Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
Problem:
g(s(x)) -> f(x)
f(0()) -> s(0())
f(s(x)) -> s(s(g(x)))
g(0()) -> 0()
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3}
transitions:
01() -> 15*
s1(15) -> 16*
s1(18) -> 19*
g1(25) -> 26*
g1(17) -> 18*
f1(7) -> 8*
f1(9) -> 10*
g0(2) -> 3*
g0(1) -> 3*
s0(2) -> 1*
s0(1) -> 1*
f0(2) -> 4*
f0(1) -> 4*
00() -> 2*
1 -> 25,9
2 -> 17,7
8 -> 26,18,3
10 -> 26,18,3
15 -> 18,3
16 -> 10,8,3,4
19 -> 15*
26 -> 18*
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ g_0(2) -> 1
, g_1(2) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(4) -> 3
, s_1(4) -> 4
, f_0(2) -> 1
, f_1(2) -> 1
, f_1(2) -> 4
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_1() -> 4}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ g_0(2) -> 1
, g_1(2) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(4) -> 3
, s_1(4) -> 4
, f_0(2) -> 1
, f_1(2) -> 1
, f_1(2) -> 4
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_1() -> 4}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g_0(2) -> 1
, g_1(2) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(4) -> 3
, s_1(4) -> 4
, f_0(2) -> 1
, f_1(2) -> 1
, f_1(2) -> 4
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g_0(2) -> 1
, g_1(2) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(4) -> 3
, s_1(4) -> 4
, f_0(2) -> 1
, f_1(2) -> 1
, f_1(2) -> 4
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g_0(2) -> 1
, g_0(4) -> 1
, g_1(2) -> 6
, g_1(4) -> 6
, s_0(2) -> 2
, s_0(4) -> 2
, s_1(5) -> 1
, s_1(5) -> 3
, s_1(6) -> 5
, s_1(6) -> 6
, f_0(2) -> 3
, f_0(4) -> 3
, f_1(2) -> 1
, f_1(2) -> 6
, f_1(4) -> 1
, f_1(4) -> 6
, 0_0() -> 4
, 0_1() -> 1
, 0_1() -> 5
, 0_1() -> 6}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g_0(2) -> 1
, g_0(4) -> 1
, g_1(2) -> 6
, g_1(4) -> 6
, s_0(2) -> 2
, s_0(4) -> 2
, s_1(5) -> 1
, s_1(5) -> 3
, s_1(6) -> 5
, s_1(6) -> 6
, f_0(2) -> 3
, f_0(4) -> 3
, f_1(2) -> 1
, f_1(2) -> 6
, f_1(4) -> 1
, f_1(4) -> 6
, 0_0() -> 4
, 0_1() -> 1
, 0_1() -> 5
, 0_1() -> 6}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g_0(2) -> 1
, g_1(2) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(4) -> 3
, s_1(4) -> 4
, f_0(2) -> 1
, f_1(2) -> 1
, f_1(2) -> 4
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 7.0305824e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.35 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g(s(x)) -> f(x)
, f(0()) -> s(0())
, f(s(x)) -> s(s(g(x)))
, g(0()) -> 0()}
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:
{ g_0(2) -> 1
, g_0(4) -> 1
, g_1(2) -> 6
, g_1(4) -> 6
, s_0(2) -> 2
, s_0(4) -> 2
, s_1(5) -> 1
, s_1(5) -> 3
, s_1(6) -> 5
, s_1(6) -> 6
, f_0(2) -> 3
, f_0(4) -> 3
, f_1(2) -> 1
, f_1(2) -> 6
, f_1(4) -> 1
, f_1(4) -> 6
, 0_0() -> 4
, 0_1() -> 1
, 0_1() -> 5
, 0_1() -> 6}
Hurray, we answered YES(?,O(n^1))