Tool CaT
stdout:
MAYBE
Problem:
f(x,x) -> g(f(x,x))
g(x) -> a()
Proof:
Complexity Transformation Processor:
strict:
f(x,x) -> g(f(x,x))
g(x) -> a()
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[a] = 0,
[g](x0) = x0 + 241,
[f](x0, x1) = x0 + x1 + 24
orientation:
f(x,x) = 2x + 24 >= 2x + 265 = g(f(x,x))
g(x) = x + 241 >= 0 = a()
problem:
strict:
f(x,x) -> g(f(x,x))
weak:
g(x) -> a()
Open
Tool 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(x, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, 2: g^#(x) -> c_1()}
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, x) -> g(f(x, x))
, g(x) -> a()}
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:
{ f^#(x, x) -> c_0(g^#(f(x, x)))
, g^#(x) -> c_1()
, f(x, x) -> g(f(x, x))
, g(x) -> a()}
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^#(x, x) -> c_0(g^#(f(x, x)))
, 2: g^#(x) -> c_1()}
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, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, g^#(x) -> c_1()
, f(x, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, 2: g^#(x) -> c_1()}
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, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, g^#(x) -> c_1()
, f(x, x) -> g(f(x, x))
, g(x) -> a()}
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(x, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, 2: g^#(x) -> c_1()}
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, x) -> g(f(x, x))
, g(x) -> a()}
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:
{ f^#(x, x) -> c_0(g^#(f(x, x)))
, g^#(x) -> c_1()
, f(x, x) -> g(f(x, x))
, g(x) -> a()}
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^#(x, x) -> c_0(g^#(f(x, x)))
, 2: g^#(x) -> c_1()}
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, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, g^#(x) -> c_1()
, f(x, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, 2: g^#(x) -> c_1()}
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, x) -> g(f(x, x))
, g(x) -> a()}
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, x) -> c_0(g^#(f(x, x)))
, g^#(x) -> c_1()
, f(x, x) -> g(f(x, x))
, g(x) -> a()}
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.