'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)))))))))))))}
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))))))))))}
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)))))))))))))}
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_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_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)))))))}
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_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)))))))))))))}
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)))) -> 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))))))))))}
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)))) -> 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))))))))))}
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)))) -> 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))))))))))}
Details:
The problem is Match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 0_1(6) -> 14
, 0_1(9) -> 8
, 0_1(12) -> 14
, 0_2(22) -> 21
, 0_2(25) -> 24
, 0_2(28) -> 27
, 0_2(32) -> 41
, 0_2(35) -> 34
, 0_2(39) -> 21
, 1_0(2) -> 2
, 1_0(3) -> 2
, 1_1(7) -> 6
, 1_1(10) -> 9
, 1_1(13) -> 12
, 1_1(14) -> 17
, 1_1(15) -> 8
, 1_1(17) -> 16
, 1_2(18) -> 14
, 1_2(20) -> 19
, 1_2(21) -> 20
, 1_2(23) -> 22
, 1_2(24) -> 20
, 1_2(26) -> 25
, 1_2(29) -> 28
, 1_2(33) -> 32
, 1_2(36) -> 35
, 1_2(40) -> 39
, 1_2(41) -> 20
, 2_0(2) -> 3
, 2_0(3) -> 3
, 2_1(2) -> 10
, 2_1(3) -> 10
, 2_1(8) -> 7
, 2_1(14) -> 13
, 2_1(16) -> 15
, 2_2(15) -> 29
, 2_2(18) -> 36
, 2_2(19) -> 18
, 2_2(24) -> 23
, 2_2(27) -> 26
, 2_2(34) -> 33
, 2_2(41) -> 40
, 0^#_0(2) -> 4
, 0^#_0(3) -> 4
, 0^#_1(6) -> 5
, 0^#_1(12) -> 11
, 0^#_2(22) -> 37
, 0^#_2(25) -> 30
, 0^#_2(32) -> 31
, 0^#_2(39) -> 38
, c_0_1(5) -> 4
, c_0_2(30) -> 5
, c_0_2(31) -> 11
, c_1_1(11) -> 4
, c_1_2(37) -> 5
, c_1_2(38) -> 11}