WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l8
      0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, [ 2<=i^0 && j^post_1==0 && i^0==i^post_1 ], cost: 1
      1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, [ 1+i^0<=2 && i^post_2==1+i^0 && j^0==j^post_2 ], cost: 1
      3: l1 -> l3 : i^0'=i^post_4, j^0'=j^post_4, [ i^0==i^post_4 && j^0==j^post_4 ], cost: 1
      2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, [ i^0==i^post_3 && j^0==j^post_3 ], cost: 1
      7: l3 -> l6 : i^0'=i^post_8, j^0'=j^post_8, [ 2<=j^0 && i^0==i^post_8 && j^0==j^post_8 ], cost: 1
      8: l3 -> l1 : i^0'=i^post_9, j^0'=j^post_9, [ 1+j^0<=2 && j^post_9==1+j^0 && i^0==i^post_9 ], cost: 1
      4: l4 -> l5 : i^0'=i^post_5, j^0'=j^post_5, [ i^0==i^post_5 && j^0==j^post_5 ], cost: 1
      5: l6 -> l4 : i^0'=i^post_6, j^0'=j^post_6, [ i^0==i^post_6 && j^0==j^post_6 ], cost: 1
      6: l6 -> l4 : i^0'=i^post_7, j^0'=j^post_7, [ i^0==i^post_7 && j^0==j^post_7 ], cost: 1
      9: l7 -> l2 : i^0'=i^post_10, j^0'=j^post_10, [ i^post_10==0 && j^0==j^post_10 ], cost: 1
     10: l8 -> l7 : i^0'=i^post_11, j^0'=j^post_11, [ i^0==i^post_11 && j^0==j^post_11 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l8 -> l7 : i^0'=i^post_11, j^0'=j^post_11, [ i^0==i^post_11 && j^0==j^post_11 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l8
      0: l0 -> l1 : i^0'=i^post_1, j^0'=j^post_1, [ 2<=i^0 && j^post_1==0 && i^0==i^post_1 ], cost: 1
      1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, [ 1+i^0<=2 && i^post_2==1+i^0 && j^0==j^post_2 ], cost: 1
      3: l1 -> l3 : i^0'=i^post_4, j^0'=j^post_4, [ i^0==i^post_4 && j^0==j^post_4 ], cost: 1
      2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, [ i^0==i^post_3 && j^0==j^post_3 ], cost: 1
      8: l3 -> l1 : i^0'=i^post_9, j^0'=j^post_9, [ 1+j^0<=2 && j^post_9==1+j^0 && i^0==i^post_9 ], cost: 1
      9: l7 -> l2 : i^0'=i^post_10, j^0'=j^post_10, [ i^post_10==0 && j^0==j^post_10 ], cost: 1
     10: l8 -> l7 : i^0'=i^post_11, j^0'=j^post_11, [ i^0==i^post_11 && j^0==j^post_11 ], cost: 1

Simplified all rules, resulting in:
   Start location: l8
      0: l0 -> l1 : j^0'=0, [ 2<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, [ 1+i^0<=2 ], cost: 1
      3: l1 -> l3 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      8: l3 -> l1 : j^0'=1+j^0, [ 1+j^0<=2 ], cost: 1
      9: l7 -> l2 : i^0'=0, [], cost: 1
     10: l8 -> l7 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l8
      0: l0 -> l1 : j^0'=0, [ 2<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, [ 1+i^0<=2 ], cost: 1
     12: l1 -> l1 : j^0'=1+j^0, [ 1+j^0<=2 ], cost: 2
      2: l2 -> l0 : [], cost: 1
     11: l8 -> l2 : i^0'=0, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     12: l1 -> l1 : j^0'=1+j^0, [ 1+j^0<=2 ], cost: 2

   Accelerated rule 12 with backward acceleration, yielding the new rule 13.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
      0: l0 -> l1 : j^0'=0, [ 2<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, [ 1+i^0<=2 ], cost: 1
     13: l1 -> l1 : j^0'=2, [ 2-j^0>=0 ], cost: 4-2*j^0
      2: l2 -> l0 : [], cost: 1
     11: l8 -> l2 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
      0: l0 -> l1 : j^0'=0, [ 2<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, [ 1+i^0<=2 ], cost: 1
     14: l0 -> l1 : j^0'=2, [ 2<=i^0 ], cost: 5
      2: l2 -> l0 : [], cost: 1
     11: l8 -> l2 : i^0'=0, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l8
      1: l0 -> l2 : i^0'=1+i^0, [ 1+i^0<=2 ], cost: 1
      2: l2 -> l0 : [], cost: 1
     11: l8 -> l2 : i^0'=0, [], cost: 2

Eliminated locations (on linear paths):
   Start location: l8
     15: l2 -> l2 : i^0'=1+i^0, [ 1+i^0<=2 ], cost: 2
     11: l8 -> l2 : i^0'=0, [], cost: 2

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

   Accelerated rule 15 with backward acceleration, yielding the new rule 16.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     16: l2 -> l2 : i^0'=2, [ 2-i^0>=0 ], cost: 4-2*i^0
     11: l8 -> l2 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
     11: l8 -> l2 : i^0'=0, [], cost: 2
     17: l8 -> l2 : i^0'=2, [], cost: 6

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l8
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l8
     <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:  [ i^0==i^post_11 && j^0==j^post_11 ]

WORST_CASE(Omega(1),?)