MAYBE
821.52/297.03 MAYBE
821.52/297.03
821.52/297.03 We are left with following problem, upon which TcT provides the
821.52/297.03 certificate MAYBE.
821.52/297.03
821.52/297.03 Strict Trs:
821.52/297.03 { min(0(), y) -> 0()
821.52/297.03 , min(s(x), 0()) -> 0()
821.52/297.03 , min(s(x), s(y)) -> min(x, y)
821.52/297.03 , len(nil()) -> 0()
821.52/297.03 , len(cons(x, xs)) -> s(len(xs))
821.52/297.03 , sum(x, 0()) -> x
821.52/297.03 , sum(x, s(y)) -> s(sum(x, y))
821.52/297.03 , le(0(), x) -> true()
821.52/297.03 , le(s(x), 0()) -> false()
821.52/297.03 , le(s(x), s(y)) -> le(x, y)
821.52/297.03 , take(0(), cons(y, ys)) -> y
821.52/297.03 , take(s(x), cons(y, ys)) -> take(x, ys)
821.52/297.03 , addList(x, y) ->
821.52/297.03 if(le(0(), min(len(x), len(y))), 0(), x, y, nil())
821.52/297.03 , if(true(), c, xs, ys, z) ->
821.52/297.03 if(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z))
821.52/297.03 , if(false(), c, x, y, z) -> z }
821.52/297.03 Obligation:
821.52/297.03 runtime complexity
821.52/297.03 Answer:
821.52/297.03 MAYBE
821.52/297.03
821.52/297.03 None of the processors succeeded.
821.52/297.03
821.52/297.03 Details of failed attempt(s):
821.52/297.03 -----------------------------
821.52/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the
821.52/297.03 following reason:
821.52/297.03
821.52/297.03 Computation stopped due to timeout after 297.0 seconds.
821.52/297.03
821.52/297.03 2) 'Best' failed due to the following reason:
821.52/297.03
821.52/297.03 None of the processors succeeded.
821.52/297.03
821.52/297.03 Details of failed attempt(s):
821.52/297.03 -----------------------------
821.52/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
821.52/297.03 seconds)' failed due to the following reason:
821.52/297.03
821.52/297.03 Computation stopped due to timeout after 148.0 seconds.
821.52/297.03
821.52/297.03 2) 'Best' failed due to the following reason:
821.52/297.03
821.52/297.03 None of the processors succeeded.
821.52/297.03
821.52/297.03 Details of failed attempt(s):
821.52/297.03 -----------------------------
821.52/297.03 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
821.52/297.03 to the following reason:
821.52/297.03
821.52/297.03 The processor is inapplicable, reason:
821.52/297.03 Processor only applicable for innermost runtime complexity analysis
821.52/297.03
821.52/297.03 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
821.52/297.03 following reason:
821.52/297.03
821.52/297.03 The processor is inapplicable, reason:
821.52/297.03 Processor only applicable for innermost runtime complexity analysis
821.52/297.03
821.52/297.03
821.52/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
821.52/297.03 failed due to the following reason:
821.52/297.03
821.52/297.03 None of the processors succeeded.
821.52/297.03
821.52/297.03 Details of failed attempt(s):
821.52/297.03 -----------------------------
821.52/297.03 1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
821.52/297.03 failed due to the following reason:
821.52/297.03
821.52/297.03 match-boundness of the problem could not be verified.
821.52/297.03
821.52/297.03 2) 'Bounds with minimal-enrichment and initial automaton 'match''
821.52/297.03 failed due to the following reason:
821.52/297.03
821.52/297.03 match-boundness of the problem could not be verified.
821.52/297.03
821.52/297.03
821.52/297.03
821.52/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
821.52/297.03 the following reason:
821.52/297.03
821.52/297.03 We add the following weak dependency pairs:
821.52/297.03
821.52/297.03 Strict DPs:
821.52/297.03 { min^#(0(), y) -> c_1()
821.52/297.03 , min^#(s(x), 0()) -> c_2()
821.52/297.03 , min^#(s(x), s(y)) -> c_3(min^#(x, y))
821.52/297.03 , len^#(nil()) -> c_4()
821.52/297.03 , len^#(cons(x, xs)) -> c_5(len^#(xs))
821.52/297.03 , sum^#(x, 0()) -> c_6(x)
821.52/297.03 , sum^#(x, s(y)) -> c_7(sum^#(x, y))
821.52/297.03 , le^#(0(), x) -> c_8()
821.52/297.03 , le^#(s(x), 0()) -> c_9()
821.52/297.03 , le^#(s(x), s(y)) -> c_10(le^#(x, y))
821.52/297.03 , take^#(0(), cons(y, ys)) -> c_11(y)
821.52/297.03 , take^#(s(x), cons(y, ys)) -> c_12(take^#(x, ys))
821.52/297.03 , addList^#(x, y) ->
821.52/297.03 c_13(if^#(le(0(), min(len(x), len(y))), 0(), x, y, nil()))
821.52/297.03 , if^#(true(), c, xs, ys, z) ->
821.52/297.03 c_14(if^#(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z)))
821.52/297.03 , if^#(false(), c, x, y, z) -> c_15(z) }
821.52/297.03
821.52/297.03 and mark the set of starting terms.
821.52/297.03
821.52/297.03 We are left with following problem, upon which TcT provides the
821.52/297.03 certificate MAYBE.
821.52/297.03
821.52/297.03 Strict DPs:
821.52/297.03 { min^#(0(), y) -> c_1()
821.52/297.03 , min^#(s(x), 0()) -> c_2()
821.52/297.03 , min^#(s(x), s(y)) -> c_3(min^#(x, y))
821.52/297.03 , len^#(nil()) -> c_4()
821.52/297.03 , len^#(cons(x, xs)) -> c_5(len^#(xs))
821.52/297.03 , sum^#(x, 0()) -> c_6(x)
821.52/297.03 , sum^#(x, s(y)) -> c_7(sum^#(x, y))
821.52/297.03 , le^#(0(), x) -> c_8()
821.52/297.03 , le^#(s(x), 0()) -> c_9()
821.52/297.03 , le^#(s(x), s(y)) -> c_10(le^#(x, y))
821.52/297.03 , take^#(0(), cons(y, ys)) -> c_11(y)
821.52/297.03 , take^#(s(x), cons(y, ys)) -> c_12(take^#(x, ys))
821.52/297.03 , addList^#(x, y) ->
821.52/297.03 c_13(if^#(le(0(), min(len(x), len(y))), 0(), x, y, nil()))
821.52/297.03 , if^#(true(), c, xs, ys, z) ->
821.52/297.03 c_14(if^#(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z)))
821.52/297.03 , if^#(false(), c, x, y, z) -> c_15(z) }
821.52/297.03 Strict Trs:
821.52/297.03 { min(0(), y) -> 0()
821.52/297.03 , min(s(x), 0()) -> 0()
821.52/297.03 , min(s(x), s(y)) -> min(x, y)
821.52/297.03 , len(nil()) -> 0()
821.52/297.03 , len(cons(x, xs)) -> s(len(xs))
821.52/297.03 , sum(x, 0()) -> x
821.52/297.03 , sum(x, s(y)) -> s(sum(x, y))
821.52/297.03 , le(0(), x) -> true()
821.52/297.03 , le(s(x), 0()) -> false()
821.52/297.03 , le(s(x), s(y)) -> le(x, y)
821.52/297.03 , take(0(), cons(y, ys)) -> y
821.52/297.03 , take(s(x), cons(y, ys)) -> take(x, ys)
821.52/297.03 , addList(x, y) ->
821.52/297.03 if(le(0(), min(len(x), len(y))), 0(), x, y, nil())
821.52/297.03 , if(true(), c, xs, ys, z) ->
821.52/297.03 if(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z))
821.52/297.03 , if(false(), c, x, y, z) -> z }
821.52/297.03 Obligation:
821.52/297.03 runtime complexity
821.52/297.03 Answer:
821.52/297.03 MAYBE
821.52/297.03
821.52/297.03 We estimate the number of application of {1,2,4,8,9} by
821.52/297.03 applications of Pre({1,2,4,8,9}) = {3,5,6,10,11,15}. Here rules are
821.52/297.03 labeled as follows:
821.52/297.03
821.52/297.03 DPs:
821.52/297.03 { 1: min^#(0(), y) -> c_1()
821.52/297.03 , 2: min^#(s(x), 0()) -> c_2()
821.52/297.03 , 3: min^#(s(x), s(y)) -> c_3(min^#(x, y))
821.52/297.03 , 4: len^#(nil()) -> c_4()
821.52/297.03 , 5: len^#(cons(x, xs)) -> c_5(len^#(xs))
821.52/297.03 , 6: sum^#(x, 0()) -> c_6(x)
821.52/297.03 , 7: sum^#(x, s(y)) -> c_7(sum^#(x, y))
821.52/297.03 , 8: le^#(0(), x) -> c_8()
821.52/297.03 , 9: le^#(s(x), 0()) -> c_9()
821.52/297.03 , 10: le^#(s(x), s(y)) -> c_10(le^#(x, y))
821.52/297.03 , 11: take^#(0(), cons(y, ys)) -> c_11(y)
821.52/297.03 , 12: take^#(s(x), cons(y, ys)) -> c_12(take^#(x, ys))
821.52/297.03 , 13: addList^#(x, y) ->
821.52/297.03 c_13(if^#(le(0(), min(len(x), len(y))), 0(), x, y, nil()))
821.52/297.03 , 14: if^#(true(), c, xs, ys, z) ->
821.52/297.03 c_14(if^#(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z)))
821.52/297.03 , 15: if^#(false(), c, x, y, z) -> c_15(z) }
821.52/297.03
821.52/297.03 We are left with following problem, upon which TcT provides the
821.52/297.03 certificate MAYBE.
821.52/297.03
821.52/297.03 Strict DPs:
821.52/297.03 { min^#(s(x), s(y)) -> c_3(min^#(x, y))
821.52/297.03 , len^#(cons(x, xs)) -> c_5(len^#(xs))
821.52/297.03 , sum^#(x, 0()) -> c_6(x)
821.52/297.03 , sum^#(x, s(y)) -> c_7(sum^#(x, y))
821.52/297.03 , le^#(s(x), s(y)) -> c_10(le^#(x, y))
821.52/297.03 , take^#(0(), cons(y, ys)) -> c_11(y)
821.52/297.03 , take^#(s(x), cons(y, ys)) -> c_12(take^#(x, ys))
821.52/297.03 , addList^#(x, y) ->
821.52/297.03 c_13(if^#(le(0(), min(len(x), len(y))), 0(), x, y, nil()))
821.52/297.03 , if^#(true(), c, xs, ys, z) ->
821.52/297.03 c_14(if^#(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z)))
821.52/297.03 , if^#(false(), c, x, y, z) -> c_15(z) }
821.52/297.03 Strict Trs:
821.52/297.03 { min(0(), y) -> 0()
821.52/297.03 , min(s(x), 0()) -> 0()
821.52/297.03 , min(s(x), s(y)) -> min(x, y)
821.52/297.03 , len(nil()) -> 0()
821.52/297.03 , len(cons(x, xs)) -> s(len(xs))
821.52/297.03 , sum(x, 0()) -> x
821.52/297.03 , sum(x, s(y)) -> s(sum(x, y))
821.52/297.03 , le(0(), x) -> true()
821.52/297.03 , le(s(x), 0()) -> false()
821.52/297.03 , le(s(x), s(y)) -> le(x, y)
821.52/297.03 , take(0(), cons(y, ys)) -> y
821.52/297.03 , take(s(x), cons(y, ys)) -> take(x, ys)
821.52/297.03 , addList(x, y) ->
821.52/297.03 if(le(0(), min(len(x), len(y))), 0(), x, y, nil())
821.52/297.03 , if(true(), c, xs, ys, z) ->
821.52/297.03 if(le(s(c), min(len(xs), len(ys))),
821.52/297.03 s(c),
821.52/297.03 xs,
821.52/297.03 ys,
821.52/297.03 cons(sum(take(c, xs), take(c, ys)), z))
821.52/297.03 , if(false(), c, x, y, z) -> z }
821.52/297.03 Weak DPs:
821.52/297.03 { min^#(0(), y) -> c_1()
821.52/297.03 , min^#(s(x), 0()) -> c_2()
821.52/297.03 , len^#(nil()) -> c_4()
821.52/297.03 , le^#(0(), x) -> c_8()
821.52/297.03 , le^#(s(x), 0()) -> c_9() }
821.52/297.03 Obligation:
821.52/297.03 runtime complexity
821.52/297.03 Answer:
821.52/297.03 MAYBE
821.52/297.03
821.52/297.03 Empty strict component of the problem is NOT empty.
821.52/297.03
821.52/297.03
821.52/297.03 Arrrr..
821.73/297.26 EOF