Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | AG01 3.47 |
|---|
stdout:
MAYBE
Problem:
f(x,c(y)) -> f(x,s(f(y,y)))
f(s(x),y) -> f(x,s(c(y)))
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | AG01 3.47 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | AG01 3.47 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, 2: f^#(s(x), y) -> c_1(f^#(x, s(c(y))))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1} [ NA ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: NA
------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {2}, Uargs(c) = {}, Uargs(s) = {1}, Uargs(f^#) = {2},
Uargs(c_0) = {1}, Uargs(c_1) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0 1] x1 + [1 2 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 1 0] [0]
c(x1) = [1 2 0] x1 + [1]
[0 1 2] [0]
[0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [2]
f^#(x1, x2) = [3 3 3] x1 + [2 1 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
Complexity induced by the adequate RMI: YES(?,O(n^3))
We have not generated a proof for the resulting sub-problem.
* Path {1}->{2}: NA
-----------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {2}, Uargs(c) = {}, Uargs(s) = {1}, Uargs(f^#) = {2},
Uargs(c_0) = {1}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0 2] x1 + [1 2 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 1 0] [0]
c(x1) = [1 2 0] x1 + [0]
[0 1 2] [1]
[0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 1] [0]
[0 0 1] [1]
f^#(x1, x2) = [0 0 0] x1 + [1 2 3] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_0(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
Complexity induced by the adequate RMI: YES(?,O(n^3))
We have not generated a proof for the resulting sub-problem.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, 2: f^#(s(x), y) -> c_1(f^#(x, s(c(y))))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1} [ inherited ]
|
`->{2} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: inherited
-------------------
This path is subsumed by the proof of path {1}->{2}.
* Path {1}->{2}: MAYBE
--------------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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:
{ f^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, f^#(s(x), y) -> c_1(f^#(x, s(c(y))))
, f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, 2: f^#(s(x), y) -> c_1(f^#(x, s(c(y))))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1} [ inherited ]
|
`->{2} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: inherited
-------------------
This path is subsumed by the proof of path {1}->{2}.
* Path {1}->{2}: MAYBE
--------------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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:
{ f^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, f^#(s(x), y) -> c_1(f^#(x, s(c(y))))
, f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | AG01 3.47 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | AG01 3.47 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, 2: f^#(s(x), y) -> c_1(f^#(x, s(c(y))))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1} [ inherited ]
|
`->{2} [ NA ]
Sub-problems:
-------------
* Path {1}: inherited
-------------------
This path is subsumed by the proof of path {1}->{2}.
* Path {1}->{2}: NA
-----------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, 2: f^#(s(x), y) -> c_1(f^#(x, s(c(y))))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1} [ inherited ]
|
`->{2} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: inherited
-------------------
This path is subsumed by the proof of path {1}->{2}.
* Path {1}->{2}: MAYBE
--------------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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:
{ f^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, f^#(s(x), y) -> c_1(f^#(x, s(c(y))))
, f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, 2: f^#(s(x), y) -> c_1(f^#(x, s(c(y))))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1} [ inherited ]
|
`->{2} [ MAYBE ]
Sub-problems:
-------------
* Path {1}: inherited
-------------------
This path is subsumed by the proof of path {1}->{2}.
* Path {1}->{2}: MAYBE
--------------------
The usable rules for this path are:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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:
{ f^#(x, c(y)) -> c_0(f^#(x, s(f(y, y))))
, f^#(s(x), y) -> c_1(f^#(x, s(c(y))))
, f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
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 pair1rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | AG01 3.47 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair2rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | AG01 3.47 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3irc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^2)) |
|---|
| Input | AG01 3.47 |
|---|
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^2))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 3 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {2}, Uargs(c) = {}, Uargs(s) = {1}
We have the following constructor-restricted (at most 2 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0 1] x1 + [1 2 0] x2 + [1]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 2 0] [0]
c(x1) = [1 2 0] x1 + [0]
[0 0 2] [2]
[0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [1]
Hurray, we answered YES(?,O(n^2))Tool pair3rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | AG01 3.47 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool rc
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | AG01 3.47 |
|---|
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Sequentially' 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) 'matrix-interpretation of dimension 4 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) 'matrix-interpretation of dimension 3 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
3) 'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) 'Fastest' 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' (timeout of 100.0 seconds)' failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match' (timeout of 5.0 seconds)' failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'dp' failed due to the following reason:
We have computed the following dependency pairs
Strict Dependency Pairs:
{ f^#(x, c(y)) -> c_1(f^#(x, s(f(y, y))))
, f^#(s(x), y) -> c_2(f^#(x, s(c(y))))}
We consider the following Problem:
Strict DPs:
{ f^#(x, c(y)) -> c_1(f^#(x, s(f(y, y))))
, f^#(s(x), y) -> c_2(f^#(x, s(c(y))))}
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'usablerules':
-----------------------------
All rules are usable.
No subproblems were generated.
Arrrr..Tool tup3irc
| Execution Time | 2.2489748ms |
|---|
| Answer | YES(?,O(n^2)) |
|---|
| Input | AG01 3.47 |
|---|
stdout:
YES(?,O(n^2))
We consider the following Problem:
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^2))
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(x, c(y)) -> f(x, s(f(y, y)))
, f(s(x), y) -> f(x, s(c(y)))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 3 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {2}, Uargs(c) = {}, Uargs(s) = {1}
We have the following constructor-restricted (at most 2 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0 1] x1 + [1 2 0] x2 + [1]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 2 0] [0]
c(x1) = [1 2 0] x1 + [0]
[0 0 2] [2]
[0 0 0] [0]
s(x1) = [1 0 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [1]
Hurray, we answered YES(?,O(n^2))