Tool CaT
stdout:
YES(?,O(n^1))
Problem:
h(f(x,y)) -> f(f(a(),h(h(y))),x)
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3}
transitions:
f1(6,16) -> 17*
f1(17,1) -> 18,15,3
f1(7,1) -> 18,15,3
f1(6,5) -> 7*
f1(17,2) -> 18,15,3
f1(7,2) -> 18,15,3
a1() -> 6*
h1(15) -> 16*
h1(2) -> 4*
h1(4) -> 5*
h1(1) -> 15*
f2(20,19) -> 21*
f2(21,7) -> 19,16
f2(21,17) -> 19,16
h0(2) -> 3*
h0(1) -> 3*
a2() -> 20*
f0(1,2) -> 1*
f0(2,1) -> 1*
f0(1,1) -> 1*
f0(2,2) -> 1*
h2(2) -> 18*
h2(1) -> 18*
h2(18) -> 19*
a0() -> 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: {h(f(x, y)) -> f(f(a(), h(h(y))), 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: {h(f(x, y)) -> f(f(a(), h(h(y))), x)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ h_0(2) -> 1
, h_1(2) -> 6
, h_1(6) -> 5
, h_2(2) -> 10
, h_2(10) -> 9
, f_0(2, 2) -> 2
, f_1(3, 2) -> 1
, f_1(3, 2) -> 6
, f_1(3, 2) -> 10
, f_1(4, 5) -> 3
, f_2(7, 3) -> 5
, f_2(7, 3) -> 9
, f_2(8, 9) -> 7
, a_0() -> 2
, a_1() -> 4
, a_2() -> 8}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: {h(f(x, y)) -> f(f(a(), h(h(y))), 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: {h(f(x, y)) -> f(f(a(), h(h(y))), x)}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ h_0(2) -> 1
, h_1(2) -> 6
, h_1(6) -> 5
, h_2(2) -> 10
, h_2(10) -> 9
, f_0(2, 2) -> 2
, f_1(3, 2) -> 1
, f_1(3, 2) -> 6
, f_1(3, 2) -> 10
, f_1(4, 5) -> 3
, f_2(7, 3) -> 5
, f_2(7, 3) -> 9
, f_2(8, 9) -> 7
, a_0() -> 2
, a_1() -> 4
, a_2() -> 8}