Tool CaT
Execution Time | Unknown |
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Answer | MAYBE |
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Input | SK90 2.59 |
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stdout:
MAYBE
Problem:
f(g(x),y,y) -> g(f(x,x,y))
Proof:
OpenTool IRC1
Execution Time | Unknown |
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Answer | MAYBE |
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Input | SK90 2.59 |
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stdout:
MAYBE
Tool IRC2
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
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(g(x), y, y) -> g(f(x, x, y))}
Proof Output:
'matrix-interpretation of dimension 1' proved the best result:
Details:
--------
'matrix-interpretation of dimension 1' succeeded with the following output:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules: {f(g(x), y, y) -> g(f(x, x, y))}
Proof Output:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2] x1 + [0] x2 + [6] x3 + [1]
g(x1) = [1] x1 + [2]Tool RC1
Execution Time | Unknown |
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Answer | MAYBE |
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Input | SK90 2.59 |
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stdout:
MAYBE
Tool RC2
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
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(g(x), y, y) -> g(f(x, x, y))}
Proof Output:
'matrix-interpretation of dimension 1' proved the best result:
Details:
--------
'matrix-interpretation of dimension 1' succeeded with the following output:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules: {f(g(x), y, y) -> g(f(x, x, y))}
Proof Output:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2] x1 + [0] x2 + [6] x3 + [1]
g(x1) = [1] x1 + [2]Tool pair1rc
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {f(g(x), y, y) -> g(f(x, 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(g(x), y, y) -> g(f(x, x, y))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [2 2] [2 2] [0]
g(x1) = [1 0] x1 + [2]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {f(g(x), y, y) -> g(f(x, 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(g(x), y, y) -> g(f(x, x, y))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [2 2] [2 2] [0]
g(x1) = [1 0] x1 + [2]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {f(g(x), y, y) -> g(f(x, 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(g(x), y, y) -> g(f(x, x, y))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [2 2] [2 2] [0]
g(x1) = [1 0] x1 + [2]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.59 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {f(g(x), y, y) -> g(f(x, 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(g(x), y, y) -> g(f(x, x, y))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [2 2] [2 2] [0]
g(x1) = [1 0] x1 + [2]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {f(g(x), y, y) -> g(f(x, 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:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [2 2] [2 2] [0]
g(x1) = [1 0] x1 + [2]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 0.19442701ms |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.59 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {f(g(x), y, y) -> g(f(x, 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(g(x), y, y) -> g(f(x, x, y))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Sequentially' proved the goal fastest:
'Fastest' succeeded:
'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' proved the goal fastest:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {1}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [1 0] x3 + [0]
[0 0] [2 2] [2 2] [0]
g(x1) = [1 0] x1 + [2]
[0 0] [0]
Hurray, we answered YES(?,O(n^1))