Tool CaT
stdout:
YES(?,O(n^1))
Problem:
f(f(X)) -> f(a(b(f(X))))
f(a(g(X))) -> b(X)
b(X) -> a(X)
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3}
transitions:
a1(19) -> 20*
a1(13) -> 14*
b1(5) -> 6*
b1(11) -> 12*
a2(27) -> 28*
a2(21) -> 22*
f0(2) -> 3*
f0(1) -> 3*
a0(2) -> 1*
a0(1) -> 1*
b0(2) -> 4*
b0(1) -> 4*
g0(2) -> 2*
g0(1) -> 2*
1 -> 13,11
2 -> 19,5
5 -> 27*
6 -> 3*
11 -> 21*
12 -> 3*
14 -> 4*
20 -> 4*
22 -> 12*
28 -> 6,3
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:
{ f(f(X)) -> f(a(b(f(X))))
, f(a(g(X))) -> b(X)
, b(X) -> a(X)}
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:
{ f(f(X)) -> f(a(b(f(X))))
, f(a(g(X))) -> b(X)
, b(X) -> a(X)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, a_0(2) -> 2
, a_1(2) -> 1
, a_2(2) -> 1
, b_0(2) -> 1
, b_1(2) -> 1
, g_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:
{ f(f(X)) -> f(a(b(f(X))))
, f(a(g(X))) -> b(X)
, b(X) -> a(X)}
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:
{ f(f(X)) -> f(a(b(f(X))))
, f(a(g(X))) -> b(X)
, b(X) -> a(X)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, a_0(2) -> 2
, a_1(2) -> 1
, a_2(2) -> 1
, b_0(2) -> 1
, b_1(2) -> 1
, g_0(2) -> 2}