Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
a(c(x1)) -> c(a(x1))
c(b(x1)) -> b(c(x1))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {3,2}
transitions:
b1(8) -> 9*
c1(7) -> 8*
a0(1) -> 2*
b0(1) -> 1*
c0(1) -> 3*
1 -> 7*
9 -> 8,3
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:
{ a(a(b(b(x1)))) -> b(b(b(a(a(a(x1))))))
, a(c(x1)) -> c(a(x1))
, c(b(x1)) -> b(c(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(c(x1)) -> c(a(x1))
, c(b(x1)) -> b(c(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, b_0(2) -> 2
, b_1(3) -> 1
, b_1(3) -> 3
, c_0(2) -> 1
, c_1(2) -> 3}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(c(x1)) -> c(a(x1))
, c(b(x1)) -> b(c(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(c(x1)) -> c(a(x1))
, c(b(x1)) -> b(c(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, b_0(2) -> 2
, b_1(3) -> 1
, b_1(3) -> 3
, c_0(2) -> 1
, c_1(2) -> 3}