WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ y>=1 && y<=5 ], cost: 1
      4: [3] -> [4] : [ x>=0 ], cost: 1
      7: [3] -> [6] : z'=-1+z, [ x<0 ], cost: 1
      5: [4] -> [5] : [ 0<=0 ], cost: 1
      6: [5] -> [3] : z'=1+z, x'=z^2-z*y, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1

Removed unreachable and leaf rules:
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ y>=1 && y<=5 ], cost: 1
      4: [3] -> [4] : [ x>=0 ], cost: 1
      5: [4] -> [5] : [ 0<=0 ], cost: 1
      6: [5] -> [3] : z'=1+z, x'=z^2-z*y, [], cost: 1

Simplified all rules, resulting in:
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ y>=1 && y<=5 ], cost: 1
      4: [3] -> [4] : [ x>=0 ], cost: 1
      5: [4] -> [5] : [], cost: 1
      6: [5] -> [3] : z'=1+z, x'=z^2-z*y, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ y>=1 && y<=5 ], cost: 1
      9: [3] -> [3] : z'=1+z, x'=z^2-z*y, [ x>=0 ], cost: 3

Accelerating simple loops of location 3.
   Accelerating the following rules:
      9: [3] -> [3] : z'=1+z, x'=z^2-z*y, [ x>=0 ], cost: 3

   Failed to prove monotonicity of the guard of rule 9.
[accelerate] Nesting with 1 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ y>=1 && y<=5 ], cost: 1
      9: [3] -> [3] : z'=1+z, x'=z^2-z*y, [ x>=0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: [0]
      0: [0] -> [1] : z'=1+z, [ z>=4 ], cost: 1
      1: [1] -> [2] : z'=1+z, [ x>=0 ], cost: 1
      2: [1] -> [2] : z'=-1+z, [ x<0 ], cost: 1
      3: [2] -> [3] : [ y>=1 && y<=5 ], cost: 1
     10: [2] -> [3] : z'=1+z, x'=z^2-z*y, [ y>=1 && y<=5 && x>=0 ], cost: 4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: [0]
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: [0]
     <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:  [ z>=4 ]

WORST_CASE(Omega(1),?)