MAYBE
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict Trs:
{ from(X) -> cons(X, from(s(X)))
, sel(s(N), cons(X, XS)) -> sel(N, XS)
, sel(0(), cons(X, XS)) -> X
, minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y)
, quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
, quot(0(), s(Y)) -> 0()
, zWquot(XS, nil()) -> nil()
, zWquot(cons(X, XS), cons(Y, YS)) ->
cons(quot(X, Y), zWquot(XS, YS))
, zWquot(nil(), XS) -> 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) '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) '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.
2) 'WithProblem (timeout of 60 seconds)' failed due to the
following reason:
We add the following innermost weak dependency pairs:
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4()
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS))
, zWquot^#(nil(), XS) -> c_10() }
and mark the set of starting terms.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4()
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS))
, zWquot^#(nil(), XS) -> c_10() }
Strict Trs:
{ from(X) -> cons(X, from(s(X)))
, sel(s(N), cons(X, XS)) -> sel(N, XS)
, sel(0(), cons(X, XS)) -> X
, minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y)
, quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y)))
, quot(0(), s(Y)) -> 0()
, zWquot(XS, nil()) -> nil()
, zWquot(cons(X, XS), cons(Y, YS)) ->
cons(quot(X, Y), zWquot(XS, YS))
, zWquot(nil(), XS) -> nil() }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We replace rewrite rules by usable rules:
Strict Usable Rules:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4()
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS))
, zWquot^#(nil(), XS) -> c_10() }
Strict Trs:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The weightgap principle applies (using the following constant
growth matrix-interpretation)
The following argument positions are usable:
Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_5) = {1},
Uargs(quot^#) = {1}, Uargs(c_6) = {1}, Uargs(c_9) = {1, 2}
TcT has computed the following constructor-restricted matrix
interpretation.
[cons](x1, x2) = [1 2] x1 + [1 0] x2 + [0]
[0 0] [0 0] [0]
[s](x1) = [0 0] x1 + [2]
[0 1] [2]
[0] = [0]
[0]
[minus](x1, x2) = [0 1] x1 + [1]
[0 0] [0]
[nil] = [0]
[0]
[from^#](x1) = [2 0] x1 + [2]
[1 1] [2]
[c_1](x1) = [1 0] x1 + [1]
[0 1] [1]
[sel^#](x1, x2) = [0 0] x1 + [0 0] x2 + [2]
[1 2] [2 2] [1]
[c_2](x1) = [1 0] x1 + [1]
[0 1] [1]
[c_3] = [1]
[1]
[minus^#](x1, x2) = [0 0] x1 + [0 0] x2 + [2]
[0 1] [1 1] [1]
[c_4] = [1]
[1]
[c_5](x1) = [1 0] x1 + [1]
[0 1] [1]
[quot^#](x1, x2) = [1 1] x1 + [0]
[0 0] [0]
[c_6](x1) = [1 0] x1 + [1]
[0 1] [2]
[c_7] = [2]
[0]
[zWquot^#](x1, x2) = [2 0] x1 + [0]
[0 0] [0]
[c_8] = [1]
[0]
[c_9](x1, x2) = [1 0] x1 + [1 0] x2 + [2]
[0 1] [0 1] [2]
[c_10] = [1]
[0]
The following symbols are considered usable
{minus, from^#, sel^#, minus^#, quot^#, zWquot^#}
The order satisfies the following ordering constraints:
[minus(X, 0())] = [0 1] X + [1]
[0 0] [0]
> [0]
[0]
= [0()]
[minus(s(X), s(Y))] = [0 1] X + [3]
[0 0] [0]
> [0 1] X + [1]
[0 0] [0]
= [minus(X, Y)]
[from^#(X)] = [2 0] X + [2]
[1 1] [2]
? [0 0] X + [7]
[0 1] [7]
= [c_1(from^#(s(X)))]
[sel^#(s(N), cons(X, XS))] = [0 0] X + [0 0] XS + [0 0] N + [2]
[2 4] [2 0] [0 2] [7]
? [0 0] XS + [0 0] N + [3]
[2 2] [1 2] [2]
= [c_2(sel^#(N, XS))]
[sel^#(0(), cons(X, XS))] = [0 0] X + [0 0] XS + [2]
[2 4] [2 0] [1]
> [1]
[1]
= [c_3()]
[minus^#(X, 0())] = [0 0] X + [2]
[0 1] [1]
> [1]
[1]
= [c_4()]
[minus^#(s(X), s(Y))] = [0 0] X + [0 0] Y + [2]
[0 1] [0 1] [7]
? [0 0] X + [0 0] Y + [3]
[0 1] [1 1] [2]
= [c_5(minus^#(X, Y))]
[quot^#(s(X), s(Y))] = [0 1] X + [4]
[0 0] [0]
? [0 1] X + [2]
[0 0] [2]
= [c_6(quot^#(minus(X, Y), s(Y)))]
[quot^#(0(), s(Y))] = [0]
[0]
? [2]
[0]
= [c_7()]
[zWquot^#(XS, nil())] = [2 0] XS + [0]
[0 0] [0]
? [1]
[0]
= [c_8()]
[zWquot^#(cons(X, XS), cons(Y, YS))] = [2 4] X + [2 0] XS + [0]
[0 0] [0 0] [0]
? [1 1] X + [2 0] XS + [2]
[0 0] [0 0] [2]
= [c_9(quot^#(X, Y), zWquot^#(XS, YS))]
[zWquot^#(nil(), XS)] = [0]
[0]
? [1]
[0]
= [c_10()]
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 DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS))
, zWquot^#(nil(), XS) -> c_10() }
Weak DPs:
{ sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4() }
Weak Trs:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {5,6,8} by applications of
Pre({5,6,8}) = {4,7}. Here rules are labeled as follows:
DPs:
{ 1: from^#(X) -> c_1(from^#(s(X)))
, 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, 3: minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, 4: quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, 5: quot^#(0(), s(Y)) -> c_7()
, 6: zWquot^#(XS, nil()) -> c_8()
, 7: zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS))
, 8: zWquot^#(nil(), XS) -> c_10()
, 9: sel^#(0(), cons(X, XS)) -> c_3()
, 10: minus^#(X, 0()) -> c_4() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS)) }
Weak DPs:
{ sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4()
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(nil(), XS) -> c_10() }
Weak Trs:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We estimate the number of application of {4} by applications of
Pre({4}) = {5}. Here rules are labeled as follows:
DPs:
{ 1: from^#(X) -> c_1(from^#(s(X)))
, 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, 3: minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, 4: quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, 5: zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS))
, 6: sel^#(0(), cons(X, XS)) -> c_3()
, 7: minus^#(X, 0()) -> c_4()
, 8: quot^#(0(), s(Y)) -> c_7()
, 9: zWquot^#(XS, nil()) -> c_8()
, 10: zWquot^#(nil(), XS) -> c_10() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS)) }
Weak DPs:
{ sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4()
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(nil(), XS) -> c_10() }
Weak Trs:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.
{ sel^#(0(), cons(X, XS)) -> c_3()
, minus^#(X, 0()) -> c_4()
, quot^#(s(X), s(Y)) -> c_6(quot^#(minus(X, Y), s(Y)))
, quot^#(0(), s(Y)) -> c_7()
, zWquot^#(XS, nil()) -> c_8()
, zWquot^#(nil(), XS) -> c_10() }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_5(minus^#(X, Y))
, zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS)) }
Weak Trs:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:
{ zWquot^#(cons(X, XS), cons(Y, YS)) ->
c_9(quot^#(X, Y), zWquot^#(XS, YS)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y))
, zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) }
Weak Trs:
{ minus(X, 0()) -> 0()
, minus(s(X), s(Y)) -> minus(X, Y) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
No rule is usable, rules are removed from the input problem.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y))
, zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) }
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:
We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.
DPs:
{ 4: zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) }
Sub-proof:
----------
The following argument positions are usable:
Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_3) = {1},
Uargs(c_4) = {1}
TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA).
[from](x1) = [7] x1 + [0]
[cons](x1, x2) = [1] x1 + [1] x2 + [2]
[s](x1) = [0]
[sel](x1, x2) = [7] x1 + [7] x2 + [0]
[0] = [0]
[minus](x1, x2) = [7] x1 + [7] x2 + [0]
[quot](x1, x2) = [7] x1 + [7] x2 + [0]
[zWquot](x1, x2) = [7] x1 + [7] x2 + [0]
[nil] = [0]
[from^#](x1) = [0]
[c_1](x1) = [7] x1 + [0]
[sel^#](x1, x2) = [0]
[c_2](x1) = [7] x1 + [0]
[c_3] = [0]
[minus^#](x1, x2) = [0]
[c_4] = [0]
[c_5](x1) = [7] x1 + [0]
[quot^#](x1, x2) = [7] x1 + [7] x2 + [0]
[c_6](x1) = [7] x1 + [0]
[c_7] = [0]
[zWquot^#](x1, x2) = [4] x1 + [1]
[c_8] = [0]
[c_9](x1, x2) = [7] x1 + [7] x2 + [0]
[c_10] = [0]
[c] = [0]
[c_1](x1) = [1] x1 + [0]
[c_2](x1) = [2] x1 + [0]
[c_3](x1) = [1] x1 + [0]
[c_4](x1) = [1] x1 + [1]
The following symbols are considered usable
{from^#, sel^#, minus^#, zWquot^#}
The order satisfies the following ordering constraints:
[from^#(X)] = [0]
>= [0]
= [c_1(from^#(s(X)))]
[sel^#(s(N), cons(X, XS))] = [0]
>= [0]
= [c_2(sel^#(N, XS))]
[minus^#(s(X), s(Y))] = [0]
>= [0]
= [c_3(minus^#(X, Y))]
[zWquot^#(cons(X, XS), cons(Y, YS))] = [4] X + [4] XS + [9]
> [4] XS + [2]
= [c_4(zWquot^#(XS, YS))]
The strictly oriented rules are moved into the weak component.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
Weak DPs:
{ zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.
{ zWquot^#(cons(X, XS), cons(Y, YS)) -> c_4(zWquot^#(XS, YS)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS))
, minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.
DPs:
{ 2: sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) }
Sub-proof:
----------
The following argument positions are usable:
Uargs(c_1) = {1}, Uargs(c_2) = {1}, Uargs(c_3) = {1}
TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA).
[from](x1) = [7] x1 + [0]
[cons](x1, x2) = [1] x1 + [1] x2 + [2]
[s](x1) = [0]
[sel](x1, x2) = [7] x1 + [7] x2 + [0]
[0] = [0]
[minus](x1, x2) = [7] x1 + [7] x2 + [0]
[quot](x1, x2) = [7] x1 + [7] x2 + [0]
[zWquot](x1, x2) = [7] x1 + [7] x2 + [0]
[nil] = [0]
[from^#](x1) = [0]
[c_1](x1) = [7] x1 + [0]
[sel^#](x1, x2) = [4] x2 + [1]
[c_2](x1) = [7] x1 + [0]
[c_3] = [0]
[minus^#](x1, x2) = [0]
[c_4] = [0]
[c_5](x1) = [7] x1 + [0]
[quot^#](x1, x2) = [7] x1 + [7] x2 + [0]
[c_6](x1) = [7] x1 + [0]
[c_7] = [0]
[zWquot^#](x1, x2) = [7] x1 + [7] x2 + [0]
[c_8] = [0]
[c_9](x1, x2) = [7] x1 + [7] x2 + [0]
[c_10] = [0]
[c] = [0]
[c_1](x1) = [1] x1 + [0]
[c_2](x1) = [1] x1 + [1]
[c_3](x1) = [4] x1 + [0]
[c_4](x1) = [7] x1 + [0]
The following symbols are considered usable
{from^#, sel^#, minus^#}
The order satisfies the following ordering constraints:
[from^#(X)] = [0]
>= [0]
= [c_1(from^#(s(X)))]
[sel^#(s(N), cons(X, XS))] = [4] X + [4] XS + [9]
> [4] XS + [2]
= [c_2(sel^#(N, XS))]
[minus^#(s(X), s(Y))] = [0]
>= [0]
= [c_3(minus^#(X, Y))]
The strictly oriented rules are moved into the weak component.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
Weak DPs: { sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.
{ sel^#(s(N), cons(X, XS)) -> c_2(sel^#(N, XS)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs:
{ from^#(X) -> c_1(from^#(s(X)))
, minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.
DPs:
{ 2: minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
Sub-proof:
----------
The following argument positions are usable:
Uargs(c_1) = {1}, Uargs(c_3) = {1}
TcT has computed the following constructor-based matrix
interpretation satisfying not(EDA).
[from](x1) = [7] x1 + [0]
[cons](x1, x2) = [1] x1 + [1] x2 + [0]
[s](x1) = [1] x1 + [4]
[sel](x1, x2) = [7] x1 + [7] x2 + [0]
[0] = [0]
[minus](x1, x2) = [7] x1 + [7] x2 + [0]
[quot](x1, x2) = [7] x1 + [7] x2 + [0]
[zWquot](x1, x2) = [7] x1 + [7] x2 + [0]
[nil] = [0]
[from^#](x1) = [0]
[c_1](x1) = [7] x1 + [0]
[sel^#](x1, x2) = [7] x1 + [7] x2 + [0]
[c_2](x1) = [7] x1 + [0]
[c_3] = [0]
[minus^#](x1, x2) = [2] x1 + [1]
[c_4] = [0]
[c_5](x1) = [7] x1 + [0]
[quot^#](x1, x2) = [7] x1 + [7] x2 + [0]
[c_6](x1) = [7] x1 + [0]
[c_7] = [0]
[zWquot^#](x1, x2) = [7] x1 + [7] x2 + [0]
[c_8] = [0]
[c_9](x1, x2) = [7] x1 + [7] x2 + [0]
[c_10] = [0]
[c] = [0]
[c_1](x1) = [1] x1 + [0]
[c_2](x1) = [7] x1 + [0]
[c_3](x1) = [1] x1 + [5]
[c_4](x1) = [7] x1 + [0]
The following symbols are considered usable
{from^#, minus^#}
The order satisfies the following ordering constraints:
[from^#(X)] = [0]
>= [0]
= [c_1(from^#(s(X)))]
[minus^#(s(X), s(Y))] = [2] X + [9]
> [2] X + [6]
= [c_3(minus^#(X, Y))]
The strictly oriented rules are moved into the weak component.
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { from^#(X) -> c_1(from^#(s(X))) }
Weak DPs: { minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
Obligation:
innermost runtime complexity
Answer:
MAYBE
The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.
{ minus^#(s(X), s(Y)) -> c_3(minus^#(X, Y)) }
We are left with following problem, upon which TcT provides the
certificate MAYBE.
Strict DPs: { from^#(X) -> c_1(from^#(s(X))) }
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) '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) 'Polynomial Path Order (PS)' failed due to the following reason:
The input cannot be shown compatible
2) 'Fastest (timeout of 5 seconds)' failed due to the following
reason:
Computation stopped due to timeout after 5.0 seconds.
3) 'Polynomial Path Order (PS)' failed due to the following reason:
The input cannot be shown compatible
Arrrr..