MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u)) }
Obligation:
runtime complexity
Answer:
MAYBE
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
Computation stopped due to timeout after 60.0 seconds.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
failed due to the following reason:
Computation stopped due to timeout after 30.0 seconds.
2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
3) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The processor is inapplicable, reason:
Processor only applicable for innermost runtime complexity analysis
3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ -^#(x, 0()) -> c_1(x)
, -^#(s(x), s(y)) -> c_2(-^#(x, y))
, <=^#(0(), y) -> c_3()
, <=^#(s(x), 0()) -> c_4()
, <=^#(s(x), s(y)) -> c_5(<=^#(x, y))
, if^#(true(), x, y) -> c_6(x)
, if^#(false(), x, y) -> c_7(y)
, perfectp^#(0()) -> c_8()
, perfectp^#(s(x)) -> c_9(f^#(x, s(0()), s(x), s(x)))
, f^#(0(), y, 0(), u) -> c_10()
, f^#(0(), y, s(z), u) -> c_11()
, f^#(s(x), 0(), z, u) -> c_12(f^#(x, u, -(z, s(x)), u))
, f^#(s(x), s(y), z, u) ->
c_13(if^#(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ -^#(x, 0()) -> c_1(x)
, -^#(s(x), s(y)) -> c_2(-^#(x, y))
, <=^#(0(), y) -> c_3()
, <=^#(s(x), 0()) -> c_4()
, <=^#(s(x), s(y)) -> c_5(<=^#(x, y))
, if^#(true(), x, y) -> c_6(x)
, if^#(false(), x, y) -> c_7(y)
, perfectp^#(0()) -> c_8()
, perfectp^#(s(x)) -> c_9(f^#(x, s(0()), s(x), s(x)))
, f^#(0(), y, 0(), u) -> c_10()
, f^#(0(), y, s(z), u) -> c_11()
, f^#(s(x), 0(), z, u) -> c_12(f^#(x, u, -(z, s(x)), u))
, f^#(s(x), s(y), z, u) ->
c_13(if^#(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))) }
Strict Trs:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u)) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {3,4,8,10,11} by
applications of Pre({3,4,8,10,11}) = {1,5,6,7,9,12}. Here rules are
labeled as follows:
DPs:
{ 1: -^#(x, 0()) -> c_1(x)
, 2: -^#(s(x), s(y)) -> c_2(-^#(x, y))
, 3: <=^#(0(), y) -> c_3()
, 4: <=^#(s(x), 0()) -> c_4()
, 5: <=^#(s(x), s(y)) -> c_5(<=^#(x, y))
, 6: if^#(true(), x, y) -> c_6(x)
, 7: if^#(false(), x, y) -> c_7(y)
, 8: perfectp^#(0()) -> c_8()
, 9: perfectp^#(s(x)) -> c_9(f^#(x, s(0()), s(x), s(x)))
, 10: f^#(0(), y, 0(), u) -> c_10()
, 11: f^#(0(), y, s(z), u) -> c_11()
, 12: f^#(s(x), 0(), z, u) -> c_12(f^#(x, u, -(z, s(x)), u))
, 13: f^#(s(x), s(y), z, u) ->
c_13(if^#(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ -^#(x, 0()) -> c_1(x)
, -^#(s(x), s(y)) -> c_2(-^#(x, y))
, <=^#(s(x), s(y)) -> c_5(<=^#(x, y))
, if^#(true(), x, y) -> c_6(x)
, if^#(false(), x, y) -> c_7(y)
, perfectp^#(s(x)) -> c_9(f^#(x, s(0()), s(x), s(x)))
, f^#(s(x), 0(), z, u) -> c_12(f^#(x, u, -(z, s(x)), u))
, f^#(s(x), s(y), z, u) ->
c_13(if^#(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u))) }
Strict Trs:
{ -(x, 0()) -> x
, -(s(x), s(y)) -> -(x, y)
, <=(0(), y) -> true()
, <=(s(x), 0()) -> false()
, <=(s(x), s(y)) -> <=(x, y)
, if(true(), x, y) -> x
, if(false(), x, y) -> y
, perfectp(0()) -> false()
, perfectp(s(x)) -> f(x, s(0()), s(x), s(x))
, f(0(), y, 0(), u) -> true()
, f(0(), y, s(z), u) -> false()
, f(s(x), 0(), z, u) -> f(x, u, -(z, s(x)), u)
, f(s(x), s(y), z, u) ->
if(<=(x, y), f(s(x), -(y, x), z, u), f(x, u, z, u)) }
Weak DPs:
{ <=^#(0(), y) -> c_3()
, <=^#(s(x), 0()) -> c_4()
, perfectp^#(0()) -> c_8()
, f^#(0(), y, 0(), u) -> c_10()
, f^#(0(), y, s(z), u) -> c_11() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..