Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
Problem:
f(0()) -> s(0())
f(s(x)) -> g(s(s(x)))
g(0()) -> s(0())
g(s(0())) -> s(0())
g(s(s(x))) -> f(x)
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3}
transitions:
f1(27) -> 28*
f1(21) -> 22*
s1(5) -> 6*
s1(17) -> 18*
s1(14) -> 15*
s1(13) -> 14*
01() -> 5*
g1(15) -> 16*
f2(31) -> 32*
f2(33) -> 34*
f0(2) -> 3*
f0(1) -> 3*
00() -> 1*
s0(2) -> 2*
s0(1) -> 2*
g0(2) -> 4*
g0(1) -> 4*
1 -> 27,17
2 -> 21,13
6 -> 32,16,22,28,4,3
13 -> 33*
16 -> 34,22,4,3
17 -> 31*
18 -> 14*
22 -> 4*
28 -> 4*
32 -> 16,3
34 -> 16,3
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, f_0(3) -> 1
, f_1(2) -> 4
, f_1(3) -> 4
, f_2(2) -> 1
, f_2(2) -> 4
, f_2(3) -> 1
, f_2(3) -> 4
, 0_0() -> 2
, 0_1() -> 5
, s_0(2) -> 3
, s_0(3) -> 3
, s_1(2) -> 7
, s_1(3) -> 7
, s_1(5) -> 1
, s_1(5) -> 4
, s_1(7) -> 6
, g_0(2) -> 4
, g_0(3) -> 4
, g_1(6) -> 1
, g_1(6) -> 4}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 13.8355255ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | TCT 09 ma9 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f(0()) -> s(0())
, f(s(x)) -> g(s(s(x)))
, g(0()) -> s(0())
, g(s(0())) -> s(0())
, g(s(s(x))) -> f(x)}
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:
{ f_0(2) -> 1
, f_1(2) -> 1
, f_2(2) -> 1
, 0_0() -> 2
, 0_1() -> 3
, s_0(2) -> 2
, s_1(2) -> 5
, s_1(3) -> 1
, s_1(5) -> 4
, g_0(2) -> 1
, g_1(4) -> 1}
Hurray, we answered YES(?,O(n^1))