -> c_8(l) 814.03/297.04 , app^#(nil(), k) -> c_9(k) 814.03/297.04 , app^#(cons(x, l), k) -> c_10(x, app^#(l, k)) 814.03/297.04 , sum^#(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 c_11(sum^#(app(l, sum(cons(x, cons(y, k)))))) 814.03/297.04 , sum^#(cons(x, nil())) -> c_12(x) 814.03/297.04 , sum^#(cons(x, cons(y, l))) -> c_13(sum^#(cons(plus(x, y), l))) } 814.03/297.04 Strict Trs: 814.03/297.04 { minus(x, 0()) -> x 814.03/297.04 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 814.03/297.04 , minus(s(x), s(y)) -> minus(x, y) 814.03/297.04 , quot(0(), s(y)) -> 0() 814.03/297.04 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 814.03/297.04 , plus(0(), y) -> y 814.03/297.04 , plus(s(x), y) -> s(plus(x, y)) 814.03/297.04 , app(l, nil()) -> l 814.03/297.04 , app(nil(), k) -> k 814.03/297.04 , app(cons(x, l), k) -> cons(x, app(l, k)) 814.03/297.04 , sum(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 sum(app(l, sum(cons(x, cons(y, k))))) 814.03/297.04 , sum(cons(x, nil())) -> cons(x, nil()) 814.03/297.04 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) } 814.03/297.04 Obligation: 814.03/297.04 runtime complexity 814.03/297.04 Answer: 814.03/297.04 MAYBE 814.03/297.04 814.03/297.04 We estimate the number of application of {4} by applications of 814.03/297.04 Pre({4}) = {1,5,6,8,9,10,12}. Here rules are labeled as follows: 814.03/297.04 814.03/297.04 DPs: 814.03/297.04 { 1: minus^#(x, 0()) -> c_1(x) 814.03/297.04 , 2: minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 814.03/297.04 , 3: minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 814.03/297.04 , 4: quot^#(0(), s(y)) -> c_4() 814.03/297.04 , 5: quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 814.03/297.04 , 6: plus^#(0(), y) -> c_6(y) 814.03/297.04 , 7: plus^#(s(x), y) -> c_7(plus^#(x, y)) 814.03/297.04 , 8: app^#(l, nil()) -> c_8(l) 814.03/297.04 , 9: app^#(nil(), k) -> c_9(k) 814.03/297.04 , 10: app^#(cons(x, l), k) -> c_10(x, app^#(l, k)) 814.03/297.04 , 11: sum^#(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 c_11(sum^#(app(l, sum(cons(x, cons(y, k)))))) 814.03/297.04 , 12: sum^#(cons(x, nil())) -> c_12(x) 814.03/297.04 , 13: sum^#(cons(x, cons(y, l))) -> 814.03/297.04 c_13(sum^#(cons(plus(x, y), l))) } 814.03/297.04 814.03/297.04 We are left with following problem, upon which TcT provides the 814.03/297.04 certificate MAYBE. 814.03/297.04 814.03/297.04 Strict DPs: 814.03/297.04 { minus^#(x, 0()) -> c_1(x) 814.03/297.04 , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z))) 814.03/297.04 , minus^#(s(x), s(y)) -> c_3(minus^#(x, y)) 814.03/297.04 , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y))) 814.03/297.04 , plus^#(0(), y) -> c_6(y) 814.03/297.04 , plus^#(s(x), y) -> c_7(plus^#(x, y)) 814.03/297.04 , app^#(l, nil()) -> c_8(l) 814.03/297.04 , app^#(nil(), k) -> c_9(k) 814.03/297.04 , app^#(cons(x, l), k) -> c_10(x, app^#(l, k)) 814.03/297.04 , sum^#(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 c_11(sum^#(app(l, sum(cons(x, cons(y, k)))))) 814.03/297.04 , sum^#(cons(x, nil())) -> c_12(x) 814.03/297.04 , sum^#(cons(x, cons(y, l))) -> c_13(sum^#(cons(plus(x, y), l))) } 814.03/297.04 Strict Trs: 814.03/297.04 { minus(x, 0()) -> x 814.03/297.04 , minus(minus(x, y), z) -> minus(x, plus(y, z)) 814.03/297.04 , minus(s(x), s(y)) -> minus(x, y) 814.03/297.04 , quot(0(), s(y)) -> 0() 814.03/297.04 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 814.03/297.04 , plus(0(), y) -> y 814.03/297.04 , plus(s(x), y) -> s(plus(x, y)) 814.03/297.04 , app(l, nil()) -> l 814.03/297.04 , app(nil(), k) -> k 814.03/297.04 , app(cons(x, l), k) -> cons(x, app(l, k)) 814.03/297.04 , sum(app(l, cons(x, cons(y, k)))) -> 814.03/297.04 sum(app(l, sum(cons(x, cons(y, k))))) 814.03/297.04 , sum(cons(x, nil())) -> cons(x, nil()) 814.03/297.04 , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)) } 814.03/297.04 Weak DPs: { quot^#(0(), s(y)) -> c_4() } 814.03/297.04 Obligation: 814.03/297.04 runtime complexity 814.03/297.04 Answer: 814.03/297.04 MAYBE 814.03/297.04 814.03/297.04 Empty strict component of the problem is NOT empty. 814.03/297.04 814.03/297.04 814.03/297.04 Arrrr.. 814.24/297.25 EOF