MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, int(x, y) -> if(le(x, y), x, y)
, if(true(), x, y) -> cons(x, int(s(x), y))
, if(false(), x, y) -> nil() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
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) 'Best' failed due to the following reason:
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:
The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(if) = {1}, Uargs(cons) = {2}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[le](x1, x2) = [4]
[0] = [7]
[true] = [1]
[s](x1) = [1] x1 + [0]
[false] = [1]
[int](x1, x2) = [1] x1 + [1] x2 + [5]
[if](x1, x2, x3) = [1] x1 + [1] x2 + [1] x3 + [0]
[cons](x1, x2) = [1] x2 + [2]
[nil] = [0]
The following symbols are considered usable
{le, int, if}
The order satisfies the following ordering constraints:
[le(0(), y)] = [4]
> [1]
= [true()]
[le(s(x), 0())] = [4]
> [1]
= [false()]
[le(s(x), s(y))] = [4]
>= [4]
= [le(x, y)]
[int(x, y)] = [1] y + [1] x + [5]
> [1] y + [1] x + [4]
= [if(le(x, y), x, y)]
[if(true(), x, y)] = [1] y + [1] x + [1]
? [1] y + [1] x + [7]
= [cons(x, int(s(x), y))]
[if(false(), x, y)] = [1] y + [1] x + [1]
> [0]
= [nil()]
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ le(s(x), s(y)) -> le(x, y)
, if(true(), x, y) -> cons(x, int(s(x), y)) }
Weak Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, int(x, y) -> if(le(x, y), x, y)
, if(false(), x, y) -> nil() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
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:
The weightgap principle applies (using the following nonconstant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(if) = {1}, Uargs(cons) = {2}
TcT has computed the following matrix interpretation satisfying
not(EDA) and not(IDA(1)).
[le](x1, x2) = [0 0] x1 + [0]
[1 0] [1]
[0] = [3]
[0]
[true] = [0]
[4]
[s](x1) = [0]
[0]
[false] = [0]
[0]
[int](x1, x2) = [1 0] x1 + [1]
[0 0] [4]
[if](x1, x2, x3) = [1 1] x1 + [0]
[0 0] [0]
[cons](x1, x2) = [1 0] x2 + [1]
[0 0] [0]
[nil] = [0]
[0]
The following symbols are considered usable
{le, int, if}
The order satisfies the following ordering constraints:
[le(0(), y)] = [0]
[4]
>= [0]
[4]
= [true()]
[le(s(x), 0())] = [0]
[1]
>= [0]
[0]
= [false()]
[le(s(x), s(y))] = [0]
[1]
? [0 0] x + [0]
[1 0] [1]
= [le(x, y)]
[int(x, y)] = [1 0] x + [1]
[0 0] [4]
>= [1 0] x + [1]
[0 0] [0]
= [if(le(x, y), x, y)]
[if(true(), x, y)] = [4]
[0]
> [2]
[0]
= [cons(x, int(s(x), y))]
[if(false(), x, y)] = [0]
[0]
>= [0]
[0]
= [nil()]
Further, it can be verified that all rules not oriented are covered by the weightgap condition.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs: { le(s(x), s(y)) -> le(x, y) }
Weak Trs:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, int(x, y) -> if(le(x, y), x, y)
, if(true(), x, y) -> cons(x, int(s(x), y))
, if(false(), x, y) -> nil() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
to the following reason:
The input cannot be shown compatible
2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
following reason:
The input cannot be shown compatible
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 minimal-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
failed due to the following reason:
match-boundness of the problem could not be verified.
Arrrr..