Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
Problem:
p(0()) -> 0()
p(s(x)) -> x
minus(x,0()) -> x
minus(x,s(y)) -> minus(p(x),y)
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3}
transitions:
minus1(6,2) -> 4*
minus1(6,1) -> 4*
p1(2) -> 6*
p1(6) -> 6*
p1(1) -> 6*
01() -> 6,3
02() -> 6,4
p0(2) -> 3*
p0(1) -> 3*
00() -> 1*
s0(2) -> 2*
s0(1) -> 2*
minus0(1,2) -> 4*
minus0(2,1) -> 4*
minus0(1,1) -> 4*
minus0(2,2) -> 4*
1 -> 6,4,3
2 -> 6,4,3
6 -> 4*
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), 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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), 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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), 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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), 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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_0(3) -> 1
, p_1(2) -> 4
, p_1(2) -> 5
, p_1(3) -> 4
, p_1(3) -> 5
, p_1(5) -> 4
, p_1(5) -> 5
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 4
, 0_0() -> 5
, 0_1() -> 1
, 0_1() -> 4
, 0_1() -> 5
, 0_2() -> 4
, 0_2() -> 5
, s_0(2) -> 1
, s_0(2) -> 3
, s_0(2) -> 4
, s_0(2) -> 5
, s_0(3) -> 1
, s_0(3) -> 3
, s_0(3) -> 4
, s_0(3) -> 5
, minus_0(2, 2) -> 4
, minus_0(2, 3) -> 4
, minus_0(3, 2) -> 4
, minus_0(3, 3) -> 4
, minus_1(5, 2) -> 4
, minus_1(5, 3) -> 4}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 8.867192e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma3 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), 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:
{ p(0()) -> 0()
, p(s(x)) -> x
, minus(x, 0()) -> x
, minus(x, s(y)) -> minus(p(x), y)}
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 2.
The enriched problem is compatible with the following automaton:
{ p_0(2) -> 1
, p_1(2) -> 1
, p_1(2) -> 3
, p_1(3) -> 1
, p_1(3) -> 3
, 0_0() -> 1
, 0_0() -> 2
, 0_0() -> 3
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 1
, s_0(2) -> 2
, s_0(2) -> 3
, minus_0(2, 2) -> 1
, minus_1(3, 2) -> 1}
Hurray, we answered YES(?,O(n^1))