Tool CaT
stdout:
YES(?,O(n^1))
Problem:
b(a(b(x1))) -> a(b(a(x1)))
b(b(a(x1))) -> b(b(b(x1)))
c(a(x1)) -> a(b(c(x1)))
c(b(x1)) -> b(a(c(x1)))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3,2}
transitions:
a1(6) -> 7*
b1(5) -> 6*
c1(4) -> 5*
a2(12) -> 13*
a2(14) -> 15*
b0(1) -> 2*
b2(13) -> 14*
a0(1) -> 1*
c0(1) -> 3*
1 -> 4*
5 -> 12*
7 -> 5,3
15 -> 6*
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:
{ b(a(b(x1))) -> a(b(a(x1)))
, b(b(a(x1))) -> b(b(b(x1)))
, c(a(x1)) -> a(b(c(x1)))
, c(b(x1)) -> b(a(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:
{ b(a(b(x1))) -> a(b(a(x1)))
, b(b(a(x1))) -> b(b(b(x1)))
, c(a(x1)) -> a(b(c(x1)))
, c(b(x1)) -> b(a(c(x1)))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(4) -> 3
, b_2(6) -> 5
, a_0(2) -> 2
, a_1(3) -> 1
, a_1(3) -> 4
, a_2(4) -> 6
, a_2(5) -> 3
, c_0(2) -> 1
, c_1(2) -> 4}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:
{ b(a(b(x1))) -> a(b(a(x1)))
, b(b(a(x1))) -> b(b(b(x1)))
, c(a(x1)) -> a(b(c(x1)))
, c(b(x1)) -> b(a(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:
{ b(a(b(x1))) -> a(b(a(x1)))
, b(b(a(x1))) -> b(b(b(x1)))
, c(a(x1)) -> a(b(c(x1)))
, c(b(x1)) -> b(a(c(x1)))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(4) -> 3
, b_2(6) -> 5
, a_0(2) -> 2
, a_1(3) -> 1
, a_1(3) -> 4
, a_2(4) -> 6
, a_2(5) -> 3
, c_0(2) -> 1
, c_1(2) -> 4}