Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(s(x1)) -> s(a(x1))
b(a(b(s(x1)))) -> a(b(s(a(x1))))
b(a(b(b(x1)))) -> c(s(x1))
c(s(x1)) -> a(b(a(b(x1))))
a(b(a(a(x1)))) -> b(a(b(a(x1))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3,2}
transitions:
a1(22) -> 23*
a1(12) -> 13*
a1(14) -> 15*
a1(8) -> 9*
b1(21) -> 22*
b1(11) -> 12*
b1(13) -> 14*
s1(9) -> 10*
a0(1) -> 2*
s0(1) -> 1*
b0(1) -> 3*
c0(1) -> 4*
1 -> 11,8
10 -> 21,9,2
15 -> 4*
23 -> 14*
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(s(x1)) -> s(a(x1))
, b(a(b(s(x1)))) -> a(b(s(a(x1))))
, b(a(b(b(x1)))) -> c(s(x1))
, c(s(x1)) -> a(b(a(b(x1))))
, a(b(a(a(x1)))) -> b(a(b(a(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(s(x1)) -> s(a(x1))
, b(a(b(s(x1)))) -> a(b(s(a(x1))))
, b(a(b(b(x1)))) -> c(s(x1))
, c(s(x1)) -> a(b(a(b(x1))))
, a(b(a(a(x1)))) -> b(a(b(a(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(4) -> 1
, a_1(6) -> 5
, a_1(7) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 6
, b_1(3) -> 7
, b_1(5) -> 4
, 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(s(x1)) -> s(a(x1))
, b(a(b(s(x1)))) -> a(b(s(a(x1))))
, b(a(b(b(x1)))) -> c(s(x1))
, c(s(x1)) -> a(b(a(b(x1))))
, a(b(a(a(x1)))) -> b(a(b(a(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(s(x1)) -> s(a(x1))
, b(a(b(s(x1)))) -> a(b(s(a(x1))))
, b(a(b(b(x1)))) -> c(s(x1))
, c(s(x1)) -> a(b(a(b(x1))))
, a(b(a(a(x1)))) -> b(a(b(a(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(4) -> 1
, a_1(6) -> 5
, a_1(7) -> 4
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 6
, b_1(3) -> 7
, b_1(5) -> 4
, c_0(2) -> 1}