WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, [ 20<=j^0 && i^0==i^post_1 && j^0==j^post_1 ], cost: 1
      1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, [ 1+j^0<=20 && i^0==i^post_2 && j^0==j^post_2 ], cost: 1
      2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, [ j^post_3==2+j^0 && i^post_3==2+j^post_3 ], cost: 1
      3: l3 -> l2 : i^0'=i^post_4, j^0'=j^post_4, [ j^post_4==0 && i^0==i^post_4 ], cost: 1
      4: l4 -> l3 : i^0'=i^post_5, j^0'=j^post_5, [ i^0==i^post_5 && j^0==j^post_5 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: l4 -> l3 : i^0'=i^post_5, j^0'=j^post_5, [ i^0==i^post_5 && j^0==j^post_5 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, [ 1+j^0<=20 && i^0==i^post_2 && j^0==j^post_2 ], cost: 1
      2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, [ j^post_3==2+j^0 && i^post_3==2+j^post_3 ], cost: 1
      3: l3 -> l2 : i^0'=i^post_4, j^0'=j^post_4, [ j^post_4==0 && i^0==i^post_4 ], cost: 1
      4: l4 -> l3 : i^0'=i^post_5, j^0'=j^post_5, [ i^0==i^post_5 && j^0==j^post_5 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      1: l0 -> l2 : [ 1+j^0<=20 ], cost: 1
      2: l2 -> l0 : i^0'=4+j^0, j^0'=2+j^0, [], cost: 1
      3: l3 -> l2 : j^0'=0, [], cost: 1
      4: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      6: l2 -> l2 : i^0'=4+j^0, j^0'=2+j^0, [ 3+j^0<=20 ], cost: 2
      5: l4 -> l2 : j^0'=0, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
      6: l2 -> l2 : i^0'=4+j^0, j^0'=2+j^0, [ 3+j^0<=20 ], cost: 2

   Accelerated rule 6 with backward acceleration, yielding the new rule 7.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 6.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      7: l2 -> l2 : i^0'=2+j^0+2*k, j^0'=j^0+2*k, [ k>=1 && 1+j^0+2*k<=20 ], cost: 2*k
      5: l4 -> l2 : j^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      5: l4 -> l2 : j^0'=0, [], cost: 2
      8: l4 -> l2 : i^0'=2+2*k, j^0'=2*k, [ k>=1 && 1+2*k<=20 ], cost: 2+2*k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
      8: l4 -> l2 : i^0'=2+2*k, j^0'=2*k, [ k>=1 && 1+2*k<=20 ], cost: 2+2*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
      8: l4 -> l2 : i^0'=2+2*k, j^0'=2*k, [ k>=1 && 1+2*k<=20 ], cost: 2+2*k

Computing asymptotic complexity for rule 8
   Resulting cost 0 has complexity: Unknown

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:  [ i^0==i^post_5 && j^0==j^post_5 ]

WORST_CASE(Omega(1),?)