Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(b(a(x1))) -> b(c(x1))
b(b(b(x1))) -> c(b(x1))
c(x1) -> a(b(x1))
c(d(x1)) -> d(c(b(a(x1))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3,2}
transitions:
d1(19) -> 20*
c1(18) -> 19*
b1(5) -> 6*
b1(17) -> 18*
a1(16) -> 17*
a1(6) -> 7*
a2(22) -> 23*
a0(1) -> 2*
b2(21) -> 22*
b0(1) -> 3*
c0(1) -> 4*
d0(1) -> 1*
1 -> 16,5
7 -> 4*
18 -> 21*
20 -> 4*
23 -> 19*
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(x1))) -> b(c(x1))
, b(b(b(x1))) -> c(b(x1))
, c(x1) -> a(b(x1))
, c(d(x1)) -> d(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(x1))) -> b(c(x1))
, b(b(b(x1))) -> c(b(x1))
, c(x1) -> a(b(x1))
, c(d(x1)) -> d(c(b(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) -> 6
, a_1(3) -> 1
, a_2(7) -> 4
, b_0(2) -> 1
, b_1(2) -> 3
, b_1(6) -> 5
, b_2(5) -> 7
, c_0(2) -> 1
, c_1(5) -> 4
, d_0(2) -> 2
, d_1(4) -> 1}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(x1))) -> b(c(x1))
, b(b(b(x1))) -> c(b(x1))
, c(x1) -> a(b(x1))
, c(d(x1)) -> d(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(x1))) -> b(c(x1))
, b(b(b(x1))) -> c(b(x1))
, c(x1) -> a(b(x1))
, c(d(x1)) -> d(c(b(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) -> 6
, a_1(3) -> 1
, a_2(7) -> 4
, b_0(2) -> 1
, b_1(2) -> 3
, b_1(6) -> 5
, b_2(5) -> 7
, c_0(2) -> 1
, c_1(5) -> 4
, d_0(2) -> 2
, d_1(4) -> 1}