Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | Der95 21 |
|---|
stdout:
MAYBE
Problem:
p(s(x)) -> x
fact(0()) -> s(0())
fact(s(x)) -> *(s(x),fact(p(s(x))))
*(0(),y) -> 0()
*(s(x),y) -> +(*(x,y),y)
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | Der95 21 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | Der95 21 |
|---|
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | Der95 21 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | Der95 21 |
|---|
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool pair1rc
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | Der95 21 |
|---|
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: none
1) None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'dp' failed due to the following reason:
We have computed the following dependency pairs
Strict Dependency Pairs:
{ p^#(s(x)) -> c_1(x)
, fact^#(0()) -> c_2()
, fact^#(s(x)) -> c_3(*^#(s(x), fact(p(s(x)))))
, *^#(0(), y) -> c_4()
, *^#(s(x), y) -> c_5(+^#(*(x, y), y))
, +^#(x, 0()) -> c_6(x)
, +^#(x, s(y)) -> c_7(+^#(x, y))}
We consider the following Problem:
Strict DPs:
{ p^#(s(x)) -> c_1(x)
, fact^#(0()) -> c_2()
, fact^#(s(x)) -> c_3(*^#(s(x), fact(p(s(x)))))
, *^#(0(), y) -> c_4()
, *^#(s(x), y) -> c_5(+^#(*(x, y), y))
, +^#(x, 0()) -> c_6(x)
, +^#(x, s(y)) -> c_7(+^#(x, y))}
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'Fastest':
-------------------------
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
'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):
-----------------------------
'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) '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 3 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) '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 minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Arrrr..Tool pair2rc
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | Der95 21 |
|---|
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: none
1) None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'dp' failed due to the following reason:
We have computed the following dependency pairs
Strict Dependency Pairs:
{ p^#(s(x)) -> c_1(x)
, fact^#(0()) -> c_2()
, fact^#(s(x)) -> c_3(*^#(s(x), fact(p(s(x)))))
, *^#(0(), y) -> c_4()
, *^#(s(x), y) -> c_5(+^#(*(x, y), y))
, +^#(x, 0()) -> c_6(x)
, +^#(x, s(y)) -> c_7(+^#(x, y))}
We consider the following Problem:
Strict DPs:
{ p^#(s(x)) -> c_1(x)
, fact^#(0()) -> c_2()
, fact^#(s(x)) -> c_3(*^#(s(x), fact(p(s(x)))))
, *^#(0(), y) -> c_4()
, *^#(s(x), y) -> c_5(+^#(*(x, y), y))
, +^#(x, 0()) -> c_6(x)
, +^#(x, s(y)) -> c_7(+^#(x, y))}
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'Fastest':
-------------------------
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
'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):
-----------------------------
'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) '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 3 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) '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 minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Arrrr..Tool pair3irc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | Der95 21 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> 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 | Der95 21 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> 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 | Der95 21 |
|---|
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> 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 3 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) '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 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) '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) 'dp' failed due to the following reason:
We have computed the following dependency pairs
Strict Dependency Pairs:
{ p^#(s(x)) -> c_1(x)
, fact^#(0()) -> c_2()
, fact^#(s(x)) -> c_3(*^#(s(x), fact(p(s(x)))))
, *^#(0(), y) -> c_4()
, *^#(s(x), y) -> c_5(+^#(*(x, y), y))
, +^#(x, 0()) -> c_6(x)
, +^#(x, s(y)) -> c_7(+^#(x, y))}
We consider the following Problem:
Strict DPs:
{ p^#(s(x)) -> c_1(x)
, fact^#(0()) -> c_2()
, fact^#(s(x)) -> c_3(*^#(s(x), fact(p(s(x)))))
, *^#(0(), y) -> c_4()
, *^#(s(x), y) -> c_5(+^#(*(x, y), y))
, +^#(x, 0()) -> c_6(x)
, +^#(x, s(y)) -> c_7(+^#(x, y))}
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> 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 | 60.062115ms |
|---|
| Answer | TIMEOUT |
|---|
| Input | Der95 21 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ p(s(x)) -> x
, fact(0()) -> s(0())
, fact(s(x)) -> *(s(x), fact(p(s(x))))
, *(0(), y) -> 0()
, *(s(x), y) -> +(*(x, y), y)
, +(x, 0()) -> x
, +(x, s(y)) -> 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..