Tool CaT
stdout:
YES(?,O(n^1))
Problem:
h(x,c(y,z)) -> h(c(s(y),x),z)
h(c(s(x),c(s(0()),y)),z) -> h(y,c(s(0()),c(x,z)))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4}
transitions:
h1(12,16) -> 4*
h1(2,16) -> 4*
h1(8,1) -> 4*
h1(8,3) -> 4*
h1(1,16) -> 4*
h1(12,1) -> 4*
h1(12,3) -> 4*
h1(8,2) -> 4*
h1(8,16) -> 4*
h1(3,16) -> 4*
h1(12,2) -> 4*
c1(2,16) -> 13*
c1(3,1) -> 13*
c1(3,3) -> 13*
c1(7,28) -> 8*
c1(7,30) -> 8*
c1(7,34) -> 8*
c1(15,13) -> 16*
c1(11,2) -> 8*
c1(1,2) -> 13*
c1(11,8) -> 8*
c1(11,12) -> 8*
c1(1,16) -> 13*
c1(7,1) -> 8*
c1(2,1) -> 13*
c1(7,3) -> 8*
c1(2,3) -> 13*
c1(11,28) -> 8*
c1(11,30) -> 8*
c1(11,34) -> 8*
c1(3,2) -> 13*
c1(3,16) -> 13*
c1(15,16) -> 16*
c1(11,1) -> 12*
c1(1,1) -> 13*
c1(11,3) -> 8*
c1(1,3) -> 13*
c1(7,2) -> 8*
c1(2,2) -> 13*
c1(7,8) -> 8*
c1(7,12) -> 8*
s1(2) -> 7*
s1(14) -> 15*
s1(1) -> 11*
s1(3) -> 7*
01() -> 14*
h2(22,16) -> 4*
h2(28,1) -> 4*
h2(28,3) -> 4*
h2(34,2) -> 4*
h2(34,16) -> 4*
h2(30,1) -> 4*
h2(30,3) -> 4*
h2(22,13) -> 4*
h2(28,2) -> 4*
h2(28,16) -> 4*
h2(34,1) -> 4*
h2(34,3) -> 4*
h2(30,2) -> 4*
h2(30,16) -> 4*
h0(3,1) -> 4*
h0(3,3) -> 4*
h0(1,2) -> 4*
h0(2,1) -> 4*
h0(2,3) -> 4*
h0(3,2) -> 4*
h0(1,1) -> 4*
h0(1,3) -> 4*
h0(2,2) -> 4*
c2(27,22) -> 28*
c2(29,22) -> 30*
c2(21,2) -> 22*
c2(21,8) -> 22*
c2(21,12) -> 22*
c2(21,22) -> 22*
c2(21,28) -> 22*
c2(21,30) -> 22*
c2(21,34) -> 22*
c2(33,22) -> 34*
c2(21,1) -> 22*
c2(21,3) -> 22*
c0(3,1) -> 1*
c0(3,3) -> 1*
c0(1,2) -> 1*
c0(2,1) -> 1*
c0(2,3) -> 1*
c0(3,2) -> 1*
c0(1,1) -> 1*
c0(1,3) -> 1*
c0(2,2) -> 1*
s2(15) -> 21*
s2(2) -> 27*
s2(1) -> 33*
s2(3) -> 29*
s0(2) -> 2*
s0(1) -> 2*
s0(3) -> 2*
00() -> 3*
problem:
QedTool IRC1
stdout:
YES(?,O(n^3))
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(x, c(y, z)) -> h(c(s(y), x), z)
, h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))}
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(x, c(y, z)) -> h(c(s(y), x), z)
, h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ h_0(2, 2) -> 1
, h_1(2, 5) -> 1
, h_1(3, 2) -> 1
, h_1(3, 5) -> 1
, h_1(9, 5) -> 1
, h_1(11, 5) -> 1
, h_2(9, 5) -> 1
, h_2(9, 7) -> 1
, h_2(11, 2) -> 1
, h_2(11, 5) -> 1
, c_0(2, 2) -> 2
, c_1(2, 2) -> 7
, c_1(2, 5) -> 7
, c_1(4, 2) -> 3
, c_1(4, 3) -> 3
, c_1(4, 11) -> 3
, c_1(6, 5) -> 5
, c_1(6, 7) -> 5
, c_2(10, 2) -> 9
, c_2(10, 3) -> 9
, c_2(10, 9) -> 9
, c_2(10, 11) -> 9
, c_2(12, 9) -> 11
, s_0(2) -> 2
, s_1(2) -> 4
, s_1(8) -> 6
, s_2(2) -> 12
, s_2(6) -> 10
, 0_0() -> 2
, 0_1() -> 8}Tool RC1
stdout:
YES(?,O(n^3))
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(x, c(y, z)) -> h(c(s(y), x), z)
, h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))}
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(x, c(y, z)) -> h(c(s(y), x), z)
, h(c(s(x), c(s(0()), y)), z) -> h(y, c(s(0()), c(x, z)))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ h_0(2, 2) -> 1
, h_1(2, 5) -> 1
, h_1(3, 2) -> 1
, h_1(3, 5) -> 1
, h_1(9, 5) -> 1
, h_1(11, 5) -> 1
, h_2(9, 5) -> 1
, h_2(9, 7) -> 1
, h_2(11, 2) -> 1
, h_2(11, 5) -> 1
, c_0(2, 2) -> 2
, c_1(2, 2) -> 7
, c_1(2, 5) -> 7
, c_1(4, 2) -> 3
, c_1(4, 3) -> 3
, c_1(4, 11) -> 3
, c_1(6, 5) -> 5
, c_1(6, 7) -> 5
, c_2(10, 2) -> 9
, c_2(10, 3) -> 9
, c_2(10, 9) -> 9
, c_2(10, 11) -> 9
, c_2(12, 9) -> 11
, s_0(2) -> 2
, s_1(2) -> 4
, s_1(8) -> 6
, s_2(2) -> 12
, s_2(6) -> 10
, 0_0() -> 2
, 0_1() -> 8}