Tool CaT
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
Problem:
rev(nil()) -> nil()
rev(rev(x)) -> x
rev(++(x,y)) -> ++(rev(y),rev(x))
++(nil(),y) -> y
++(x,nil()) -> x
++(.(x,y),z) -> .(x,++(y,z))
++(x,++(y,z)) -> ++(++(x,y),z)
make(x) -> .(x,nil())
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3}
transitions:
.1(1,6) -> 6,4
.1(2,3) -> 5*
.1(2,9) -> 6,4
.1(1,3) -> 5*
.1(1,9) -> 6,4
.1(2,6) -> 6,4
nil1() -> 3*
++1(1,2) -> 9*
++1(2,1) -> 6*
++1(1,1) -> 6*
++1(2,2) -> 6*
rev0(2) -> 3*
rev0(1) -> 3*
nil0() -> 1*
++0(1,2) -> 4*
++0(2,1) -> 4*
++0(1,1) -> 4*
++0(2,2) -> 4*
.0(1,2) -> 2*
.0(2,1) -> 2*
.0(1,1) -> 2*
.0(2,2) -> 2*
make0(2) -> 5*
make0(1) -> 5*
1 -> 6,4
2 -> 6,9,4
problem:
QedTool IRC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | SK90 4.26 |
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stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}Tool RC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}Tool pair1rc
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 0.87453294ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 4.26 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev(nil()) -> nil()
, rev(rev(x)) -> x
, rev(++(x, y)) -> ++(rev(y), rev(x))
, ++(nil(), y) -> y
, ++(x, nil()) -> x
, ++(.(x, y), z) -> .(x, ++(y, z))
, ++(x, ++(y, z)) -> ++(++(x, y), z)
, make(x) -> .(x, nil())}
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:
{ rev_0(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_0() -> 3
, nil_1() -> 1
, ++_0(2, 2) -> 1
, ++_1(2, 2) -> 3
, ._0(2, 2) -> 1
, ._0(2, 2) -> 2
, ._0(2, 2) -> 3
, ._1(2, 1) -> 1
, ._1(2, 3) -> 1
, ._1(2, 3) -> 3
, make_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))