Tool CaT
stdout:
YES(?,O(n^1))
Problem:
d(a(x1)) -> b(d(x1))
b(x1) -> a(a(a(x1)))
c(d(c(x1))) -> a(d(x1))
b(d(d(x1))) -> c(c(d(d(c(x1)))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3,2}
transitions:
a1(15) -> 16*
a1(17) -> 18*
a1(16) -> 17*
b1(6) -> 7*
d1(5) -> 6*
a2(25) -> 26*
a2(24) -> 25*
a2(23) -> 24*
d0(1) -> 2*
a0(1) -> 1*
b0(1) -> 3*
c0(1) -> 4*
1 -> 15,5
6 -> 23*
7 -> 6,2
18 -> 3*
26 -> 7,2
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:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(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:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ d_0(2) -> 1
, d_1(2) -> 3
, a_0(2) -> 2
, a_1(2) -> 5
, a_1(4) -> 1
, a_1(5) -> 4
, a_2(3) -> 7
, a_2(6) -> 1
, a_2(6) -> 3
, a_2(7) -> 6
, b_0(2) -> 1
, b_1(3) -> 1
, b_1(3) -> 3
, 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:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(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:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ d_0(2) -> 1
, d_1(2) -> 3
, a_0(2) -> 2
, a_1(2) -> 5
, a_1(4) -> 1
, a_1(5) -> 4
, a_2(3) -> 7
, a_2(6) -> 1
, a_2(6) -> 3
, a_2(7) -> 6
, b_0(2) -> 1
, b_1(3) -> 1
, b_1(3) -> 3
, c_0(2) -> 1}