Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(d(x1)) -> d(b(x1))
a(x1) -> b(b(b(x1)))
b(d(b(x1))) -> a(c(x1))
c(x1) -> d(x1)
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3,2}
transitions:
d1(17) -> 18*
d1(6) -> 7*
b1(15) -> 16*
b1(5) -> 6*
b1(14) -> 15*
a0(1) -> 2*
d0(1) -> 1*
b0(1) -> 3*
c0(1) -> 4*
1 -> 17,5
6 -> 14*
7 -> 2*
16 -> 2*
18 -> 4*
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(d(x1)) -> d(b(x1))
, a(x1) -> b(b(b(x1)))
, b(d(b(x1))) -> a(c(x1))
, c(x1) -> d(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(d(x1)) -> d(b(x1))
, a(x1) -> b(b(b(x1)))
, b(d(b(x1))) -> a(c(x1))
, c(x1) -> d(x1)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, d_0(2) -> 2
, d_1(2) -> 1
, d_1(3) -> 1
, b_0(2) -> 1
, b_1(2) -> 3
, b_1(3) -> 4
, b_1(4) -> 1
, c_0(2) -> 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(d(x1)) -> d(b(x1))
, a(x1) -> b(b(b(x1)))
, b(d(b(x1))) -> a(c(x1))
, c(x1) -> d(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(d(x1)) -> d(b(x1))
, a(x1) -> b(b(b(x1)))
, b(d(b(x1))) -> a(c(x1))
, c(x1) -> d(x1)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, d_0(2) -> 2
, d_1(2) -> 1
, d_1(3) -> 1
, b_0(2) -> 1
, b_1(2) -> 3
, b_1(3) -> 4
, b_1(4) -> 1
, c_0(2) -> 1}