Tool CaT
stdout:
MAYBE
Problem:
f(h(x),c()) -> f(i(x),s(x))
h(x) -> f(h(x),c())
i(x) -> h(x)
f(i(x),y) -> x
Proof:
OpenTool IRC1
stdout:
MAYBE
Warning when parsing problem:
Unsupported strategy 'OUTERMOST'Tool IRC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(h(x), c()) -> f(i(x), s(x))
, h(x) -> f(h(x), c())
, i(x) -> h(x)
, f(i(x), y) -> x}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(h(x), c()) -> c_0(f^#(i(x), s(x)))
, 2: h^#(x) -> c_1(f^#(h(x), c()))
, 3: i^#(x) -> c_2(h^#(x))
, 4: f^#(i(x), y) -> c_3()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ inherited ]
|
`->{2} [ inherited ]
|
|->{1} [ inherited ]
| |
| `->{4} [ NA ]
|
`->{4} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: inherited
-------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}: inherited
------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}: inherited
-----------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}->{4}: NA
---------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}->{2}->{4}: MAYBE
-------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ h^#(x) -> c_1(f^#(h(x), c()))
, i^#(x) -> c_2(h^#(x))
, f^#(i(x), y) -> c_3()
, h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
Proof Output:
The input cannot be shown compatible
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(h(x), c()) -> c_0(f^#(i(x), s(x)))
, 2: h^#(x) -> c_1(f^#(h(x), c()))
, 3: i^#(x) -> c_2(h^#(x))
, 4: f^#(i(x), y) -> c_3()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ inherited ]
|
`->{2} [ inherited ]
|
|->{1} [ inherited ]
| |
| `->{4} [ NA ]
|
`->{4} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: inherited
-------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}: inherited
------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}: inherited
-----------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}->{4}: NA
---------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}->{2}->{4}: MAYBE
-------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ h^#(x) -> c_1(f^#(h(x), c()))
, i^#(x) -> c_2(h^#(x))
, f^#(i(x), y) -> c_3()
, h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
Proof Output:
The input cannot be shown compatible
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(h(x), c()) -> c_0(f^#(i(x), s(x)))
, 2: h^#(x) -> c_1(f^#(h(x), c()))
, 3: i^#(x) -> c_2(h^#(x))
, 4: f^#(i(x), y) -> c_3()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ inherited ]
|
`->{2} [ inherited ]
|
|->{1} [ inherited ]
| |
| `->{4} [ NA ]
|
`->{4} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: inherited
-------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}: inherited
------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}: inherited
-----------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}->{4}: NA
---------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}->{2}->{4}: MAYBE
-------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ h^#(x) -> c_1(f^#(h(x), c()))
, i^#(x) -> c_2(h^#(x))
, f^#(i(x), y) -> c_3()
, h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
Proof Output:
The input cannot be shown compatible
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Tool RC1
stdout:
MAYBE
Warning when parsing problem:
Unsupported strategy 'OUTERMOST'Tool RC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f(h(x), c()) -> f(i(x), s(x))
, h(x) -> f(h(x), c())
, i(x) -> h(x)
, f(i(x), y) -> x}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(h(x), c()) -> c_0(f^#(i(x), s(x)))
, 2: h^#(x) -> c_1(f^#(h(x), c()))
, 3: i^#(x) -> c_2(h^#(x))
, 4: f^#(i(x), y) -> c_3(x)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ inherited ]
|
`->{2} [ inherited ]
|
|->{1} [ inherited ]
| |
| `->{4} [ NA ]
|
`->{4} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: inherited
-------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}: inherited
------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}: inherited
-----------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}->{4}: NA
---------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}->{2}->{4}: MAYBE
-------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ h^#(x) -> c_1(f^#(h(x), c()))
, i^#(x) -> c_2(h^#(x))
, f^#(i(x), y) -> c_3(x)
, h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
Proof Output:
The input cannot be shown compatible
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(h(x), c()) -> c_0(f^#(i(x), s(x)))
, 2: h^#(x) -> c_1(f^#(h(x), c()))
, 3: i^#(x) -> c_2(h^#(x))
, 4: f^#(i(x), y) -> c_3(x)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ inherited ]
|
`->{2} [ inherited ]
|
|->{1} [ inherited ]
| |
| `->{4} [ NA ]
|
`->{4} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: inherited
-------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}: inherited
------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}: inherited
-----------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}->{4}: NA
---------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}->{2}->{4}: MAYBE
-------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ h^#(x) -> c_1(f^#(h(x), c()))
, i^#(x) -> c_2(h^#(x))
, f^#(i(x), y) -> c_3(x)
, h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
Proof Output:
The input cannot be shown compatible
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(h(x), c()) -> c_0(f^#(i(x), s(x)))
, 2: h^#(x) -> c_1(f^#(h(x), c()))
, 3: i^#(x) -> c_2(h^#(x))
, 4: f^#(i(x), y) -> c_3(x)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{3} [ inherited ]
|
`->{2} [ inherited ]
|
|->{1} [ inherited ]
| |
| `->{4} [ NA ]
|
`->{4} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: inherited
-------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}: inherited
------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}: inherited
-----------------------------
This path is subsumed by the proof of path {3}->{2}->{1}->{4}.
* Path {3}->{2}->{1}->{4}: NA
---------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {3}->{2}->{4}: MAYBE
-------------------------
The usable rules for this path are:
{ h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ h^#(x) -> c_1(f^#(h(x), c()))
, i^#(x) -> c_2(h^#(x))
, f^#(i(x), y) -> c_3(x)
, h(x) -> f(h(x), c())
, f(h(x), c()) -> f(i(x), s(x))
, f(i(x), y) -> x
, i(x) -> h(x)}
Proof Output:
The input cannot be shown compatible
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.