'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)))))))))))))))))))))))))
, 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(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))))))))))))))))))))))
, 0^#(1(2(1(x1)))) ->
c_6(0^#(1(2(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)))))))))))))))))))))))))
, 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(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_6(0^#(1(2(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_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_6(0^#(1(2(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_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_6(0^#(1(2(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_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_6(0^#(1(2(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_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_6(0^#(1(2(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_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_6(0^#(1(2(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_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)))))))}
{0^#(1(2(1(x1)))) ->
c_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_6(0^#(1(2(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_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)))))))))))))))))))))))))
, 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(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)))) ->
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(0(1(2(x1))))))))))))))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_6(0^#(1(2(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_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)))) ->
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(0(1(2(x1))))))))))))))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_6(0^#(1(2(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_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)))) ->
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(0(1(2(x1))))))))))))))))))))))))))))
, 0^#(1(2(1(x1)))) -> c_0(0^#(1(2(0(1(2(x1)))))))
, 0^#(1(2(1(x1)))) ->
c_6(0^#(1(2(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_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) -> 27
, 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_1(25) -> 24
, 0_2(40) -> 39
, 0_2(43) -> 42
, 0_2(46) -> 45
, 0_2(52) -> 51
, 0_2(55) -> 54
, 0_2(58) -> 57
, 0_2(61) -> 60
, 0_2(67) -> 66
, 0_2(70) -> 69
, 0_2(73) -> 72
, 0_2(76) -> 75
, 0_2(79) -> 78
, 0_2(85) -> 84
, 0_2(88) -> 87
, 0_2(91) -> 90
, 0_2(94) -> 93
, 0_2(97) -> 96
, 0_2(100) -> 99
, 0_2(106) -> 105
, 0_2(109) -> 108
, 0_2(112) -> 111
, 0_2(115) -> 114
, 0_2(118) -> 117
, 0_2(121) -> 120
, 0_2(124) -> 123
, 0_2(130) -> 129
, 0_2(133) -> 132
, 0_2(136) -> 135
, 0_2(139) -> 138
, 0_2(142) -> 141
, 0_2(145) -> 144
, 0_2(148) -> 147
, 0_2(151) -> 150
, 0_2(160) -> 189
, 0_2(163) -> 162
, 0_2(172) -> 129
, 0_2(175) -> 174
, 0_2(178) -> 177
, 0_2(181) -> 180
, 0_2(184) -> 183
, 0_2(187) -> 186
, 1_0(2) -> 2
, 1_1(5) -> 4
, 1_1(8) -> 7
, 1_1(11) -> 10
, 1_1(12) -> 35
, 1_1(14) -> 13
, 1_1(15) -> 35
, 1_1(17) -> 16
, 1_1(18) -> 35
, 1_1(20) -> 19
, 1_1(21) -> 35
, 1_1(23) -> 22
, 1_1(24) -> 35
, 1_1(26) -> 25
, 1_1(27) -> 35
, 1_1(33) -> 6
, 1_1(35) -> 34
, 1_2(36) -> 27
, 1_2(38) -> 37
, 1_2(39) -> 38
, 1_2(41) -> 40
, 1_2(42) -> 38
, 1_2(44) -> 43
, 1_2(47) -> 46
, 1_2(48) -> 24
, 1_2(50) -> 49
, 1_2(51) -> 50
, 1_2(53) -> 52
, 1_2(54) -> 50
, 1_2(56) -> 55
, 1_2(57) -> 50
, 1_2(59) -> 58
, 1_2(62) -> 61
, 1_2(63) -> 21
, 1_2(65) -> 64
, 1_2(66) -> 65
, 1_2(68) -> 67
, 1_2(69) -> 65
, 1_2(71) -> 70
, 1_2(72) -> 65
, 1_2(74) -> 73
, 1_2(75) -> 65
, 1_2(77) -> 76
, 1_2(80) -> 79
, 1_2(81) -> 18
, 1_2(83) -> 82
, 1_2(84) -> 83
, 1_2(86) -> 85
, 1_2(87) -> 83
, 1_2(89) -> 88
, 1_2(90) -> 83
, 1_2(92) -> 91
, 1_2(93) -> 83
, 1_2(95) -> 94
, 1_2(96) -> 83
, 1_2(98) -> 97
, 1_2(101) -> 100
, 1_2(102) -> 15
, 1_2(104) -> 103
, 1_2(105) -> 104
, 1_2(107) -> 106
, 1_2(108) -> 104
, 1_2(110) -> 109
, 1_2(111) -> 104
, 1_2(113) -> 112
, 1_2(114) -> 104
, 1_2(116) -> 115
, 1_2(117) -> 104
, 1_2(119) -> 118
, 1_2(120) -> 104
, 1_2(122) -> 121
, 1_2(125) -> 124
, 1_2(126) -> 12
, 1_2(128) -> 127
, 1_2(129) -> 128
, 1_2(131) -> 130
, 1_2(132) -> 128
, 1_2(134) -> 133
, 1_2(135) -> 128
, 1_2(137) -> 136
, 1_2(138) -> 128
, 1_2(140) -> 139
, 1_2(141) -> 128
, 1_2(143) -> 142
, 1_2(144) -> 128
, 1_2(146) -> 145
, 1_2(147) -> 128
, 1_2(149) -> 148
, 1_2(152) -> 151
, 1_2(161) -> 160
, 1_2(164) -> 163
, 1_2(173) -> 172
, 1_2(174) -> 128
, 1_2(176) -> 175
, 1_2(177) -> 128
, 1_2(179) -> 178
, 1_2(180) -> 128
, 1_2(182) -> 181
, 1_2(183) -> 128
, 1_2(185) -> 184
, 1_2(186) -> 128
, 1_2(188) -> 187
, 1_2(189) -> 128
, 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(27) -> 26
, 2_1(34) -> 33
, 2_2(33) -> 47
, 2_2(36) -> 62
, 2_2(37) -> 36
, 2_2(39) -> 41
, 2_2(42) -> 41
, 2_2(45) -> 44
, 2_2(48) -> 80
, 2_2(49) -> 48
, 2_2(51) -> 53
, 2_2(54) -> 53
, 2_2(57) -> 56
, 2_2(60) -> 59
, 2_2(63) -> 101
, 2_2(64) -> 63
, 2_2(66) -> 68
, 2_2(69) -> 68
, 2_2(72) -> 71
, 2_2(75) -> 74
, 2_2(78) -> 77
, 2_2(81) -> 125
, 2_2(82) -> 81
, 2_2(84) -> 86
, 2_2(87) -> 86
, 2_2(90) -> 89
, 2_2(93) -> 92
, 2_2(96) -> 95
, 2_2(99) -> 98
, 2_2(102) -> 152
, 2_2(103) -> 102
, 2_2(105) -> 107
, 2_2(108) -> 107
, 2_2(111) -> 110
, 2_2(114) -> 113
, 2_2(117) -> 116
, 2_2(120) -> 119
, 2_2(123) -> 122
, 2_2(126) -> 164
, 2_2(127) -> 126
, 2_2(132) -> 131
, 2_2(135) -> 134
, 2_2(138) -> 137
, 2_2(141) -> 140
, 2_2(144) -> 143
, 2_2(147) -> 146
, 2_2(150) -> 149
, 2_2(162) -> 161
, 2_2(174) -> 173
, 2_2(177) -> 176
, 2_2(180) -> 179
, 2_2(183) -> 182
, 2_2(186) -> 185
, 2_2(189) -> 188
, 0^#_0(2) -> 1
, 0^#_1(4) -> 3
, 0^#_1(10) -> 9
, 0^#_1(13) -> 28
, 0^#_1(16) -> 29
, 0^#_1(19) -> 30
, 0^#_1(22) -> 31
, 0^#_1(25) -> 32
, 0^#_2(40) -> 165
, 0^#_2(43) -> 153
, 0^#_2(52) -> 166
, 0^#_2(55) -> 204
, 0^#_2(58) -> 154
, 0^#_2(67) -> 167
, 0^#_2(70) -> 199
, 0^#_2(73) -> 205
, 0^#_2(76) -> 155
, 0^#_2(85) -> 168
, 0^#_2(88) -> 195
, 0^#_2(91) -> 200
, 0^#_2(94) -> 206
, 0^#_2(97) -> 156
, 0^#_2(106) -> 169
, 0^#_2(109) -> 192
, 0^#_2(112) -> 196
, 0^#_2(115) -> 201
, 0^#_2(118) -> 207
, 0^#_2(121) -> 157
, 0^#_2(130) -> 170
, 0^#_2(133) -> 190
, 0^#_2(136) -> 193
, 0^#_2(139) -> 197
, 0^#_2(142) -> 202
, 0^#_2(145) -> 208
, 0^#_2(148) -> 158
, 0^#_2(160) -> 159
, 0^#_2(172) -> 171
, 0^#_2(175) -> 191
, 0^#_2(178) -> 194
, 0^#_2(181) -> 198
, 0^#_2(184) -> 203
, 0^#_2(187) -> 209
, c_0_1(3) -> 1
, c_0_2(153) -> 3
, c_0_2(154) -> 32
, c_0_2(155) -> 31
, c_0_2(156) -> 30
, c_0_2(157) -> 29
, c_0_2(158) -> 28
, c_0_2(159) -> 9
, c_1_1(32) -> 1
, c_1_2(165) -> 3
, c_1_2(204) -> 32
, c_1_2(205) -> 31
, c_1_2(206) -> 30
, c_1_2(207) -> 29
, c_1_2(208) -> 28
, c_1_2(209) -> 9
, c_2_1(31) -> 1
, c_2_2(165) -> 3
, c_2_2(166) -> 32
, c_2_2(199) -> 31
, c_2_2(200) -> 30
, c_2_2(201) -> 29
, c_2_2(202) -> 28
, c_2_2(203) -> 9
, c_3_1(30) -> 1
, c_3_2(165) -> 3
, c_3_2(166) -> 32
, c_3_2(167) -> 31
, c_3_2(195) -> 30
, c_3_2(196) -> 29
, c_3_2(197) -> 28
, c_3_2(198) -> 9
, c_4_1(29) -> 1
, c_4_2(165) -> 3
, c_4_2(166) -> 32
, c_4_2(167) -> 31
, c_4_2(168) -> 30
, c_4_2(192) -> 29
, c_4_2(193) -> 28
, c_4_2(194) -> 9
, c_5_1(28) -> 1
, c_5_2(165) -> 3
, c_5_2(166) -> 32
, c_5_2(167) -> 31
, c_5_2(168) -> 30
, c_5_2(169) -> 29
, c_5_2(190) -> 28
, c_5_2(191) -> 9
, c_6_1(9) -> 1
, c_6_2(165) -> 3
, c_6_2(166) -> 32
, c_6_2(167) -> 31
, c_6_2(168) -> 30
, c_6_2(169) -> 29
, c_6_2(170) -> 28
, c_6_2(171) -> 9}