Tool CaT
stdout:
YES(?,O(n^1))
Problem:
s(b(x1)) -> b(s(s(s(x1))))
s(b(s(x1))) -> b(t(x1))
t(b(x1)) -> b(s(x1))
t(b(s(x1))) -> u(t(b(x1)))
b(u(x1)) -> b(s(x1))
t(s(x1)) -> t(t(x1))
t(u(x1)) -> u(t(x1))
s(u(x1)) -> s(s(x1))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3,2}
transitions:
s1(19) -> 20*
s1(8) -> 9*
u1(12) -> 13*
t1(11) -> 12*
b1(9) -> 10*
s0(1) -> 2*
b0(1) -> 4*
t0(1) -> 3*
u0(1) -> 1*
1 -> 11,8
9 -> 19*
10 -> 4*
13 -> 12,3
20 -> 9,19,2
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:
{ s(b(x1)) -> b(s(s(s(x1))))
, s(b(s(x1))) -> b(t(x1))
, t(b(x1)) -> b(s(x1))
, t(b(s(x1))) -> u(t(b(x1)))
, b(u(x1)) -> b(s(x1))
, t(s(x1)) -> t(t(x1))
, t(u(x1)) -> u(t(x1))
, s(u(x1)) -> s(s(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:
{ s(b(x1)) -> b(s(s(s(x1))))
, s(b(s(x1))) -> b(t(x1))
, t(b(x1)) -> b(s(x1))
, t(b(s(x1))) -> u(t(b(x1)))
, b(u(x1)) -> b(s(x1))
, t(s(x1)) -> t(t(x1))
, t(u(x1)) -> u(t(x1))
, s(u(x1)) -> s(s(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ s_0(2) -> 1
, s_1(2) -> 3
, s_1(3) -> 1
, s_1(3) -> 3
, b_0(2) -> 1
, b_1(3) -> 1
, t_0(2) -> 1
, t_1(2) -> 4
, u_0(2) -> 2
, u_1(4) -> 1
, u_1(4) -> 4}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:
{ s(b(x1)) -> b(s(s(s(x1))))
, s(b(s(x1))) -> b(t(x1))
, t(b(x1)) -> b(s(x1))
, t(b(s(x1))) -> u(t(b(x1)))
, b(u(x1)) -> b(s(x1))
, t(s(x1)) -> t(t(x1))
, t(u(x1)) -> u(t(x1))
, s(u(x1)) -> s(s(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:
{ s(b(x1)) -> b(s(s(s(x1))))
, s(b(s(x1))) -> b(t(x1))
, t(b(x1)) -> b(s(x1))
, t(b(s(x1))) -> u(t(b(x1)))
, b(u(x1)) -> b(s(x1))
, t(s(x1)) -> t(t(x1))
, t(u(x1)) -> u(t(x1))
, s(u(x1)) -> s(s(x1))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ s_0(2) -> 1
, s_1(2) -> 3
, s_1(3) -> 1
, s_1(3) -> 3
, b_0(2) -> 1
, b_1(3) -> 1
, t_0(2) -> 1
, t_1(2) -> 4
, u_0(2) -> 2
, u_1(4) -> 1
, u_1(4) -> 4}