Tool CaT
stdout:
MAYBE
Problem:
f(s(x),y) -> f(x,f(x,y))
f(0(),y) -> c(y,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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(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: f^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, 2: f^#(0(), y) -> 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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 3'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, f^#(0(), y) -> c_1()
, f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, y)}
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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, 2: f^#(0(), y) -> 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, f^#(0(), y) -> c_1()
, f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, 2: f^#(0(), y) -> 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, f^#(0(), y) -> c_1()
, f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(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: f^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, 2: f^#(0(), y) -> c_1(y, 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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 3'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, f^#(0(), y) -> c_1(y, y)
, f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, y)}
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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, 2: f^#(0(), y) -> c_1(y, 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, f^#(0(), y) -> c_1(y, y)
, f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, 2: f^#(0(), y) -> c_1(y, 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(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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^#(s(x), y) -> c_0(f^#(x, f(x, y)))
, f^#(0(), y) -> c_1(y, y)
, f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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 pair3rc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, 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 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) '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) 'dp' failed due to the following reason:
We have computed the following dependency pairs
Strict Dependency Pairs:
{ f^#(s(x), y) -> c_1(f^#(x, f(x, y)))
, f^#(0(), y) -> c_2(y, y)}
We consider the following Problem:
Strict DPs:
{ f^#(s(x), y) -> c_1(f^#(x, f(x, y)))
, f^#(0(), y) -> c_2(y, y)}
Strict Trs:
{ f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, y)}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'usablerules':
-----------------------------
All rules are usable.
No subproblems were generated.
Arrrr..Tool tup3irc
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, f(x, y))
, f(0(), y) -> c(y, y)}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..