Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(x1) -> g(d(x1))
b(b(b(x1))) -> c(d(c(x1)))
b(b(x1)) -> a(g(g(x1)))
c(d(x1)) -> g(g(x1))
g(g(g(x1))) -> b(b(x1))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {5,4,3,2}
transitions:
g1(10) -> 11*
g1(12) -> 13*
g1(13) -> 14*
d1(9) -> 10*
a0(1) -> 2*
g0(1) -> 5*
d0(1) -> 1*
b0(1) -> 3*
c0(1) -> 4*
1 -> 12,9
11 -> 2*
14 -> 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(x1) -> g(d(x1))
, b(b(b(x1))) -> c(d(c(x1)))
, b(b(x1)) -> a(g(g(x1)))
, c(d(x1)) -> g(g(x1))
, g(g(g(x1))) -> b(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(x1) -> g(d(x1))
, b(b(b(x1))) -> c(d(c(x1)))
, b(b(x1)) -> a(g(g(x1)))
, c(d(x1)) -> g(g(x1))
, g(g(g(x1))) -> b(b(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, g_0(2) -> 1
, g_1(2) -> 3
, g_1(3) -> 1
, d_0(2) -> 2
, d_1(2) -> 3
, b_0(2) -> 1
, 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:
{ a(x1) -> g(d(x1))
, b(b(b(x1))) -> c(d(c(x1)))
, b(b(x1)) -> a(g(g(x1)))
, c(d(x1)) -> g(g(x1))
, g(g(g(x1))) -> b(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(x1) -> g(d(x1))
, b(b(b(x1))) -> c(d(c(x1)))
, b(b(x1)) -> a(g(g(x1)))
, c(d(x1)) -> g(g(x1))
, g(g(g(x1))) -> b(b(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, g_0(2) -> 1
, g_1(2) -> 3
, g_1(3) -> 1
, d_0(2) -> 2
, d_1(2) -> 3
, b_0(2) -> 1
, c_0(2) -> 1}