Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.51 |
|---|
stdout:
MAYBE
Problem:
ack(0(),y) -> s(y)
ack(s(x),0()) -> ack(x,s(0()))
ack(s(x),s(y)) -> ack(x,ack(s(x),y))
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.51 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.51 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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: ack^#(0(), y) -> c_0()
, 2: ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, 3: ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{2} [ inherited ]
|
|->{1} [ YES(?,O(n^1)) ]
|
`->{3} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{1}: YES(?,O(n^1))
----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(ack) = {}, Uargs(s) = {}, Uargs(ack^#) = {},
Uargs(c_1) = {1}, Uargs(c_2) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
ack(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
ack^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_2(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {ack^#(0(), y) -> c_0()}
Weak Rules: {ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[3]
[0]
s(x1) = [1 1 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
ack^#(x1, x2) = [2 2 0] x1 + [2 3 0] x2 + [0]
[0 0 0] [0 0 0] [1]
[0 2 0] [0 0 0] [0]
c_0() = [1]
[1]
[0]
c_1(x1) = [1 2 0] x1 + [1]
[0 0 0] [1]
[0 0 0] [0]
* Path {2}->{3}: inherited
------------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{3}->{1}: NA
----------------------
The usable rules for this path are:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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: ack^#(0(), y) -> c_0()
, 2: ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, 3: ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{2} [ inherited ]
|
|->{1} [ YES(?,O(n^1)) ]
|
`->{3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{1}: YES(?,O(n^1))
----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(ack) = {}, Uargs(s) = {}, Uargs(ack^#) = {},
Uargs(c_1) = {1}, Uargs(c_2) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
ack(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
ack^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {ack^#(0(), y) -> c_0()}
Weak Rules: {ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [1]
[3]
s(x1) = [1 2] x1 + [2]
[0 0] [0]
ack^#(x1, x2) = [0 0] x1 + [0 1] x2 + [1]
[2 0] [4 0] [0]
c_0() = [0]
[0]
c_1(x1) = [4 0] x1 + [0]
[0 0] [7]
* Path {2}->{3}: inherited
------------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{3}->{1}: MAYBE
-------------------------
The usable rules for this path are:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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:
{ ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))
, ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, ack^#(0(), y) -> c_0()
, ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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: ack^#(0(), y) -> c_0()
, 2: ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, 3: ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{2} [ inherited ]
|
|->{1} [ YES(?,O(n^1)) ]
|
`->{3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{1}: YES(?,O(n^1))
----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(ack) = {}, Uargs(s) = {}, Uargs(ack^#) = {},
Uargs(c_1) = {1}, Uargs(c_2) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
ack(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
ack^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {ack^#(0(), y) -> c_0()}
Weak Rules: {ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
s(x1) = [1] x1 + [2]
ack^#(x1, x2) = [2] x1 + [2] x2 + [0]
c_0() = [1]
c_1(x1) = [1] x1 + [0]
* Path {2}->{3}: inherited
------------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{3}->{1}: MAYBE
-------------------------
The usable rules for this path are:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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:
{ ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))
, ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, ack^#(0(), y) -> c_0()
, ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.51 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.51 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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: ack^#(0(), y) -> c_0(y)
, 2: ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, 3: ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{2} [ inherited ]
|
|->{1} [ YES(?,O(n^1)) ]
|
`->{3} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{1}: YES(?,O(n^1))
----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(ack) = {}, Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {1}, Uargs(c_2) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
ack(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
0() = [0]
[0]
[0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
ack^#(x1, x2) = [0 0 0] x1 + [3 3 3] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [1 1 1] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
c_2(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {ack^#(0(), y) -> c_0(y)}
Weak Rules: {ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[2]
[2]
s(x1) = [1 2 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
ack^#(x1, x2) = [1 2 0] x1 + [0 0 0] x2 + [0]
[2 0 2] [4 0 0] [0]
[2 0 0] [4 0 0] [0]
c_0(x1) = [0 0 0] x1 + [1]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [1 0 0] x1 + [0]
[0 0 0] [3]
[0 0 0] [7]
* Path {2}->{3}: inherited
------------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{3}->{1}: NA
----------------------
The usable rules for this path are:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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: ack^#(0(), y) -> c_0(y)
, 2: ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, 3: ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{2} [ inherited ]
|
|->{1} [ YES(?,O(n^1)) ]
|
`->{3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{1}: YES(?,O(n^1))
----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(ack) = {}, Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {1}, Uargs(c_2) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
ack(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
0() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
ack^#(x1, x2) = [0 0] x1 + [3 3] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [1 1] x1 + [0]
[0 0] [0]
c_1(x1) = [1 0] x1 + [0]
[0 1] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {ack^#(0(), y) -> c_0(y)}
Weak Rules: {ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [2]
[1]
s(x1) = [1 2] x1 + [0]
[0 0] [0]
ack^#(x1, x2) = [2 0] x1 + [2 4] x2 + [0]
[2 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [1]
[0 0] [0]
c_1(x1) = [1 0] x1 + [0]
[0 0] [0]
* Path {2}->{3}: inherited
------------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{3}->{1}: MAYBE
-------------------------
The usable rules for this path are:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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:
{ ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))
, ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, ack^#(0(), y) -> c_0(y)
, ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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: ack^#(0(), y) -> c_0(y)
, 2: ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, 3: ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{2} [ inherited ]
|
|->{1} [ YES(?,O(n^1)) ]
|
`->{3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{1}: YES(?,O(n^1))
----------------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(ack) = {}, Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_0) = {},
Uargs(c_1) = {1}, Uargs(c_2) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
ack(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
ack^#(x1, x2) = [0] x1 + [3] x2 + [0]
c_0(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [0] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {ack^#(0(), y) -> c_0(y)}
Weak Rules: {ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))}
Proof Output:
The following argument positions are usable:
Uargs(s) = {}, Uargs(ack^#) = {}, Uargs(c_0) = {}, Uargs(c_1) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
0() = [4]
s(x1) = [1] x1 + [2]
ack^#(x1, x2) = [2] x1 + [2] x2 + [0]
c_0(x1) = [0] x1 + [1]
c_1(x1) = [1] x1 + [0]
* Path {2}->{3}: inherited
------------------------
This path is subsumed by the proof of path {2}->{3}->{1}.
* Path {2}->{3}->{1}: MAYBE
-------------------------
The usable rules for this path are:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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:
{ ack^#(s(x), s(y)) -> c_2(ack^#(x, ack(s(x), y)))
, ack^#(s(x), 0()) -> c_1(ack^#(x, s(0())))
, ack^#(0(), y) -> c_0(y)
, ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(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 pair1rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.51 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), 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 pair3irc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.51 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), y))}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.51 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), 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 | SK90 2.51 |
|---|
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), 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:
{ ack^#(0(), y) -> c_1(y)
, ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
, ack^#(s(x), s(y)) -> c_3(ack^#(x, ack(s(x), y)))}
We consider the following Problem:
Strict DPs:
{ ack^#(0(), y) -> c_1(y)
, ack^#(s(x), 0()) -> c_2(ack^#(x, s(0())))
, ack^#(s(x), s(y)) -> c_3(ack^#(x, ack(s(x), y)))}
Strict Trs:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), y))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'usablerules':
-----------------------------
All rules are usable.
No subproblems were generated.
Arrrr..Tool tup3irc
| Execution Time | 61.54607ms |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.51 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ ack(0(), y) -> s(y)
, ack(s(x), 0()) -> ack(x, s(0()))
, ack(s(x), s(y)) -> ack(x, ack(s(x), 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..