'Weak Dependency Graph [60.0]'
------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))}
Details:
We have computed the following set of weak (innermost) dependency pairs:
{ 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))
, 0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
The usable rules are:
{ 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))}
The estimated dependency graph contains the following edges:
{0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
==> {0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
==> {0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
==> {0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
==> {0^#(1(2(1(x1)))) ->
c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
{0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
==> {0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
{0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
==> {0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
{0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
{0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
==> {0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
{0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
==> {0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
{0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
{0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
{0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
{0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
{0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
{0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
{0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
{0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
{0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
{0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
{0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))}
{0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
==> {0^#(1(2(1(x1)))) ->
c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))}
{0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
{0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))}
==> {0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))}
We consider the following path(s):
1) { 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
The usable rules for this path are the following:
{ 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))}
We have applied the subprocessor on the union of usable rules and weak (innermost) dependency pairs.
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
Details:
'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment''
------------------------------------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
Details:
The problem was solved by processor 'Bounds with default enrichment':
'Bounds with default enrichment'
--------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
, 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0(1(2(1(x1)))) ->
1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_5(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_4(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_3(0^#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_2(0^#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))
, 0^#(1(2(1(x1)))) -> c_1(0^#(1(2(0(1(2(0(1(2(x1))))))))))}
Details:
The problem is Match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 0_1(4) -> 24
, 0_1(7) -> 6
, 0_1(10) -> 12
, 0_1(13) -> 12
, 0_1(16) -> 15
, 0_1(19) -> 18
, 0_1(22) -> 21
, 0_2(36) -> 35
, 0_2(39) -> 38
, 0_2(42) -> 41
, 0_2(48) -> 47
, 0_2(51) -> 50
, 0_2(54) -> 53
, 0_2(57) -> 56
, 0_2(63) -> 62
, 0_2(66) -> 65
, 0_2(69) -> 68
, 0_2(72) -> 71
, 0_2(75) -> 74
, 0_2(81) -> 80
, 0_2(84) -> 83
, 0_2(87) -> 86
, 0_2(90) -> 89
, 0_2(93) -> 92
, 0_2(96) -> 95
, 0_2(102) -> 101
, 0_2(105) -> 104
, 0_2(108) -> 107
, 0_2(111) -> 110
, 0_2(114) -> 113
, 0_2(117) -> 116
, 0_2(120) -> 119
, 0_2(128) -> 153
, 0_2(131) -> 130
, 0_2(139) -> 101
, 0_2(142) -> 141
, 0_2(145) -> 144
, 0_2(148) -> 147
, 0_2(151) -> 150
, 1_0(2) -> 2
, 1_1(5) -> 4
, 1_1(8) -> 7
, 1_1(11) -> 10
, 1_1(12) -> 31
, 1_1(14) -> 13
, 1_1(15) -> 31
, 1_1(17) -> 16
, 1_1(18) -> 31
, 1_1(20) -> 19
, 1_1(21) -> 31
, 1_1(23) -> 22
, 1_1(24) -> 31
, 1_1(29) -> 6
, 1_1(31) -> 30
, 1_2(32) -> 24
, 1_2(34) -> 33
, 1_2(35) -> 34
, 1_2(37) -> 36
, 1_2(38) -> 34
, 1_2(40) -> 39
, 1_2(43) -> 42
, 1_2(44) -> 21
, 1_2(46) -> 45
, 1_2(47) -> 46
, 1_2(49) -> 48
, 1_2(50) -> 46
, 1_2(52) -> 51
, 1_2(53) -> 46
, 1_2(55) -> 54
, 1_2(58) -> 57
, 1_2(59) -> 18
, 1_2(61) -> 60
, 1_2(62) -> 61
, 1_2(64) -> 63
, 1_2(65) -> 61
, 1_2(67) -> 66
, 1_2(68) -> 61
, 1_2(70) -> 69
, 1_2(71) -> 61
, 1_2(73) -> 72
, 1_2(76) -> 75
, 1_2(77) -> 15
, 1_2(79) -> 78
, 1_2(80) -> 79
, 1_2(82) -> 81
, 1_2(83) -> 79
, 1_2(85) -> 84
, 1_2(86) -> 79
, 1_2(88) -> 87
, 1_2(89) -> 79
, 1_2(91) -> 90
, 1_2(92) -> 79
, 1_2(94) -> 93
, 1_2(97) -> 96
, 1_2(98) -> 12
, 1_2(100) -> 99
, 1_2(101) -> 100
, 1_2(103) -> 102
, 1_2(104) -> 100
, 1_2(106) -> 105
, 1_2(107) -> 100
, 1_2(109) -> 108
, 1_2(110) -> 100
, 1_2(112) -> 111
, 1_2(113) -> 100
, 1_2(115) -> 114
, 1_2(116) -> 100
, 1_2(118) -> 117
, 1_2(121) -> 120
, 1_2(129) -> 128
, 1_2(132) -> 131
, 1_2(140) -> 139
, 1_2(141) -> 100
, 1_2(143) -> 142
, 1_2(144) -> 100
, 1_2(146) -> 145
, 1_2(147) -> 100
, 1_2(149) -> 148
, 1_2(150) -> 100
, 1_2(152) -> 151
, 1_2(153) -> 100
, 2_0(2) -> 2
, 2_1(2) -> 8
, 2_1(6) -> 5
, 2_1(12) -> 11
, 2_1(15) -> 14
, 2_1(18) -> 17
, 2_1(21) -> 20
, 2_1(24) -> 23
, 2_1(30) -> 29
, 2_2(29) -> 43
, 2_2(32) -> 58
, 2_2(33) -> 32
, 2_2(35) -> 37
, 2_2(38) -> 37
, 2_2(41) -> 40
, 2_2(44) -> 76
, 2_2(45) -> 44
, 2_2(47) -> 49
, 2_2(50) -> 49
, 2_2(53) -> 52
, 2_2(56) -> 55
, 2_2(59) -> 97
, 2_2(60) -> 59
, 2_2(62) -> 64
, 2_2(65) -> 64
, 2_2(68) -> 67
, 2_2(71) -> 70
, 2_2(74) -> 73
, 2_2(77) -> 121
, 2_2(78) -> 77
, 2_2(80) -> 82
, 2_2(83) -> 82
, 2_2(86) -> 85
, 2_2(89) -> 88
, 2_2(92) -> 91
, 2_2(95) -> 94
, 2_2(98) -> 132
, 2_2(99) -> 98
, 2_2(104) -> 103
, 2_2(107) -> 106
, 2_2(110) -> 109
, 2_2(113) -> 112
, 2_2(116) -> 115
, 2_2(119) -> 118
, 2_2(130) -> 129
, 2_2(141) -> 140
, 2_2(144) -> 143
, 2_2(147) -> 146
, 2_2(150) -> 149
, 2_2(153) -> 152
, 0^#_0(2) -> 1
, 0^#_1(4) -> 3
, 0^#_1(10) -> 9
, 0^#_1(13) -> 25
, 0^#_1(16) -> 26
, 0^#_1(19) -> 27
, 0^#_1(22) -> 28
, 0^#_2(36) -> 133
, 0^#_2(39) -> 122
, 0^#_2(48) -> 134
, 0^#_2(51) -> 163
, 0^#_2(54) -> 123
, 0^#_2(63) -> 135
, 0^#_2(66) -> 159
, 0^#_2(69) -> 164
, 0^#_2(72) -> 124
, 0^#_2(81) -> 136
, 0^#_2(84) -> 156
, 0^#_2(87) -> 160
, 0^#_2(90) -> 165
, 0^#_2(93) -> 125
, 0^#_2(102) -> 137
, 0^#_2(105) -> 154
, 0^#_2(108) -> 157
, 0^#_2(111) -> 161
, 0^#_2(114) -> 166
, 0^#_2(117) -> 126
, 0^#_2(128) -> 127
, 0^#_2(139) -> 138
, 0^#_2(142) -> 155
, 0^#_2(145) -> 158
, 0^#_2(148) -> 162
, 0^#_2(151) -> 167
, c_0_1(3) -> 1
, c_0_2(122) -> 3
, c_0_2(123) -> 28
, c_0_2(124) -> 27
, c_0_2(125) -> 26
, c_0_2(126) -> 25
, c_0_2(127) -> 9
, c_1_1(28) -> 1
, c_1_2(133) -> 3
, c_1_2(163) -> 28
, c_1_2(164) -> 27
, c_1_2(165) -> 26
, c_1_2(166) -> 25
, c_1_2(167) -> 9
, c_2_1(27) -> 1
, c_2_2(133) -> 3
, c_2_2(134) -> 28
, c_2_2(159) -> 27
, c_2_2(160) -> 26
, c_2_2(161) -> 25
, c_2_2(162) -> 9
, c_3_1(26) -> 1
, c_3_2(133) -> 3
, c_3_2(134) -> 28
, c_3_2(135) -> 27
, c_3_2(156) -> 26
, c_3_2(157) -> 25
, c_3_2(158) -> 9
, c_4_1(25) -> 1
, c_4_2(133) -> 3
, c_4_2(134) -> 28
, c_4_2(135) -> 27
, c_4_2(136) -> 26
, c_4_2(154) -> 25
, c_4_2(155) -> 9
, c_5_1(9) -> 1
, c_5_2(133) -> 3
, c_5_2(134) -> 28
, c_5_2(135) -> 27
, c_5_2(136) -> 26
, c_5_2(137) -> 25
, c_5_2(138) -> 9}