Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
Problem:
flatten(nil()) -> nil()
flatten(unit(x)) -> flatten(x)
flatten(++(x,y)) -> ++(flatten(x),flatten(y))
flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y))
flatten(flatten(x)) -> flatten(x)
rev(nil()) -> nil()
rev(unit(x)) -> unit(x)
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(rev(x)) -> x
++(x,nil()) -> x
++(nil(),y) -> y
++(++(x,y),z) -> ++(x,++(y,z))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3}
transitions:
unit1(2) -> 4*
unit1(1) -> 4*
nil1() -> 4,3
flatten1(2) -> 3*
flatten1(1) -> 3*
flatten0(2) -> 3*
flatten0(1) -> 3*
nil0() -> 1*
unit0(2) -> 2*
unit0(1) -> 2*
++0(1,2) -> 5*
++0(2,1) -> 5*
++0(1,1) -> 5*
++0(2,2) -> 5*
rev0(2) -> 4*
rev0(1) -> 4*
1 -> 5*
2 -> 5*
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(x, y), z) -> ++(x, ++(y, z))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(x, y), z) -> ++(x, ++(y, z))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(x, y), z) -> ++(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:
{ flatten_0(2) -> 1
, flatten_0(3) -> 1
, flatten_1(2) -> 1
, flatten_1(3) -> 1
, nil_0() -> 2
, nil_0() -> 4
, nil_1() -> 1
, nil_1() -> 5
, unit_0(2) -> 3
, unit_0(2) -> 4
, unit_0(3) -> 3
, unit_0(3) -> 4
, unit_1(2) -> 5
, unit_1(3) -> 5
, ++_0(2, 2) -> 4
, ++_0(2, 3) -> 4
, ++_0(3, 2) -> 4
, ++_0(3, 3) -> 4
, rev_0(2) -> 5
, rev_0(3) -> 5}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(x, y), z) -> ++(x, ++(y, z))}
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:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 8.699298e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.42 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(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:
{ flatten(nil()) -> nil()
, flatten(unit(x)) -> flatten(x)
, flatten(++(x, y)) -> ++(flatten(x), flatten(y))
, flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y))
, flatten(flatten(x)) -> flatten(x)
, rev(nil()) -> nil()
, rev(unit(x)) -> unit(x)
, rev(++(x, y)) -> ++(rev(y), rev(x))
, rev(rev(x)) -> x
, ++(x, nil()) -> x
, ++(nil(), y) -> y
, ++(++(x, y), z) -> ++(x, ++(y, z))}
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:
{ flatten_0(2) -> 1
, flatten_1(2) -> 1
, nil_0() -> 1
, nil_0() -> 2
, nil_1() -> 1
, unit_0(2) -> 1
, unit_0(2) -> 2
, unit_1(2) -> 1
, ++_0(2, 2) -> 1
, rev_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))