Tool CaT
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
Problem:
*(i(x),x) -> 1()
*(1(),y) -> y
*(x,0()) -> 0()
*(*(x,y),z) -> *(x,*(y,z))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {7,6,5,4}
transitions:
01() -> 6*,3,4
11() -> 7*,2,4
*0(3,1) -> 4*
*0(3,3) -> 4*
*0(3,5) -> 4*
*0(3,7) -> 4*
*0(5,1) -> 4*
*0(5,3) -> 4*
*0(5,5) -> 4*
*0(5,7) -> 4*
*0(6,2) -> 4*
*0(1,2) -> 4*
*0(6,6) -> 4*
*0(1,6) -> 4*
*0(7,1) -> 4*
*0(2,1) -> 4*
*0(7,3) -> 4*
*0(2,3) -> 4*
*0(7,5) -> 4*
*0(2,5) -> 4*
*0(7,7) -> 4*
*0(2,7) -> 4*
*0(3,2) -> 4*
*0(3,6) -> 4*
*0(5,2) -> 4*
*0(5,6) -> 4*
*0(6,1) -> 4*
*0(1,1) -> 4*
*0(6,3) -> 4*
*0(1,3) -> 4*
*0(6,5) -> 4*
*0(1,5) -> 4*
*0(6,7) -> 4*
*0(1,7) -> 4*
*0(7,2) -> 4*
*0(2,2) -> 4*
*0(7,6) -> 4*
*0(2,6) -> 4*
i0(5) -> 4,5*
i0(7) -> 4,5*
i0(2) -> 5*,4,1
i0(6) -> 4,5*
i0(1) -> 5*,4,1
i0(3) -> 5*,4,1
1 -> 4*
2 -> 4*
3 -> 4*
5 -> 4*
6 -> 4*
7 -> 4*
problem:
QedTool IRC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 4.07 |
---|
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ *_0(2, 2) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 1}Tool RC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ *_0(2, 2) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 1}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *_0(2, 2) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *_0(2, 2) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *_0(2, 2) -> 1
, *_0(2, 3) -> 1
, *_0(2, 4) -> 1
, *_0(3, 2) -> 1
, *_0(3, 3) -> 1
, *_0(3, 4) -> 1
, *_0(4, 2) -> 1
, *_0(4, 3) -> 1
, *_0(4, 4) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, i_0(3) -> 1
, i_0(3) -> 2
, i_0(4) -> 1
, i_0(4) -> 2
, 1_0() -> 1
, 1_0() -> 3
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 4
, 0_1() -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *_0(2, 2) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 1}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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 minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ *_0(2, 2) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 1}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 3.6760862ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *(i(x), x) -> 1()
, *(1(), y) -> y
, *(x, 0()) -> 0()
, *(*(x, y), z) -> *(x, *(y, z))}
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:
{ *_0(2, 2) -> 1
, *_0(2, 3) -> 1
, *_0(2, 4) -> 1
, *_0(3, 2) -> 1
, *_0(3, 3) -> 1
, *_0(3, 4) -> 1
, *_0(4, 2) -> 1
, *_0(4, 3) -> 1
, *_0(4, 4) -> 1
, i_0(2) -> 1
, i_0(2) -> 2
, i_0(3) -> 1
, i_0(3) -> 2
, i_0(4) -> 1
, i_0(4) -> 2
, 1_0() -> 1
, 1_0() -> 3
, 1_1() -> 1
, 0_0() -> 1
, 0_0() -> 4
, 0_1() -> 1}
Hurray, we answered YES(?,O(n^1))