Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(d(x1)) -> d(b(c(b(d(x1)))))
a(x1) -> b(b(f(b(b(x1)))))
b(d(b(x1))) -> a(d(x1))
d(f(x1)) -> b(d(x1))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3}
transitions:
b1(20) -> 21*
b1(10) -> 11*
b1(7) -> 8*
b1(9) -> 10*
b1(6) -> 7*
b1(23) -> 24*
d1(30) -> 31*
d1(22) -> 23*
f1(8) -> 9*
a0(2) -> 3*
a0(1) -> 3*
d0(2) -> 5*
d0(1) -> 5*
b0(2) -> 4*
b0(1) -> 4*
c0(2) -> 1*
c0(1) -> 1*
f0(2) -> 2*
f0(1) -> 2*
1 -> 30,6
2 -> 22,20
11 -> 3*
21 -> 7*
24 -> 23,5
31 -> 23*
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(c(b(d(x1)))))
, a(x1) -> b(b(f(b(b(x1)))))
, b(d(b(x1))) -> a(d(x1))
, d(f(x1)) -> b(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(c(b(d(x1)))))
, a(x1) -> b(b(f(b(b(x1)))))
, b(d(b(x1))) -> a(d(x1))
, d(f(x1)) -> b(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) -> 1
, d_1(2) -> 3
, b_0(2) -> 1
, b_1(2) -> 6
, b_1(3) -> 1
, b_1(3) -> 3
, b_1(4) -> 3
, b_1(6) -> 5
, c_0(2) -> 2
, f_0(2) -> 2
, f_1(5) -> 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:
{ a(d(x1)) -> d(b(c(b(d(x1)))))
, a(x1) -> b(b(f(b(b(x1)))))
, b(d(b(x1))) -> a(d(x1))
, d(f(x1)) -> b(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(c(b(d(x1)))))
, a(x1) -> b(b(f(b(b(x1)))))
, b(d(b(x1))) -> a(d(x1))
, d(f(x1)) -> b(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) -> 1
, d_1(2) -> 3
, b_0(2) -> 1
, b_1(2) -> 6
, b_1(3) -> 1
, b_1(3) -> 3
, b_1(4) -> 3
, b_1(6) -> 5
, c_0(2) -> 2
, f_0(2) -> 2
, f_1(5) -> 4}