Tool CaT
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.02 |
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stdout:
YES(?,O(n^1))
Problem:
+(+(x,y),z) -> +(x,+(y,z))
+(f(x),f(y)) -> f(+(x,y))
+(f(x),+(f(y),z)) -> +(f(+(x,y)),z)
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {2}
transitions:
f1(4) -> 4,2
+1(1,1) -> 4*
+0(1,1) -> 2*
f0(1) -> 1*
problem:
QedTool IRC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.02 |
---|
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 2.02 |
---|
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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}Tool RC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(x, y)), z)}
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:
{ +_0(2, 2) -> 1
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(x, y)), z)}
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:
{ +_0(2, 2) -> 1
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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 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:
{ +_0(2, 2) -> 1
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 5.9257984e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.02 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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:
{ +(+(x, y), z) -> +(x, +(y, z))
, +(f(x), f(y)) -> f(+(x, y))
, +(f(x), +(f(y), z)) -> +(f(+(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
, +_1(2, 2) -> 3
, f_0(2) -> 2
, f_1(3) -> 1
, f_1(3) -> 3}
Hurray, we answered YES(?,O(n^1))