Tool CaT
stdout:
YES(?,O(n^1))
Problem:
b(a(a(x1))) -> a(b(c(x1)))
c(a(x1)) -> a(c(x1))
b(c(a(x1))) -> a(b(c(x1)))
c(b(x1)) -> d(x1)
a(d(x1)) -> d(a(x1))
d(x1) -> b(a(x1))
L(a(a(x1))) -> L(a(b(c(x1))))
c(R(x1)) -> c(b(R(x1)))
Proof:
Bounds Processor:
bound: 3
enrichment: match
automaton:
final states: {6,5,4,3,2}
transitions:
c1(15) -> 16*
b1(14) -> 15*
b1(11) -> 12*
R1(13) -> 14*
a1(10) -> 11*
d2(23) -> 24*
b3(29) -> 30*
a3(28) -> 29*
b0(1) -> 2*
a0(1) -> 4*
c0(1) -> 3*
d0(1) -> 5*
L0(1) -> 6*
R0(1) -> 1*
1 -> 13,10
12 -> 5*
14 -> 23*
16 -> 3*
23 -> 28*
24 -> 16,3
30 -> 24,16
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(a(x1))) -> a(b(c(x1)))
, c(a(x1)) -> a(c(x1))
, b(c(a(x1))) -> a(b(c(x1)))
, c(b(x1)) -> d(x1)
, a(d(x1)) -> d(a(x1))
, d(x1) -> b(a(x1))
, L(a(a(x1))) -> L(a(b(c(x1))))
, c(R(x1)) -> c(b(R(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(a(x1))) -> a(b(c(x1)))
, c(a(x1)) -> a(c(x1))
, b(c(a(x1))) -> a(b(c(x1)))
, c(b(x1)) -> d(x1)
, a(d(x1)) -> d(a(x1))
, d(x1) -> b(a(x1))
, L(a(a(x1))) -> L(a(b(c(x1))))
, c(R(x1)) -> c(b(R(x1)))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(3) -> 1
, b_1(5) -> 4
, b_3(6) -> 1
, a_0(2) -> 1
, a_1(2) -> 3
, a_3(5) -> 6
, c_0(2) -> 1
, c_1(4) -> 1
, d_0(2) -> 1
, d_2(5) -> 1
, L_0(2) -> 1
, R_0(2) -> 2
, R_1(2) -> 5}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(a(x1))) -> a(b(c(x1)))
, c(a(x1)) -> a(c(x1))
, b(c(a(x1))) -> a(b(c(x1)))
, c(b(x1)) -> d(x1)
, a(d(x1)) -> d(a(x1))
, d(x1) -> b(a(x1))
, L(a(a(x1))) -> L(a(b(c(x1))))
, c(R(x1)) -> c(b(R(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(a(x1))) -> a(b(c(x1)))
, c(a(x1)) -> a(c(x1))
, b(c(a(x1))) -> a(b(c(x1)))
, c(b(x1)) -> d(x1)
, a(d(x1)) -> d(a(x1))
, d(x1) -> b(a(x1))
, L(a(a(x1))) -> L(a(b(c(x1))))
, c(R(x1)) -> c(b(R(x1)))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ b_0(2) -> 1
, b_1(3) -> 1
, b_1(5) -> 4
, b_3(6) -> 1
, a_0(2) -> 1
, a_1(2) -> 3
, a_3(5) -> 6
, c_0(2) -> 1
, c_1(4) -> 1
, d_0(2) -> 1
, d_2(5) -> 1
, L_0(2) -> 1
, R_0(2) -> 2
, R_1(2) -> 5}