Tool CaT
stdout:
YES(?,O(n^1))
Problem:
c(c(c(a(x1)))) -> d(d(x1))
d(b(x1)) -> c(c(x1))
b(c(x1)) -> b(a(c(x1)))
c(x1) -> a(a(x1))
d(x1) -> b(c(x1))
Proof:
Bounds Processor:
bound: 3
enrichment: match
automaton:
final states: {4,3,2}
transitions:
b1(12) -> 13*
c1(11) -> 12*
a1(9) -> 10*
a1(8) -> 9*
a2(22) -> 23*
a2(29) -> 30*
a2(28) -> 29*
b2(23) -> 24*
c0(1) -> 2*
c2(21) -> 22*
a0(1) -> 1*
a3(32) -> 33*
a3(31) -> 32*
d0(1) -> 3*
b0(1) -> 4*
1 -> 11,8
10 -> 2*
11 -> 28,21
13 -> 3*
21 -> 31*
24 -> 13,3
30 -> 12*
33 -> 22*
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:
{ c(c(c(a(x1)))) -> d(d(x1))
, d(b(x1)) -> c(c(x1))
, b(c(x1)) -> b(a(c(x1)))
, c(x1) -> a(a(x1))
, d(x1) -> b(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:
{ c(c(c(a(x1)))) -> d(d(x1))
, d(b(x1)) -> c(c(x1))
, b(c(x1)) -> b(a(c(x1)))
, c(x1) -> a(a(x1))
, d(x1) -> b(c(x1))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ c_0(2) -> 1
, c_1(2) -> 4
, c_2(2) -> 6
, a_0(2) -> 2
, a_1(2) -> 3
, a_1(3) -> 1
, a_2(2) -> 7
, a_2(6) -> 5
, a_2(7) -> 4
, a_3(2) -> 8
, a_3(8) -> 6
, d_0(2) -> 1
, b_0(2) -> 1
, b_1(4) -> 1
, b_2(5) -> 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:
{ c(c(c(a(x1)))) -> d(d(x1))
, d(b(x1)) -> c(c(x1))
, b(c(x1)) -> b(a(c(x1)))
, c(x1) -> a(a(x1))
, d(x1) -> b(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:
{ c(c(c(a(x1)))) -> d(d(x1))
, d(b(x1)) -> c(c(x1))
, b(c(x1)) -> b(a(c(x1)))
, c(x1) -> a(a(x1))
, d(x1) -> b(c(x1))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ c_0(2) -> 1
, c_1(2) -> 4
, c_2(2) -> 6
, a_0(2) -> 2
, a_1(2) -> 3
, a_1(3) -> 1
, a_2(2) -> 7
, a_2(6) -> 5
, a_2(7) -> 4
, a_3(2) -> 8
, a_3(8) -> 6
, d_0(2) -> 1
, b_0(2) -> 1
, b_1(4) -> 1
, b_2(5) -> 1}