Tool CaT
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^2)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^2))
Problem:
f(x,g(x)) -> x
f(x,h(y)) -> f(h(x),y)
Proof:
Complexity Transformation Processor:
strict:
f(x,g(x)) -> x
f(x,h(y)) -> f(h(x),y)
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[h](x0) = x0 + 66,
[f](x0, x1) = x0 + x1 + 252,
[g](x0) = x0 + 8
orientation:
f(x,g(x)) = 2x + 260 >= x = x
f(x,h(y)) = x + y + 318 >= x + y + 318 = f(h(x),y)
problem:
strict:
f(x,h(y)) -> f(h(x),y)
weak:
f(x,g(x)) -> x
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 2]
[0 1]
interpretation:
[0]
[h](x0) = x0 + [4],
[1 2] [1]
[f](x0, x1) = x0 + [0 1]x1 + [2],
[1 0] [0]
[g](x0) = [0 0]x0 + [2]
orientation:
[1 2] [9] [1 2] [1]
f(x,h(y)) = x + [0 1]y + [6] >= x + [0 1]y + [6] = f(h(x),y)
[2 0] [5]
f(x,g(x)) = [0 1]x + [4] >= x = x
problem:
strict:
weak:
f(x,h(y)) -> f(h(x),y)
f(x,g(x)) -> x
Qed
Tool IRC1
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_1(3, 2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(2) -> 1
, h_1(2) -> 3
, h_1(3) -> 1
, h_1(3) -> 3}Tool RC1
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_1(3, 2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(2) -> 1
, h_1(2) -> 3
, h_1(3) -> 1
, h_1(3) -> 3}Tool pair1rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
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:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_1(3, 2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(2) -> 1
, h_1(2) -> 3
, h_1(3) -> 1
, h_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
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:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_1(3, 2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(2) -> 1
, h_1(2) -> 3
, h_1(3) -> 1
, h_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_0(2, 3) -> 1
, f_0(3, 2) -> 1
, f_0(3, 3) -> 1
, f_1(4, 2) -> 1
, f_1(4, 3) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, g_0(3) -> 1
, g_0(3) -> 2
, h_0(2) -> 1
, h_0(2) -> 3
, h_0(3) -> 1
, h_0(3) -> 3
, h_1(2) -> 1
, h_1(2) -> 4
, h_1(3) -> 1
, h_1(3) -> 4
, h_1(4) -> 1
, h_1(4) -> 4}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair3 (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:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_0(2, 3) -> 1
, f_0(3, 2) -> 1
, f_0(3, 3) -> 1
, f_1(4, 2) -> 1
, f_1(4, 3) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, g_0(3) -> 1
, g_0(3) -> 2
, h_0(2) -> 1
, h_0(2) -> 3
, h_0(3) -> 1
, h_0(3) -> 3
, h_1(2) -> 1
, h_1(2) -> 4
, h_1(3) -> 1
, h_1(3) -> 4
, h_1(4) -> 1
, h_1(4) -> 4}
Hurray, we answered YES(?,O(n^1))Tool rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match' (timeout of 5.0 seconds)' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_0(2, 3) -> 1
, f_0(3, 2) -> 1
, f_0(3, 3) -> 1
, f_1(4, 2) -> 1
, f_1(4, 3) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, g_0(3) -> 1
, g_0(3) -> 2
, h_0(2) -> 1
, h_0(2) -> 3
, h_0(3) -> 1
, h_0(3) -> 3
, h_1(2) -> 1
, h_1(2) -> 4
, h_1(3) -> 1
, h_1(3) -> 4
, h_1(4) -> 1
, h_1(4) -> 4}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
| Execution Time | 0.10067415ms |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | SK90 2.55 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(x, g(x)) -> x
, f(x, h(y)) -> f(h(x), y)}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2) -> 1
, f_1(3, 2) -> 1
, g_0(2) -> 1
, g_0(2) -> 2
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(2) -> 1
, h_1(2) -> 3
, h_1(3) -> 1
, h_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))