WORST_CASE(Omega(1),?)

### Pre-processing the ITS problem ###

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : __const_100^0'=__const_100^post_1, __const_10^0'=__const_10^post_1, __const_11^0'=__const_11^post_1, e^0'=e^post_1, n^0'=n^post_1, [ 1<=e^0 && n^0<=__const_100^0 && n^post_1==__const_11^0+n^0 && e^post_1==1+e^0 && __const_10^0==__const_10^post_1 && __const_100^0==__const_100^post_1 && __const_11^0==__const_11^post_1 ], cost: 1
      2: l0 -> l2 : __const_100^0'=__const_100^post_3, __const_10^0'=__const_10^post_3, __const_11^0'=__const_11^post_3, e^0'=e^post_3, n^0'=n^post_3, [ 1<=e^0 && 1+__const_100^0<=n^0 && n^post_3==n^0-__const_10^0 && e^post_3==-1+e^0 && __const_10^0==__const_10^post_3 && __const_100^0==__const_100^post_3 && __const_11^0==__const_11^post_3 ], cost: 1
      1: l1 -> l0 : __const_100^0'=__const_100^post_2, __const_10^0'=__const_10^post_2, __const_11^0'=__const_11^post_2, e^0'=e^post_2, n^0'=n^post_2, [ __const_10^0==__const_10^post_2 && __const_100^0==__const_100^post_2 && __const_11^0==__const_11^post_2 && e^0==e^post_2 && n^0==n^post_2 ], cost: 1
      3: l2 -> l0 : __const_100^0'=__const_100^post_4, __const_10^0'=__const_10^post_4, __const_11^0'=__const_11^post_4, e^0'=e^post_4, n^0'=n^post_4, [ __const_10^0==__const_10^post_4 && __const_100^0==__const_100^post_4 && __const_11^0==__const_11^post_4 && e^0==e^post_4 && n^0==n^post_4 ], cost: 1
      4: l3 -> l0 : __const_100^0'=__const_100^post_5, __const_10^0'=__const_10^post_5, __const_11^0'=__const_11^post_5, e^0'=e^post_5, n^0'=n^post_5, [ n^post_5==n^post_5 && e^post_5==1 && __const_10^0==__const_10^post_5 && __const_100^0==__const_100^post_5 && __const_11^0==__const_11^post_5 ], cost: 1
      5: l4 -> l3 : __const_100^0'=__const_100^post_6, __const_10^0'=__const_10^post_6, __const_11^0'=__const_11^post_6, e^0'=e^post_6, n^0'=n^post_6, [ __const_10^0==__const_10^post_6 && __const_100^0==__const_100^post_6 && __const_11^0==__const_11^post_6 && e^0==e^post_6 && n^0==n^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l3 : __const_100^0'=__const_100^post_6, __const_10^0'=__const_10^post_6, __const_11^0'=__const_11^post_6, e^0'=e^post_6, n^0'=n^post_6, [ __const_10^0==__const_10^post_6 && __const_100^0==__const_100^post_6 && __const_11^0==__const_11^post_6 && e^0==e^post_6 && n^0==n^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : e^0'=1+e^0, n^0'=__const_11^0+n^0, [ 1<=e^0 && n^0<=__const_100^0 ], cost: 1
      2: l0 -> l2 : e^0'=-1+e^0, n^0'=n^0-__const_10^0, [ 1<=e^0 && 1+__const_100^0<=n^0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      3: l2 -> l0 : [], cost: 1
      4: l3 -> l0 : e^0'=1, n^0'=n^post_5, [], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      7: l0 -> l0 : e^0'=1+e^0, n^0'=__const_11^0+n^0, [ 1<=e^0 && n^0<=__const_100^0 ], cost: 2
      8: l0 -> l0 : e^0'=-1+e^0, n^0'=n^0-__const_10^0, [ 1<=e^0 && 1+__const_100^0<=n^0 ], cost: 2
      6: l4 -> l0 : e^0'=1, n^0'=n^post_5, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      7: l0 -> l0 : e^0'=1+e^0, n^0'=__const_11^0+n^0, [ 1<=e^0 && n^0<=__const_100^0 ], cost: 2
      8: l0 -> l0 : e^0'=-1+e^0, n^0'=n^0-__const_10^0, [ 1<=e^0 && 1+__const_100^0<=n^0 ], cost: 2

   Found no metering function for rule 7.
   Found no metering function for rule 8.
   Removing the simple loops:.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      7: l0 -> l0 : e^0'=1+e^0, n^0'=__const_11^0+n^0, [ 1<=e^0 && n^0<=__const_100^0 ], cost: 2
      8: l0 -> l0 : e^0'=-1+e^0, n^0'=n^0-__const_10^0, [ 1<=e^0 && 1+__const_100^0<=n^0 ], cost: 2
      6: l4 -> l0 : e^0'=1, n^0'=n^post_5, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l0 : e^0'=1, n^0'=n^post_5, [], cost: 2
      9: l4 -> l0 : e^0'=2, n^0'=n^post_5+__const_11^0, [ n^post_5<=__const_100^0 ], cost: 4
     10: l4 -> l0 : e^0'=0, n^0'=n^post_5-__const_10^0, [ 1+__const_100^0<=n^post_5 ], cost: 4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     <empty>

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Constant
   Cpx degree:  0
   Solved cost: 1
   Rule cost:   1
   Rule guard:  [ __const_10^0==__const_10^post_6 && __const_100^0==__const_100^post_6 && __const_11^0==__const_11^post_6 && e^0==e^post_6 && n^0==n^post_6 ]

WORST_CASE(Omega(1),?)