WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l3
      0: l0 -> l1 : __const_100^0'=__const_100^post_1, __const_200^0'=__const_200^post_1, __const_300^0'=__const_300^post_1, __const_400^0'=__const_400^post_1, x^0'=x^post_1, [ x^post_1==__const_300^0+x^0 && 1+__const_100^0<=x^post_1 && __const_100^0==__const_100^post_1 && __const_200^0==__const_200^post_1 && __const_300^0==__const_300^post_1 && __const_400^0==__const_400^post_1 ], cost: 1
      1: l1 -> l0 : __const_100^0'=__const_100^post_2, __const_200^0'=__const_200^post_2, __const_300^0'=__const_300^post_2, __const_400^0'=__const_400^post_2, x^0'=x^post_2, [ x^post_2==__const_400^0+x^0 && 1+__const_100^0<=x^post_2 && __const_100^0==__const_100^post_2 && __const_200^0==__const_200^post_2 && __const_300^0==__const_300^post_2 && __const_400^0==__const_400^post_2 ], cost: 1
      2: l2 -> l0 : __const_100^0'=__const_100^post_3, __const_200^0'=__const_200^post_3, __const_300^0'=__const_300^post_3, __const_400^0'=__const_400^post_3, x^0'=x^post_3, [ x^post_3==x^0+__const_200^0 && 1+__const_100^0<=x^post_3 && __const_100^0==__const_100^post_3 && __const_200^0==__const_200^post_3 && __const_300^0==__const_300^post_3 && __const_400^0==__const_400^post_3 ], cost: 1
      3: l2 -> l1 : __const_100^0'=__const_100^post_4, __const_200^0'=__const_200^post_4, __const_300^0'=__const_300^post_4, __const_400^0'=__const_400^post_4, x^0'=x^post_4, [ x^post_4==__const_100^0+x^0 && 1+__const_100^0<=x^post_4 && __const_100^0==__const_100^post_4 && __const_200^0==__const_200^post_4 && __const_300^0==__const_300^post_4 && __const_400^0==__const_400^post_4 ], cost: 1
      4: l3 -> l2 : __const_100^0'=__const_100^post_5, __const_200^0'=__const_200^post_5, __const_300^0'=__const_300^post_5, __const_400^0'=__const_400^post_5, x^0'=x^post_5, [ __const_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && __const_300^0==__const_300^post_5 && __const_400^0==__const_400^post_5 && x^0==x^post_5 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: l3 -> l2 : __const_100^0'=__const_100^post_5, __const_200^0'=__const_200^post_5, __const_300^0'=__const_300^post_5, __const_400^0'=__const_400^post_5, x^0'=x^post_5, [ __const_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && __const_300^0==__const_300^post_5 && __const_400^0==__const_400^post_5 && x^0==x^post_5 ], cost: 1

Simplified all rules, resulting in:
   Start location: l3
      0: l0 -> l1 : x^0'=__const_300^0+x^0, [ 1+__const_100^0<=__const_300^0+x^0 ], cost: 1
      1: l1 -> l0 : x^0'=__const_400^0+x^0, [ 1+__const_100^0<=__const_400^0+x^0 ], cost: 1
      2: l2 -> l0 : x^0'=x^0+__const_200^0, [ 1+__const_100^0<=x^0+__const_200^0 ], cost: 1
      3: l2 -> l1 : x^0'=__const_100^0+x^0, [ 1+__const_100^0<=__const_100^0+x^0 ], cost: 1
      4: l3 -> l2 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on tree-shaped paths):
   Start location: l3
      0: l0 -> l1 : x^0'=__const_300^0+x^0, [ 1+__const_100^0<=__const_300^0+x^0 ], cost: 1
      1: l1 -> l0 : x^0'=__const_400^0+x^0, [ 1+__const_100^0<=__const_400^0+x^0 ], cost: 1
      5: l3 -> l0 : x^0'=x^0+__const_200^0, [ 1+__const_100^0<=x^0+__const_200^0 ], cost: 2
      6: l3 -> l1 : x^0'=__const_100^0+x^0, [ 1+__const_100^0<=__const_100^0+x^0 ], cost: 2

Eliminated location l0 (as a last resort):
   Start location: l3
      7: l1 -> l1 : x^0'=__const_300^0+__const_400^0+x^0, [ 1+__const_100^0<=__const_400^0+x^0 && 1+__const_100^0<=__const_300^0+__const_400^0+x^0 ], cost: 2
      6: l3 -> l1 : x^0'=__const_100^0+x^0, [ 1+__const_100^0<=__const_100^0+x^0 ], cost: 2
      8: l3 -> l1 : x^0'=__const_300^0+x^0+__const_200^0, [ 1+__const_100^0<=x^0+__const_200^0 && 1+__const_100^0<=__const_300^0+x^0+__const_200^0 ], cost: 3

Accelerating simple loops of location 1.
   Accelerating the following rules:
      7: l1 -> l1 : x^0'=__const_300^0+__const_400^0+x^0, [ 1+__const_100^0<=__const_400^0+x^0 && 1+__const_100^0<=__const_300^0+__const_400^0+x^0 ], cost: 2

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

Accelerated all simple loops using metering functions (where possible):
   Start location: l3
      7: l1 -> l1 : x^0'=__const_300^0+__const_400^0+x^0, [ 1+__const_100^0<=__const_400^0+x^0 && 1+__const_100^0<=__const_300^0+__const_400^0+x^0 ], cost: 2
      6: l3 -> l1 : x^0'=__const_100^0+x^0, [ 1+__const_100^0<=__const_100^0+x^0 ], cost: 2
      8: l3 -> l1 : x^0'=__const_300^0+x^0+__const_200^0, [ 1+__const_100^0<=x^0+__const_200^0 && 1+__const_100^0<=__const_300^0+x^0+__const_200^0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l3
      6: l3 -> l1 : x^0'=__const_100^0+x^0, [ 1+__const_100^0<=__const_100^0+x^0 ], cost: 2
      8: l3 -> l1 : x^0'=__const_300^0+x^0+__const_200^0, [ 1+__const_100^0<=x^0+__const_200^0 && 1+__const_100^0<=__const_300^0+x^0+__const_200^0 ], cost: 3
      9: l3 -> l1 : x^0'=__const_300^0+__const_400^0+__const_100^0+x^0, [ 1+__const_100^0<=__const_100^0+x^0 && 1+__const_100^0<=__const_400^0+__const_100^0+x^0 && 1+__const_100^0<=__const_300^0+__const_400^0+__const_100^0+x^0 ], cost: 4
     10: l3 -> l1 : x^0'=2*__const_300^0+__const_400^0+x^0+__const_200^0, [ 1+__const_100^0<=x^0+__const_200^0 && 1+__const_100^0<=__const_300^0+x^0+__const_200^0 && 1+__const_100^0<=__const_300^0+__const_400^0+x^0+__const_200^0 && 1+__const_100^0<=2*__const_300^0+__const_400^0+x^0+__const_200^0 ], cost: 5

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l3
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l3
     <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_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && __const_300^0==__const_300^post_5 && __const_400^0==__const_400^post_5 && x^0==x^post_5 ]

WORST_CASE(Omega(1),?)