Tool CaT
stdout:
MAYBE
Problem:
g(x,x) -> f(f(x,x),x)
f(x,x) -> g(x,x)
f(x,y) -> y
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:
{ g(x, x) -> f(f(x, x), x)
, f(x, x) -> g(x, x)
, f(x, y) -> 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: g^#(x, x) -> c_0(f^#(f(x, x), x))
, 2: f^#(x, x) -> c_1(g^#(x, x))
, 3: f^#(x, y) -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ inherited ]
|
`->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: inherited
---------------------
This path is subsumed by the proof of path {1,2}->{3}.
* Path {1,2}->{3}: MAYBE
----------------------
The usable rules for this path are:
{ f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g^#(x, x) -> c_0(f^#(f(x, x), x))
, f^#(x, x) -> c_1(g^#(x, x))
, f^#(x, y) -> c_2()
, f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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: g^#(x, x) -> c_0(f^#(f(x, x), x))
, 2: f^#(x, x) -> c_1(g^#(x, x))
, 3: f^#(x, y) -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ inherited ]
|
`->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: inherited
---------------------
This path is subsumed by the proof of path {1,2}->{3}.
* Path {1,2}->{3}: MAYBE
----------------------
The usable rules for this path are:
{ f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g^#(x, x) -> c_0(f^#(f(x, x), x))
, f^#(x, x) -> c_1(g^#(x, x))
, f^#(x, y) -> c_2()
, f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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: g^#(x, x) -> c_0(f^#(f(x, x), x))
, 2: f^#(x, x) -> c_1(g^#(x, x))
, 3: f^#(x, y) -> c_2()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ inherited ]
|
`->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: inherited
---------------------
This path is subsumed by the proof of path {1,2}->{3}.
* Path {1,2}->{3}: MAYBE
----------------------
The usable rules for this path are:
{ f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g^#(x, x) -> c_0(f^#(f(x, x), x))
, f^#(x, x) -> c_1(g^#(x, x))
, f^#(x, y) -> c_2()
, f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g(x, x) -> f(f(x, x), x)
, f(x, x) -> g(x, x)
, f(x, y) -> 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: g^#(x, x) -> c_0(f^#(f(x, x), x))
, 2: f^#(x, x) -> c_1(g^#(x, x))
, 3: f^#(x, y) -> c_2(y)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ inherited ]
|
`->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: inherited
---------------------
This path is subsumed by the proof of path {1,2}->{3}.
* Path {1,2}->{3}: MAYBE
----------------------
The usable rules for this path are:
{ f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g^#(x, x) -> c_0(f^#(f(x, x), x))
, f^#(x, x) -> c_1(g^#(x, x))
, f^#(x, y) -> c_2(y)
, f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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: g^#(x, x) -> c_0(f^#(f(x, x), x))
, 2: f^#(x, x) -> c_1(g^#(x, x))
, 3: f^#(x, y) -> c_2(y)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ inherited ]
|
`->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: inherited
---------------------
This path is subsumed by the proof of path {1,2}->{3}.
* Path {1,2}->{3}: MAYBE
----------------------
The usable rules for this path are:
{ f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g^#(x, x) -> c_0(f^#(f(x, x), x))
, f^#(x, x) -> c_1(g^#(x, x))
, f^#(x, y) -> c_2(y)
, f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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: g^#(x, x) -> c_0(f^#(f(x, x), x))
, 2: f^#(x, x) -> c_1(g^#(x, x))
, 3: f^#(x, y) -> c_2(y)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ inherited ]
|
`->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: inherited
---------------------
This path is subsumed by the proof of path {1,2}->{3}.
* Path {1,2}->{3}: MAYBE
----------------------
The usable rules for this path are:
{ f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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:
{ g^#(x, x) -> c_0(f^#(f(x, x), x))
, f^#(x, x) -> c_1(g^#(x, x))
, f^#(x, y) -> c_2(y)
, f(x, x) -> g(x, x)
, f(x, y) -> y
, g(x, x) -> f(f(x, x), 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.