MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ exp(x, 0()) -> s(0())
, exp(x, s(y)) -> *(x, exp(x, y))
, *(0(), y) -> 0()
, *(s(x), y) -> +(y, *(x, y))
, -(x, 0()) -> x
, -(0(), y) -> 0()
, -(s(x), s(y)) -> -(x, y) }
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:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'WithProblem' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'Best' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) '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
2) '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
3) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
due to the following reason:
We add the following weak dependency pairs:
Strict DPs:
{ exp^#(x, 0()) -> c_1()
, exp^#(x, s(y)) -> c_2(*^#(x, exp(x, y)))
, *^#(0(), y) -> c_3()
, *^#(s(x), y) -> c_4(y, *^#(x, y))
, -^#(x, 0()) -> c_5(x)
, -^#(0(), y) -> c_6()
, -^#(s(x), s(y)) -> c_7(-^#(x, y)) }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ exp^#(x, 0()) -> c_1()
, exp^#(x, s(y)) -> c_2(*^#(x, exp(x, y)))
, *^#(0(), y) -> c_3()
, *^#(s(x), y) -> c_4(y, *^#(x, y))
, -^#(x, 0()) -> c_5(x)
, -^#(0(), y) -> c_6()
, -^#(s(x), s(y)) -> c_7(-^#(x, y)) }
Strict Trs:
{ exp(x, 0()) -> s(0())
, exp(x, s(y)) -> *(x, exp(x, y))
, *(0(), y) -> 0()
, *(s(x), y) -> +(y, *(x, y))
, -(x, 0()) -> x
, -(0(), y) -> 0()
, -(s(x), s(y)) -> -(x, y) }
Obligation:
runtime complexity
Answer:
MAYBE
We estimate the number of application of {1,3,6} by applications of
Pre({1,3,6}) = {2,4,5,7}. Here rules are labeled as follows:
DPs:
{ 1: exp^#(x, 0()) -> c_1()
, 2: exp^#(x, s(y)) -> c_2(*^#(x, exp(x, y)))
, 3: *^#(0(), y) -> c_3()
, 4: *^#(s(x), y) -> c_4(y, *^#(x, y))
, 5: -^#(x, 0()) -> c_5(x)
, 6: -^#(0(), y) -> c_6()
, 7: -^#(s(x), s(y)) -> c_7(-^#(x, y)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ exp^#(x, s(y)) -> c_2(*^#(x, exp(x, y)))
, *^#(s(x), y) -> c_4(y, *^#(x, y))
, -^#(x, 0()) -> c_5(x)
, -^#(s(x), s(y)) -> c_7(-^#(x, y)) }
Strict Trs:
{ exp(x, 0()) -> s(0())
, exp(x, s(y)) -> *(x, exp(x, y))
, *(0(), y) -> 0()
, *(s(x), y) -> +(y, *(x, y))
, -(x, 0()) -> x
, -(0(), y) -> 0()
, -(s(x), s(y)) -> -(x, y) }
Weak DPs:
{ exp^#(x, 0()) -> c_1()
, *^#(0(), y) -> c_3()
, -^#(0(), y) -> c_6() }
Obligation:
runtime complexity
Answer:
MAYBE
Empty strict component of the problem is NOT empty.
Arrrr..