Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
a(c(b(x1))) -> a(a(b(c(b(a(x1))))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {3}
transitions:
a1(20) -> 21*
a1(9) -> 10*
a1(4) -> 5*
a1(8) -> 9*
b1(5) -> 6*
b1(7) -> 8*
c1(6) -> 7*
a0(2) -> 3*
a0(1) -> 3*
b0(2) -> 1*
b0(1) -> 1*
c0(2) -> 2*
c0(1) -> 2*
1 -> 20*
2 -> 4*
10 -> 5,3
21 -> 5*
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(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
, a(c(b(x1))) -> a(a(b(c(b(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(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
, a(c(b(x1))) -> a(a(b(c(b(a(x1))))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 7
, a_1(3) -> 1
, a_1(3) -> 7
, a_1(4) -> 3
, b_0(2) -> 2
, b_1(5) -> 4
, b_1(7) -> 6
, c_0(2) -> 2
, c_1(6) -> 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:
{ a(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
, a(c(b(x1))) -> a(a(b(c(b(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(b(a(a(x1)))) -> c(b(a(b(a(x1)))))
, a(c(b(x1))) -> a(a(b(c(b(a(x1))))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 7
, a_1(3) -> 1
, a_1(3) -> 7
, a_1(4) -> 3
, b_0(2) -> 2
, b_1(5) -> 4
, b_1(7) -> 6
, c_0(2) -> 2
, c_1(6) -> 5}