'Weak Dependency Graph [60.0]'
------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 3(4(5(x1))) -> 4(3(5(x1)))
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
Details:
We have computed the following set of weak (innermost) dependency pairs:
{ 0^#(x1) -> c_0()
, 0^#(0(x1)) -> c_1(0^#(x1))
, 3^#(4(5(x1))) -> c_2(3^#(5(x1)))
, 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
The usable rules are:
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
The estimated dependency graph contains the following edges:
{0^#(0(x1)) -> c_1(0^#(x1))}
==> {0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
{0^#(0(x1)) -> c_1(0^#(x1))}
==> {0^#(0(x1)) -> c_1(0^#(x1))}
{0^#(0(x1)) -> c_1(0^#(x1))}
==> {0^#(x1) -> c_0()}
{2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
==> {0^#(x1) -> c_0()}
{0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
==> {2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
We consider the following path(s):
1) { 0^#(0(x1)) -> c_1(0^#(x1))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
The usable rules for this path are the following:
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
0(x1) = [1] x1 + [10]
1(x1) = [1] x1 + [1]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [1] x1 + [8]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
Weak Rules:
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
We apply the weight gap principle, strictly orienting the rules
{2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
and weakly orienting the rules
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
Details:
Interpretation Functions:
0(x1) = [1] x1 + [6]
1(x1) = [1] x1 + [5]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [1] x1 + [8]
0^#(x1) = [1] x1 + [8]
c_0() = [0]
c_1(x1) = [1] x1 + [1]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [1] x1 + [8]
c_3(x1) = [1] x1 + [1]
c_4(x1) = [1] x1 + [8]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules:
{ 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
The given problem does not contain any strict rules
2) { 0^#(0(x1)) -> c_1(0^#(x1))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(x1) -> c_0()}
The usable rules for this path are the following:
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
0(x1) = [1] x1 + [10]
1(x1) = [1] x1 + [1]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [1] x1 + [8]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {0^#(x1) -> c_0()}
Weak Rules:
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
We apply the weight gap principle, strictly orienting the rules
{0^#(x1) -> c_0()}
and weakly orienting the rules
{ 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{0^#(x1) -> c_0()}
Details:
Interpretation Functions:
0(x1) = [1] x1 + [0]
1(x1) = [1] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [1] x1 + [0]
0^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [1] x1 + [1]
c_3(x1) = [1] x1 + [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules:
{ 0^#(x1) -> c_0()
, 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_3(0^#(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
The given problem does not contain any strict rules
3) { 0^#(0(x1)) -> c_1(0^#(x1))
, 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
The usable rules for this path are the following:
{ 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
0(x1) = [1] x1 + [9]
1(x1) = [1] x1 + [2]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [1] x1 + [8]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
Weak Rules:
{ 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
We apply the weight gap principle, strictly orienting the rules
{0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
and weakly orienting the rules
{ 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}
Details:
Interpretation Functions:
0(x1) = [1] x1 + [0]
1(x1) = [1] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [1] x1 + [0]
0^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules:
{ 0^#(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
c_4(2^#(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
0(1(0(1(0(0(1(0(0(0(0(0(0(1(0(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(1(0(0(0(1(1(0(0(0(0(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0(x1) -> 1(x1)
, 0(0(x1)) -> 0(x1)
, 0(0(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(0(0(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(0(1(1(1(0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(1(1(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(1(1(1(1(0(1(0(1(1(0(1(1(0(1(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
->
2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
The given problem does not contain any strict rules
4) {3^#(4(5(x1))) -> c_2(3^#(5(x1)))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
0(x1) = [0] x1 + [0]
1(x1) = [0] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [0] x1 + [0]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {3^#(4(5(x1))) -> c_2(3^#(5(x1)))}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{3^#(4(5(x1))) -> c_2(3^#(5(x1)))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{3^#(4(5(x1))) -> c_2(3^#(5(x1)))}
Details:
Interpretation Functions:
0(x1) = [0] x1 + [0]
1(x1) = [0] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [1] x1 + [8]
5(x1) = [1] x1 + [0]
2(x1) = [0] x1 + [0]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [1] x1 + [10]
c_2(x1) = [1] x1 + [2]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules: {3^#(4(5(x1))) -> c_2(3^#(5(x1)))}
Details:
The given problem does not contain any strict rules
5) { 0^#(0(x1)) -> c_1(0^#(x1))
, 0^#(x1) -> c_0()}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
0(x1) = [0] x1 + [0]
1(x1) = [0] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [0] x1 + [0]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {0^#(x1) -> c_0()}
Weak Rules: {0^#(0(x1)) -> c_1(0^#(x1))}
Details:
We apply the weight gap principle, strictly orienting the rules
{0^#(x1) -> c_0()}
and weakly orienting the rules
{0^#(0(x1)) -> c_1(0^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{0^#(x1) -> c_0()}
Details:
Interpretation Functions:
0(x1) = [1] x1 + [0]
1(x1) = [0] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [0] x1 + [0]
0^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1(x1) = [1] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules:
{ 0^#(x1) -> c_0()
, 0^#(0(x1)) -> c_1(0^#(x1))}
Details:
The given problem does not contain any strict rules
6) {0^#(0(x1)) -> c_1(0^#(x1))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
0(x1) = [0] x1 + [0]
1(x1) = [0] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [0] x1 + [0]
0^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {0^#(0(x1)) -> c_1(0^#(x1))}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{0^#(0(x1)) -> c_1(0^#(x1))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{0^#(0(x1)) -> c_1(0^#(x1))}
Details:
Interpretation Functions:
0(x1) = [1] x1 + [8]
1(x1) = [0] x1 + [0]
3(x1) = [0] x1 + [0]
4(x1) = [0] x1 + [0]
5(x1) = [0] x1 + [0]
2(x1) = [0] x1 + [0]
0^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1(x1) = [1] x1 + [3]
3^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
2^#(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [0] x1 + [0]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules: {0^#(0(x1)) -> c_1(0^#(x1))}
Details:
The given problem does not contain any strict rules