MAYBE
798.90/297.03 MAYBE
798.90/297.03
798.90/297.03 We are left with following problem, upon which TcT provides the
798.90/297.03 certificate MAYBE.
798.90/297.03
798.90/297.03 Strict Trs:
798.90/297.03 { minus(x, 0()) -> x
798.90/297.03 , minus(s(x), s(y)) -> minus(x, y)
798.90/297.03 , quot(0(), s(y)) -> 0()
798.90/297.03 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
798.90/297.03 , le(0(), y) -> true()
798.90/297.03 , le(s(x), 0()) -> false()
798.90/297.03 , le(s(x), s(y)) -> le(x, y)
798.90/297.03 , app(nil(), y) -> y
798.90/297.03 , app(add(n, x), y) -> add(n, app(x, y))
798.90/297.03 , low(n, nil()) -> nil()
798.90/297.03 , low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
798.90/297.03 , if_low(true(), n, add(m, x)) -> add(m, low(n, x))
798.90/297.03 , if_low(false(), n, add(m, x)) -> low(n, x)
798.90/297.03 , high(n, nil()) -> nil()
798.90/297.03 , high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
798.90/297.03 , if_high(true(), n, add(m, x)) -> high(n, x)
798.90/297.03 , if_high(false(), n, add(m, x)) -> add(m, high(n, x))
798.90/297.03 , quicksort(nil()) -> nil()
798.90/297.03 , quicksort(add(n, x)) ->
798.90/297.03 app(quicksort(low(n, x)), add(n, quicksort(high(n, x)))) }
798.90/297.03 Obligation:
798.90/297.03 runtime complexity
798.90/297.03 Answer:
798.90/297.03 MAYBE
798.90/297.03
798.90/297.03 None of the processors succeeded.
798.90/297.03
798.90/297.03 Details of failed attempt(s):
798.90/297.03 -----------------------------
798.90/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the
798.90/297.03 following reason:
798.90/297.03
798.90/297.03 Computation stopped due to timeout after 297.0 seconds.
798.90/297.03
798.90/297.03 2) 'Best' failed due to the following reason:
798.90/297.03
798.90/297.03 None of the processors succeeded.
798.90/297.03
798.90/297.03 Details of failed attempt(s):
798.90/297.03 -----------------------------
798.90/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
798.90/297.03 seconds)' failed due to the following reason:
798.90/297.03
798.90/297.03 Computation stopped due to timeout after 148.0 seconds.
798.90/297.03
798.90/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
798.90/297.03 failed due to the following reason:
798.90/297.03
798.90/297.03 None of the processors succeeded.
798.90/297.03
798.90/297.03 Details of failed attempt(s):
798.90/297.03 -----------------------------
798.90/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match''
798.90/297.03 failed due to the following reason:
798.90/297.03
798.90/297.03 match-boundness of the problem could not be verified.
798.90/297.03
798.90/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
798.90/297.03 failed due to the following reason:
798.90/297.03
798.90/297.03 match-boundness of the problem could not be verified.
798.90/297.03
798.90/297.03
798.90/297.03 3) 'Best' failed due to the following reason:
798.90/297.03
798.90/297.03 None of the processors succeeded.
798.90/297.03
798.90/297.03 Details of failed attempt(s):
798.90/297.03 -----------------------------
798.90/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
798.90/297.03 following reason:
798.90/297.03
798.90/297.03 The processor is inapplicable, reason:
798.90/297.03 Processor only applicable for innermost runtime complexity analysis
798.90/297.03
798.90/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
798.90/297.03 to the following reason:
798.90/297.03
798.90/297.03 The processor is inapplicable, reason:
798.90/297.03 Processor only applicable for innermost runtime complexity analysis
798.90/297.03
798.90/297.03
798.90/297.03
798.90/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
798.90/297.03 the following reason:
798.90/297.03
798.90/297.03 We add the following weak dependency pairs:
798.90/297.03
798.90/297.03 Strict DPs:
798.90/297.03 { minus^#(x, 0()) -> c_1(x)
798.90/297.03 , minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
798.90/297.03 , quot^#(0(), s(y)) -> c_3()
798.90/297.03 , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y)))
798.90/297.03 , le^#(0(), y) -> c_5()
798.90/297.03 , le^#(s(x), 0()) -> c_6()
798.90/297.03 , le^#(s(x), s(y)) -> c_7(le^#(x, y))
798.90/297.03 , app^#(nil(), y) -> c_8(y)
798.90/297.03 , app^#(add(n, x), y) -> c_9(n, app^#(x, y))
798.90/297.03 , low^#(n, nil()) -> c_10()
798.90/297.03 , low^#(n, add(m, x)) -> c_11(if_low^#(le(m, n), n, add(m, x)))
798.90/297.03 , if_low^#(true(), n, add(m, x)) -> c_12(m, low^#(n, x))
798.90/297.03 , if_low^#(false(), n, add(m, x)) -> c_13(low^#(n, x))
798.90/297.03 , high^#(n, nil()) -> c_14()
798.90/297.03 , high^#(n, add(m, x)) -> c_15(if_high^#(le(m, n), n, add(m, x)))
798.90/297.03 , if_high^#(true(), n, add(m, x)) -> c_16(high^#(n, x))
798.90/297.03 , if_high^#(false(), n, add(m, x)) -> c_17(m, high^#(n, x))
798.90/297.03 , quicksort^#(nil()) -> c_18()
798.90/297.03 , quicksort^#(add(n, x)) ->
798.90/297.03 c_19(app^#(quicksort(low(n, x)), add(n, quicksort(high(n, x))))) }
798.90/297.03
798.90/297.03 and mark the set of starting terms.
798.90/297.03
798.90/297.03 We are left with following problem, upon which TcT provides the
798.90/297.03 certificate MAYBE.
798.90/297.03
798.90/297.03 Strict DPs:
798.90/297.03 { minus^#(x, 0()) -> c_1(x)
798.90/297.03 , minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
798.90/297.03 , quot^#(0(), s(y)) -> c_3()
798.90/297.03 , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y)))
798.90/297.03 , le^#(0(), y) -> c_5()
798.90/297.03 , le^#(s(x), 0()) -> c_6()
798.90/297.03 , le^#(s(x), s(y)) -> c_7(le^#(x, y))
798.90/297.03 , app^#(nil(), y) -> c_8(y)
798.90/297.03 , app^#(add(n, x), y) -> c_9(n, app^#(x, y))
798.90/297.03 , low^#(n, nil()) -> c_10()
798.90/297.03 , low^#(n, add(m, x)) -> c_11(if_low^#(le(m, n), n, add(m, x)))
798.90/297.03 , if_low^#(true(), n, add(m, x)) -> c_12(m, low^#(n, x))
798.90/297.03 , if_low^#(false(), n, add(m, x)) -> c_13(low^#(n, x))
798.90/297.03 , high^#(n, nil()) -> c_14()
798.90/297.03 , high^#(n, add(m, x)) -> c_15(if_high^#(le(m, n), n, add(m, x)))
798.90/297.03 , if_high^#(true(), n, add(m, x)) -> c_16(high^#(n, x))
798.90/297.03 , if_high^#(false(), n, add(m, x)) -> c_17(m, high^#(n, x))
798.90/297.03 , quicksort^#(nil()) -> c_18()
798.90/297.03 , quicksort^#(add(n, x)) ->
798.90/297.03 c_19(app^#(quicksort(low(n, x)), add(n, quicksort(high(n, x))))) }
798.90/297.03 Strict Trs:
798.90/297.03 { minus(x, 0()) -> x
798.90/297.03 , minus(s(x), s(y)) -> minus(x, y)
798.90/297.03 , quot(0(), s(y)) -> 0()
798.90/297.03 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
798.90/297.03 , le(0(), y) -> true()
798.90/297.03 , le(s(x), 0()) -> false()
798.90/297.03 , le(s(x), s(y)) -> le(x, y)
798.90/297.03 , app(nil(), y) -> y
798.90/297.03 , app(add(n, x), y) -> add(n, app(x, y))
798.90/297.03 , low(n, nil()) -> nil()
798.90/297.03 , low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
798.90/297.03 , if_low(true(), n, add(m, x)) -> add(m, low(n, x))
798.90/297.03 , if_low(false(), n, add(m, x)) -> low(n, x)
798.90/297.03 , high(n, nil()) -> nil()
798.90/297.03 , high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
798.90/297.03 , if_high(true(), n, add(m, x)) -> high(n, x)
798.90/297.03 , if_high(false(), n, add(m, x)) -> add(m, high(n, x))
798.90/297.03 , quicksort(nil()) -> nil()
798.90/297.03 , quicksort(add(n, x)) ->
798.90/297.03 app(quicksort(low(n, x)), add(n, quicksort(high(n, x)))) }
798.90/297.03 Obligation:
798.90/297.03 runtime complexity
798.90/297.03 Answer:
798.90/297.03 MAYBE
798.90/297.03
798.90/297.03 We estimate the number of application of {3,5,6,10,14,18} by
798.90/297.03 applications of Pre({3,5,6,10,14,18}) = {1,4,7,8,9,12,13,16,17}.
798.90/297.03 Here rules are labeled as follows:
798.90/297.03
798.90/297.03 DPs:
798.90/297.03 { 1: minus^#(x, 0()) -> c_1(x)
798.90/297.03 , 2: minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
798.90/297.03 , 3: quot^#(0(), s(y)) -> c_3()
798.90/297.03 , 4: quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y)))
798.90/297.03 , 5: le^#(0(), y) -> c_5()
798.90/297.03 , 6: le^#(s(x), 0()) -> c_6()
798.90/297.03 , 7: le^#(s(x), s(y)) -> c_7(le^#(x, y))
798.90/297.03 , 8: app^#(nil(), y) -> c_8(y)
798.90/297.03 , 9: app^#(add(n, x), y) -> c_9(n, app^#(x, y))
798.90/297.03 , 10: low^#(n, nil()) -> c_10()
798.90/297.03 , 11: low^#(n, add(m, x)) -> c_11(if_low^#(le(m, n), n, add(m, x)))
798.90/297.03 , 12: if_low^#(true(), n, add(m, x)) -> c_12(m, low^#(n, x))
798.90/297.03 , 13: if_low^#(false(), n, add(m, x)) -> c_13(low^#(n, x))
798.90/297.03 , 14: high^#(n, nil()) -> c_14()
798.90/297.03 , 15: high^#(n, add(m, x)) ->
798.90/297.03 c_15(if_high^#(le(m, n), n, add(m, x)))
798.90/297.03 , 16: if_high^#(true(), n, add(m, x)) -> c_16(high^#(n, x))
798.90/297.03 , 17: if_high^#(false(), n, add(m, x)) -> c_17(m, high^#(n, x))
798.90/297.03 , 18: quicksort^#(nil()) -> c_18()
798.90/297.03 , 19: quicksort^#(add(n, x)) ->
798.90/297.03 c_19(app^#(quicksort(low(n, x)), add(n, quicksort(high(n, x))))) }
798.90/297.03
798.90/297.03 We are left with following problem, upon which TcT provides the
798.90/297.03 certificate MAYBE.
798.90/297.03
798.90/297.03 Strict DPs:
798.90/297.03 { minus^#(x, 0()) -> c_1(x)
798.90/297.03 , minus^#(s(x), s(y)) -> c_2(minus^#(x, y))
798.90/297.03 , quot^#(s(x), s(y)) -> c_4(quot^#(minus(x, y), s(y)))
798.90/297.03 , le^#(s(x), s(y)) -> c_7(le^#(x, y))
798.90/297.03 , app^#(nil(), y) -> c_8(y)
798.90/297.03 , app^#(add(n, x), y) -> c_9(n, app^#(x, y))
798.90/297.03 , low^#(n, add(m, x)) -> c_11(if_low^#(le(m, n), n, add(m, x)))
798.90/297.03 , if_low^#(true(), n, add(m, x)) -> c_12(m, low^#(n, x))
798.90/297.03 , if_low^#(false(), n, add(m, x)) -> c_13(low^#(n, x))
798.90/297.03 , high^#(n, add(m, x)) -> c_15(if_high^#(le(m, n), n, add(m, x)))
798.90/297.03 , if_high^#(true(), n, add(m, x)) -> c_16(high^#(n, x))
798.90/297.03 , if_high^#(false(), n, add(m, x)) -> c_17(m, high^#(n, x))
798.90/297.03 , quicksort^#(add(n, x)) ->
798.90/297.03 c_19(app^#(quicksort(low(n, x)), add(n, quicksort(high(n, x))))) }
798.90/297.03 Strict Trs:
798.90/297.03 { minus(x, 0()) -> x
798.90/297.03 , minus(s(x), s(y)) -> minus(x, y)
798.90/297.03 , quot(0(), s(y)) -> 0()
798.90/297.03 , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
798.90/297.03 , le(0(), y) -> true()
798.90/297.03 , le(s(x), 0()) -> false()
798.90/297.03 , le(s(x), s(y)) -> le(x, y)
798.90/297.03 , app(nil(), y) -> y
798.90/297.03 , app(add(n, x), y) -> add(n, app(x, y))
798.90/297.03 , low(n, nil()) -> nil()
798.90/297.03 , low(n, add(m, x)) -> if_low(le(m, n), n, add(m, x))
798.90/297.03 , if_low(true(), n, add(m, x)) -> add(m, low(n, x))
798.90/297.03 , if_low(false(), n, add(m, x)) -> low(n, x)
798.90/297.03 , high(n, nil()) -> nil()
798.90/297.03 , high(n, add(m, x)) -> if_high(le(m, n), n, add(m, x))
798.90/297.03 , if_high(true(), n, add(m, x)) -> high(n, x)
798.90/297.03 , if_high(false(), n, add(m, x)) -> add(m, high(n, x))
798.90/297.03 , quicksort(nil()) -> nil()
798.90/297.03 , quicksort(add(n, x)) ->
798.90/297.03 app(quicksort(low(n, x)), add(n, quicksort(high(n, x)))) }
798.90/297.03 Weak DPs:
798.90/297.03 { quot^#(0(), s(y)) -> c_3()
798.90/297.03 , le^#(0(), y) -> c_5()
798.90/297.03 , le^#(s(x), 0()) -> c_6()
798.90/297.03 , low^#(n, nil()) -> c_10()
798.90/297.03 , high^#(n, nil()) -> c_14()
798.90/297.03 , quicksort^#(nil()) -> c_18() }
798.90/297.03 Obligation:
798.90/297.03 runtime complexity
798.90/297.03 Answer:
798.90/297.03 MAYBE
798.90/297.03
798.90/297.03 Empty strict component of the problem is NOT empty.
798.90/297.03
798.90/297.03
798.90/297.03 Arrrr..
799.12/297.22 EOF