Tool CaT
stdout:
MAYBE
Problem:
f(f(0(),x),1()) -> f(g(f(x,x)),x)
f(g(x),y) -> g(f(x,y))
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, 2: f^#(g(x), y) -> c_1(f^#(x, y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ NA ]
Sub-problems:
-------------
* Path {1,2}: NA
--------------
The usable rules for this path are:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, 2: f^#(g(x), y) -> c_1(f^#(x, y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: MAYBE
-----------------
The usable rules for this path are:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, f^#(g(x), y) -> c_1(f^#(x, y))
, f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, 2: f^#(g(x), y) -> c_1(f^#(x, y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: MAYBE
-----------------
The usable rules for this path are:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, f^#(g(x), y) -> c_1(f^#(x, y))
, f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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
stdout:
MAYBE
Tool RC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, 2: f^#(g(x), y) -> c_1(f^#(x, y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ NA ]
Sub-problems:
-------------
* Path {1,2}: NA
--------------
The usable rules for this path are:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, 2: f^#(g(x), y) -> c_1(f^#(x, y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: MAYBE
-----------------
The usable rules for this path are:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, f^#(g(x), y) -> c_1(f^#(x, y))
, f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, 2: f^#(g(x), y) -> c_1(f^#(x, y))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{1,2} [ MAYBE ]
Sub-problems:
-------------
* Path {1,2}: MAYBE
-----------------
The usable rules for this path are:
{ f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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^#(f(0(), x), 1()) -> c_0(f^#(g(f(x, x)), x))
, f^#(g(x), y) -> c_1(f^#(x, y))
, f(f(0(), x), 1()) -> f(g(f(x, x)), x)
, f(g(x), y) -> g(f(x, 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.