Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(x1) -> 1(x1)
4(5(4(5(x1)))) -> 4(4(5(5(x1))))
5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3}
transitions:
11(10) -> 11*
11(8) -> 9*
00(2) -> 3*
00(1) -> 3*
10(2) -> 1*
10(1) -> 1*
40(2) -> 4*
40(1) -> 4*
50(2) -> 5*
50(1) -> 5*
20(2) -> 2*
20(1) -> 2*
1 -> 8*
2 -> 10*
9 -> 3*
11 -> 3*
problem:
QedTool IRC1
stdout:
YES(?,O(n^1))
Tool IRC2
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:
{ 0(x1) -> 1(x1)
, 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
, 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)}
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:
{ 0(x1) -> 1(x1)
, 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
, 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 1_0(2) -> 2
, 1_1(2) -> 1
, 4_0(2) -> 1
, 5_0(2) -> 1
, 2_0(2) -> 2}Tool RC1
stdout:
YES(?,O(n^1))
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(x1) -> 1(x1)
, 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
, 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)}
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:
{ 0(x1) -> 1(x1)
, 4(5(4(5(x1)))) -> 4(4(5(5(x1))))
, 5(5(5(5(5(5(4(4(4(4(4(4(x1)))))))))))) -> 2(x1)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 1_0(2) -> 2
, 1_1(2) -> 1
, 4_0(2) -> 1
, 5_0(2) -> 1
, 2_0(2) -> 2}