Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.15 |
|---|
stdout:
MAYBE
Problem:
f(0()) -> 1()
f(s(x)) -> g(f(x))
g(x) -> +(x,s(x))
f(s(x)) -> +(f(x),s(f(x)))
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.15 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.15 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
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^#(0()) -> c_0()
, 2: f^#(s(x)) -> c_1(g^#(f(x)))
, 3: g^#(x) -> c_2()
, 4: f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ inherited ]
|
|->{1} [ MAYBE ]
|
`->{2} [ inherited ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* Path {4}: inherited
-------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{1}: MAYBE
--------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(+) = {},
Uargs(f^#) = {}, Uargs(c_1) = {}, Uargs(g^#) = {},
Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
0() = [0]
[0]
[0]
1() = [0]
[0]
[0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
+(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]
f^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {f^#(0()) -> c_0()}
Weak Rules: {f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Proof Output:
The input cannot be shown compatible
* Path {4}->{2}: inherited
------------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{2}->{3}: NA
----------------------
The usable rules for this path are:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x))}
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^#(0()) -> c_0()
, 2: f^#(s(x)) -> c_1(g^#(f(x)))
, 3: g^#(x) -> c_2()
, 4: f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ inherited ]
|
|->{1} [ MAYBE ]
|
`->{2} [ inherited ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* Path {4}: inherited
-------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{1}: MAYBE
--------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(+) = {},
Uargs(f^#) = {}, Uargs(c_1) = {}, Uargs(g^#) = {},
Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
1() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
+(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
f^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {f^#(0()) -> c_0()}
Weak Rules: {f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Proof Output:
The input cannot be shown compatible
* Path {4}->{2}: inherited
------------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{2}->{3}: NA
----------------------
The usable rules for this path are:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x))}
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.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(0()) -> c_0()
, 2: f^#(s(x)) -> c_1(g^#(f(x)))
, 3: g^#(x) -> c_2()
, 4: f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ inherited ]
|
|->{1} [ MAYBE ]
|
`->{2} [ inherited ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* Path {4}: inherited
-------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{1}: MAYBE
--------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(+) = {},
Uargs(f^#) = {}, Uargs(c_1) = {}, Uargs(g^#) = {},
Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
0() = [0]
1() = [0]
s(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
+(x1, x2) = [0] x1 + [0] x2 + [0]
f^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {f^#(0()) -> c_0()}
Weak Rules: {f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Proof Output:
The input cannot be shown compatible
* Path {4}->{2}: inherited
------------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{2}->{3}: NA
----------------------
The usable rules for this path are:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x))}
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.
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 2.15 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 2.15 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
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^#(0()) -> c_0()
, 2: f^#(s(x)) -> c_1(g^#(f(x)))
, 3: g^#(x) -> c_2(x, x)
, 4: f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ inherited ]
|
|->{1} [ MAYBE ]
|
`->{2} [ inherited ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* Path {4}: inherited
-------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{1}: MAYBE
--------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(+) = {},
Uargs(f^#) = {}, Uargs(c_1) = {}, Uargs(g^#) = {}, Uargs(c_2) = {},
Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
0() = [0]
[0]
[0]
1() = [0]
[0]
[0]
s(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
+(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]
f^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
g^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2(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_3(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {f^#(0()) -> c_0()}
Weak Rules: {f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Proof Output:
The input cannot be shown compatible
* Path {4}->{2}: inherited
------------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{2}->{3}: NA
----------------------
The usable rules for this path are:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x))}
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^#(0()) -> c_0()
, 2: f^#(s(x)) -> c_1(g^#(f(x)))
, 3: g^#(x) -> c_2(x, x)
, 4: f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ inherited ]
|
|->{1} [ MAYBE ]
|
`->{2} [ inherited ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* Path {4}: inherited
-------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{1}: MAYBE
--------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(+) = {},
Uargs(f^#) = {}, Uargs(c_1) = {}, Uargs(g^#) = {}, Uargs(c_2) = {},
Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1) = [0 0] x1 + [0]
[0 0] [0]
0() = [0]
[0]
1() = [0]
[0]
s(x1) = [0 0] x1 + [0]
[0 0] [0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
+(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
f^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
g^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {f^#(0()) -> c_0()}
Weak Rules: {f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Proof Output:
The input cannot be shown compatible
* Path {4}->{2}: inherited
------------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{2}->{3}: NA
----------------------
The usable rules for this path are:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x))}
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.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(0()) -> c_0()
, 2: f^#(s(x)) -> c_1(g^#(f(x)))
, 3: g^#(x) -> c_2(x, x)
, 4: f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ inherited ]
|
|->{1} [ MAYBE ]
|
`->{2} [ inherited ]
|
`->{3} [ NA ]
Sub-problems:
-------------
* Path {4}: inherited
-------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{1}: MAYBE
--------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(s) = {}, Uargs(g) = {}, Uargs(+) = {},
Uargs(f^#) = {}, Uargs(c_1) = {}, Uargs(g^#) = {}, Uargs(c_2) = {},
Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
0() = [0]
1() = [0]
s(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
+(x1, x2) = [0] x1 + [0] x2 + [0]
f^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
g^#(x1) = [0] x1 + [0]
c_2(x1, x2) = [0] x1 + [0] x2 + [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {f^#(0()) -> c_0()}
Weak Rules: {f^#(s(x)) -> c_3(f^#(x), f^#(x))}
Proof Output:
The input cannot be shown compatible
* Path {4}->{2}: inherited
------------------------
This path is subsumed by the proof of path {4}->{2}->{3}.
* Path {4}->{2}->{3}: NA
----------------------
The usable rules for this path are:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, f(s(x)) -> +(f(x), s(f(x)))
, g(x) -> +(x, s(x))}
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.
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 pair2rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.15 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
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 pair3irc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.15 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
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 2.15 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
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 | TIMEOUT |
|---|
| Input | SK90 2.15 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool tup3irc
| Execution Time | 60.05495ms |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 2.15 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(0()) -> 1()
, f(s(x)) -> g(f(x))
, g(x) -> +(x, s(x))
, f(s(x)) -> +(f(x), s(f(x)))}
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..