Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(l(x1)) -> l(a(x1))
r(a(a(x1))) -> a(a(r(x1)))
b(l(x1)) -> b(a(r(x1)))
r(b(x1)) -> l(b(x1))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3,2}
transitions:
b1(17) -> 18*
a1(5) -> 6*
a1(16) -> 17*
r1(15) -> 16*
l1(6) -> 7*
a0(1) -> 2*
l0(1) -> 1*
r0(1) -> 3*
b0(1) -> 4*
1 -> 15,5
7 -> 6,2
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(l(x1)) -> l(a(x1))
, r(a(a(x1))) -> a(a(r(x1)))
, b(l(x1)) -> b(a(r(x1)))
, r(b(x1)) -> l(b(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(l(x1)) -> l(a(x1))
, r(a(a(x1))) -> a(a(r(x1)))
, b(l(x1)) -> b(a(r(x1)))
, r(b(x1)) -> l(b(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 3
, a_1(5) -> 4
, l_0(2) -> 2
, l_1(3) -> 1
, l_1(3) -> 3
, r_0(2) -> 1
, r_1(2) -> 5
, b_0(2) -> 1
, b_1(4) -> 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(l(x1)) -> l(a(x1))
, r(a(a(x1))) -> a(a(r(x1)))
, b(l(x1)) -> b(a(r(x1)))
, r(b(x1)) -> l(b(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(l(x1)) -> l(a(x1))
, r(a(a(x1))) -> a(a(r(x1)))
, b(l(x1)) -> b(a(r(x1)))
, r(b(x1)) -> l(b(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 3
, a_1(5) -> 4
, l_0(2) -> 2
, l_1(3) -> 1
, l_1(3) -> 3
, r_0(2) -> 1
, r_1(2) -> 5
, b_0(2) -> 1
, b_1(4) -> 1}