Tool CaT
stdout:
MAYBE
Problem:
f(s(x),y) -> f(x,g(x,y))
f(0(),y) -> y
g(x,y) -> y
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
Proof Output:
The following argument positions are usable:
Uargs(f) = {2}, Uargs(s) = {}, Uargs(g) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [3] x1 + [2] x2 + [4]
s(x1) = [1] x1 + [2]
g(x1, x2) = [0] x1 + [1] x2 + [2]
0() = [2]Tool RC1
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> y}
Proof Output:
The following argument positions are usable:
Uargs(f) = {2}, Uargs(s) = {}, Uargs(g) = {2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [2] x1 + [2] x2 + [4]
s(x1) = [1] x1 + [4]
g(x1, x2) = [0] x1 + [1] x2 + [2]
0() = [0]Tool pair1rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, Uargs(s) = {}, Uargs(g) = {2}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 1] x1 + [1 0] x2 + [2]
[0 0] [0 1] [0]
s(x1) = [0 0] x1 + [0]
[0 1] [2]
g(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[0 0] [0 1] [0]
0() = [0]
[2]
Hurray, we answered YES(?,O(n^1))Tool pair2rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, Uargs(s) = {}, Uargs(g) = {2}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 1] x1 + [1 0] x2 + [2]
[0 0] [0 1] [0]
s(x1) = [0 0] x1 + [0]
[0 1] [2]
g(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[0 0] [0 1] [0]
0() = [0]
[2]
Hurray, we answered YES(?,O(n^1))Tool pair3irc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, Uargs(s) = {}, Uargs(g) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 2] x1 + [1 0] x2 + [0]
[0 0] [0 2] [0]
s(x1) = [0 0] x1 + [0]
[0 1] [2]
g(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[0 0] [0 1] [0]
0() = [0]
[1]
Hurray, we answered YES(?,O(n^1))Tool pair3rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, Uargs(s) = {}, Uargs(g) = {2}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 1] x1 + [1 0] x2 + [2]
[0 0] [0 1] [0]
s(x1) = [0 0] x1 + [0]
[0 1] [2]
g(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[0 0] [0 1] [0]
0() = [0]
[2]
Hurray, we answered YES(?,O(n^1))Tool rc
| Execution Time | Unknown |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, Uargs(s) = {}, Uargs(g) = {2}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 1] x1 + [1 0] x2 + [2]
[0 0] [0 1] [0]
s(x1) = [0 0] x1 + [0]
[0 1] [2]
g(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[0 0] [0 1] [0]
0() = [0]
[2]
Hurray, we answered YES(?,O(n^1))Tool tup3irc
| Execution Time | 42.964058ms |
|---|
| Answer | YES(?,O(n^1)) |
|---|
| Input | TCT 09 ma1 |
|---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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(s(x), y) -> f(x, g(x, y))
, f(0(), y) -> y
, g(x, y) -> 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) = {2}, Uargs(s) = {}, Uargs(g) = {}
We have the following constructor-restricted (at most 1 in the main diagonals) matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 2] x1 + [1 0] x2 + [0]
[0 0] [0 2] [0]
s(x1) = [0 0] x1 + [0]
[0 1] [2]
g(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
[0 0] [0 1] [0]
0() = [0]
[1]
Hurray, we answered YES(?,O(n^1))