Tool CaT
stdout:
YES(?,O(n^1))
Problem:
1(2(1(x1))) -> 2(0(2(x1)))
0(2(1(x1))) -> 1(0(2(x1)))
L(2(1(x1))) -> L(1(0(2(x1))))
1(2(0(x1))) -> 2(0(1(x1)))
1(2(R(x1))) -> 2(0(1(R(x1))))
0(2(0(x1))) -> 1(0(1(x1)))
L(2(0(x1))) -> L(1(0(1(x1))))
0(2(R(x1))) -> 1(0(1(R(x1))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3}
transitions:
11(20) -> 21*
11(7) -> 8*
01(8) -> 9*
R1(6) -> 7*
R1(18) -> 19*
21(9) -> 10*
10(2) -> 3*
10(1) -> 3*
20(2) -> 1*
20(1) -> 1*
00(2) -> 4*
00(1) -> 4*
L0(2) -> 5*
L0(1) -> 5*
R0(2) -> 2*
R0(1) -> 2*
1 -> 18*
2 -> 6*
9 -> 20*
10 -> 3*
19 -> 7*
21 -> 4*
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:
{ 1(2(1(x1))) -> 2(0(2(x1)))
, 0(2(1(x1))) -> 1(0(2(x1)))
, L(2(1(x1))) -> L(1(0(2(x1))))
, 1(2(0(x1))) -> 2(0(1(x1)))
, 1(2(R(x1))) -> 2(0(1(R(x1))))
, 0(2(0(x1))) -> 1(0(1(x1)))
, L(2(0(x1))) -> L(1(0(1(x1))))
, 0(2(R(x1))) -> 1(0(1(R(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:
{ 1(2(1(x1))) -> 2(0(2(x1)))
, 0(2(1(x1))) -> 1(0(2(x1)))
, L(2(1(x1))) -> L(1(0(2(x1))))
, 1(2(0(x1))) -> 2(0(1(x1)))
, 1(2(R(x1))) -> 2(0(1(R(x1))))
, 0(2(0(x1))) -> 1(0(1(x1)))
, L(2(0(x1))) -> L(1(0(1(x1))))
, 0(2(R(x1))) -> 1(0(1(R(x1))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 1_0(2) -> 1
, 1_1(3) -> 1
, 1_1(5) -> 4
, 2_0(2) -> 2
, 2_1(3) -> 1
, 0_0(2) -> 1
, 0_1(4) -> 3
, L_0(2) -> 1
, R_0(2) -> 2
, R_1(2) -> 5}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:
{ 1(2(1(x1))) -> 2(0(2(x1)))
, 0(2(1(x1))) -> 1(0(2(x1)))
, L(2(1(x1))) -> L(1(0(2(x1))))
, 1(2(0(x1))) -> 2(0(1(x1)))
, 1(2(R(x1))) -> 2(0(1(R(x1))))
, 0(2(0(x1))) -> 1(0(1(x1)))
, L(2(0(x1))) -> L(1(0(1(x1))))
, 0(2(R(x1))) -> 1(0(1(R(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:
{ 1(2(1(x1))) -> 2(0(2(x1)))
, 0(2(1(x1))) -> 1(0(2(x1)))
, L(2(1(x1))) -> L(1(0(2(x1))))
, 1(2(0(x1))) -> 2(0(1(x1)))
, 1(2(R(x1))) -> 2(0(1(R(x1))))
, 0(2(0(x1))) -> 1(0(1(x1)))
, L(2(0(x1))) -> L(1(0(1(x1))))
, 0(2(R(x1))) -> 1(0(1(R(x1))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 1_0(2) -> 1
, 1_1(3) -> 1
, 1_1(5) -> 4
, 2_0(2) -> 2
, 2_1(3) -> 1
, 0_0(2) -> 1
, 0_1(4) -> 3
, L_0(2) -> 1
, R_0(2) -> 2
, R_1(2) -> 5}