Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(a(a(x1))) -> b(x1)
b(c(x1)) -> c(c(a(a(a(a(x1))))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3,2}
transitions:
c1(9) -> 10*
c1(8) -> 9*
a1(5) -> 6*
a1(7) -> 8*
a1(4) -> 5*
a1(6) -> 7*
b2(20) -> 21*
b2(22) -> 23*
a0(1) -> 2*
b0(1) -> 3*
c0(1) -> 1*
1 -> 4*
4 -> 20*
5 -> 22*
10 -> 21,7,3
21 -> 7*
23 -> 8*
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(a(x1))) -> b(x1)
, b(c(x1)) -> c(c(a(a(a(a(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(a(x1))) -> b(x1)
, b(c(x1)) -> c(c(a(a(a(a(x1))))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 7
, a_1(5) -> 4
, a_1(6) -> 5
, a_1(7) -> 6
, b_0(2) -> 1
, b_2(2) -> 5
, b_2(7) -> 4
, c_0(2) -> 2
, c_1(3) -> 1
, c_1(3) -> 5
, c_1(4) -> 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(a(x1))) -> b(x1)
, b(c(x1)) -> c(c(a(a(a(a(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(a(x1))) -> b(x1)
, b(c(x1)) -> c(c(a(a(a(a(x1))))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 7
, a_1(5) -> 4
, a_1(6) -> 5
, a_1(7) -> 6
, b_0(2) -> 1
, b_2(2) -> 5
, b_2(7) -> 4
, c_0(2) -> 2
, c_1(3) -> 1
, c_1(3) -> 5
, c_1(4) -> 3}