Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
a(x1) -> x1
Proof:
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {2}
transitions:
a0(1) -> 2*
b0(1) -> 1*
1 -> 2*
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:
{ a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
, a(x1) -> 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:
{ a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
, a(x1) -> x1}
Proof Output:
The problem is match-bounded by 0.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, b_0(2) -> 1
, b_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:
{ a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
, a(x1) -> 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:
{ a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
, a(x1) -> x1}
Proof Output:
The problem is match-bounded by 0.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, b_0(2) -> 1
, b_0(2) -> 2}