Tool CaT
stdout:
YES(?,O(n^1))
Problem:
b(a(x1)) -> a(a(d(x1)))
a(c(x1)) -> b(b(x1))
d(a(b(x1))) -> b(d(d(c(x1))))
d(x1) -> a(x1)
b(a(c(a(x1)))) -> x1
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3,2}
transitions:
a1(11) -> 12*
b1(9) -> 10*
b1(8) -> 9*
b0(1) -> 2*
a0(1) -> 3*
d0(1) -> 4*
c0(1) -> 1*
1 -> 11,8
10 -> 12,4,3
12 -> 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:
{ b(a(x1)) -> a(a(d(x1)))
, a(c(x1)) -> b(b(x1))
, d(a(b(x1))) -> b(d(d(c(x1))))
, d(x1) -> a(x1)
, b(a(c(a(x1)))) -> 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:
{ b(a(x1)) -> a(a(d(x1)))
, a(c(x1)) -> b(b(x1))
, d(a(b(x1))) -> b(d(d(c(x1))))
, d(x1) -> a(x1)
, b(a(c(a(x1)))) -> x1}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(2) -> 3
, b_1(3) -> 1
, a_0(2) -> 1
, a_1(2) -> 1
, d_0(2) -> 1
, c_0(2) -> 2}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:
{ b(a(x1)) -> a(a(d(x1)))
, a(c(x1)) -> b(b(x1))
, d(a(b(x1))) -> b(d(d(c(x1))))
, d(x1) -> a(x1)
, b(a(c(a(x1)))) -> 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:
{ b(a(x1)) -> a(a(d(x1)))
, a(c(x1)) -> b(b(x1))
, d(a(b(x1))) -> b(d(d(c(x1))))
, d(x1) -> a(x1)
, b(a(c(a(x1)))) -> x1}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(2) -> 3
, b_1(3) -> 1
, a_0(2) -> 1
, a_1(2) -> 1
, d_0(2) -> 1
, c_0(2) -> 2}