WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l5
      0: l0 -> l1 : counter^0'=counter^post_1, y^0'=y^post_1, z^0'=z^post_1, [ 36<=counter^0 && counter^0==counter^post_1 && y^0==y^post_1 && z^0==z^post_1 ], cost: 1
      1: l0 -> l2 : counter^0'=counter^post_2, y^0'=y^post_2, z^0'=z^post_2, [ 1+counter^0<=36 && z^post_2==1+z^0 && counter^post_2==1+counter^0 && y^0==y^post_2 ], cost: 1
      4: l2 -> l0 : counter^0'=counter^post_5, y^0'=y^post_5, z^0'=z^post_5, [ counter^0==counter^post_5 && y^0==y^post_5 && z^0==z^post_5 ], cost: 1
      2: l3 -> l2 : counter^0'=counter^post_3, y^0'=y^post_3, z^0'=z^post_3, [ y^0<=127 && z^post_3==z^post_3 && counter^0==counter^post_3 && y^0==y^post_3 ], cost: 1
      3: l3 -> l1 : counter^0'=counter^post_4, y^0'=y^post_4, z^0'=z^post_4, [ 128<=y^0 && counter^0==counter^post_4 && y^0==y^post_4 && z^0==z^post_4 ], cost: 1
      5: l4 -> l3 : counter^0'=counter^post_6, y^0'=y^post_6, z^0'=z^post_6, [ counter^post_6==0 && y^0==y^post_6 && z^0==z^post_6 ], cost: 1
      6: l5 -> l4 : counter^0'=counter^post_7, y^0'=y^post_7, z^0'=z^post_7, [ counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l4 : counter^0'=counter^post_7, y^0'=y^post_7, z^0'=z^post_7, [ counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      1: l0 -> l2 : counter^0'=counter^post_2, y^0'=y^post_2, z^0'=z^post_2, [ 1+counter^0<=36 && z^post_2==1+z^0 && counter^post_2==1+counter^0 && y^0==y^post_2 ], cost: 1
      4: l2 -> l0 : counter^0'=counter^post_5, y^0'=y^post_5, z^0'=z^post_5, [ counter^0==counter^post_5 && y^0==y^post_5 && z^0==z^post_5 ], cost: 1
      2: l3 -> l2 : counter^0'=counter^post_3, y^0'=y^post_3, z^0'=z^post_3, [ y^0<=127 && z^post_3==z^post_3 && counter^0==counter^post_3 && y^0==y^post_3 ], cost: 1
      5: l4 -> l3 : counter^0'=counter^post_6, y^0'=y^post_6, z^0'=z^post_6, [ counter^post_6==0 && y^0==y^post_6 && z^0==z^post_6 ], cost: 1
      6: l5 -> l4 : counter^0'=counter^post_7, y^0'=y^post_7, z^0'=z^post_7, [ counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      1: l0 -> l2 : counter^0'=1+counter^0, z^0'=1+z^0, [ 1+counter^0<=36 ], cost: 1
      4: l2 -> l0 : [], cost: 1
      2: l3 -> l2 : z^0'=z^post_3, [ y^0<=127 ], cost: 1
      5: l4 -> l3 : counter^0'=0, [], cost: 1
      6: l5 -> l4 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      9: l2 -> l2 : counter^0'=1+counter^0, z^0'=1+z^0, [ 1+counter^0<=36 ], cost: 2
      8: l5 -> l2 : counter^0'=0, z^0'=z^post_3, [ y^0<=127 ], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
      9: l2 -> l2 : counter^0'=1+counter^0, z^0'=1+z^0, [ 1+counter^0<=36 ], cost: 2

   Accelerated rule 9 with backward acceleration, yielding the new rule 10.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
     10: l2 -> l2 : counter^0'=36, z^0'=36+z^0-counter^0, [ 36-counter^0>=0 ], cost: 72-2*counter^0
      8: l5 -> l2 : counter^0'=0, z^0'=z^post_3, [ y^0<=127 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l5
      8: l5 -> l2 : counter^0'=0, z^0'=z^post_3, [ y^0<=127 ], cost: 3
     11: l5 -> l2 : counter^0'=36, z^0'=36+z^post_3, [ y^0<=127 ], cost: 75

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     <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:  [ counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ]

WORST_CASE(Omega(1),?)