WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l8
      0: l0 -> l1 : j^0'=j^post_1, tmp3^0'=tmp3^post_1, x1^0'=x1^post_1, y2^0'=y2^post_1, [ x1^post_1==j^0 && y2^post_1==1+j^0 && tmp3^post_1==tmp3^post_1 && j^0==j^post_1 ], cost: 1
      1: l0 -> l1 : j^0'=j^post_2, tmp3^0'=tmp3^post_2, x1^0'=x1^post_2, y2^0'=y2^post_2, [ j^0==j^post_2 && tmp3^0==tmp3^post_2 && x1^0==x1^post_2 && y2^0==y2^post_2 ], cost: 1
      8: l1 -> l6 : j^0'=j^post_9, tmp3^0'=tmp3^post_9, x1^0'=x1^post_9, y2^0'=y2^post_9, [ j^post_9==1+j^0 && tmp3^0==tmp3^post_9 && x1^0==x1^post_9 && y2^0==y2^post_9 ], cost: 1
      2: l2 -> l3 : j^0'=j^post_3, tmp3^0'=tmp3^post_3, x1^0'=x1^post_3, y2^0'=y2^post_3, [ 4<=j^0 && j^0==j^post_3 && tmp3^0==tmp3^post_3 && x1^0==x1^post_3 && y2^0==y2^post_3 ], cost: 1
      3: l2 -> l0 : j^0'=j^post_4, tmp3^0'=tmp3^post_4, x1^0'=x1^post_4, y2^0'=y2^post_4, [ 1+j^0<=4 && j^0==j^post_4 && tmp3^0==tmp3^post_4 && x1^0==x1^post_4 && y2^0==y2^post_4 ], cost: 1
      6: l3 -> l4 : j^0'=j^post_7, tmp3^0'=tmp3^post_7, x1^0'=x1^post_7, y2^0'=y2^post_7, [ j^0==j^post_7 && tmp3^0==tmp3^post_7 && x1^0==x1^post_7 && y2^0==y2^post_7 ], cost: 1
      7: l3 -> l4 : j^0'=j^post_8, tmp3^0'=tmp3^post_8, x1^0'=x1^post_8, y2^0'=y2^post_8, [ j^0==j^post_8 && tmp3^0==tmp3^post_8 && x1^0==x1^post_8 && y2^0==y2^post_8 ], cost: 1
      4: l4 -> l5 : j^0'=j^post_5, tmp3^0'=tmp3^post_5, x1^0'=x1^post_5, y2^0'=y2^post_5, [ j^0==j^post_5 && tmp3^0==tmp3^post_5 && x1^0==x1^post_5 && y2^0==y2^post_5 ], cost: 1
      5: l6 -> l2 : j^0'=j^post_6, tmp3^0'=tmp3^post_6, x1^0'=x1^post_6, y2^0'=y2^post_6, [ j^0==j^post_6 && tmp3^0==tmp3^post_6 && x1^0==x1^post_6 && y2^0==y2^post_6 ], cost: 1
      9: l7 -> l6 : j^0'=j^post_10, tmp3^0'=tmp3^post_10, x1^0'=x1^post_10, y2^0'=y2^post_10, [ j^post_10==0 && tmp3^0==tmp3^post_10 && x1^0==x1^post_10 && y2^0==y2^post_10 ], cost: 1
     10: l8 -> l7 : j^0'=j^post_11, tmp3^0'=tmp3^post_11, x1^0'=x1^post_11, y2^0'=y2^post_11, [ j^0==j^post_11 && tmp3^0==tmp3^post_11 && x1^0==x1^post_11 && y2^0==y2^post_11 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l8 -> l7 : j^0'=j^post_11, tmp3^0'=tmp3^post_11, x1^0'=x1^post_11, y2^0'=y2^post_11, [ j^0==j^post_11 && tmp3^0==tmp3^post_11 && x1^0==x1^post_11 && y2^0==y2^post_11 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l8
      0: l0 -> l1 : j^0'=j^post_1, tmp3^0'=tmp3^post_1, x1^0'=x1^post_1, y2^0'=y2^post_1, [ x1^post_1==j^0 && y2^post_1==1+j^0 && tmp3^post_1==tmp3^post_1 && j^0==j^post_1 ], cost: 1
      1: l0 -> l1 : j^0'=j^post_2, tmp3^0'=tmp3^post_2, x1^0'=x1^post_2, y2^0'=y2^post_2, [ j^0==j^post_2 && tmp3^0==tmp3^post_2 && x1^0==x1^post_2 && y2^0==y2^post_2 ], cost: 1
      8: l1 -> l6 : j^0'=j^post_9, tmp3^0'=tmp3^post_9, x1^0'=x1^post_9, y2^0'=y2^post_9, [ j^post_9==1+j^0 && tmp3^0==tmp3^post_9 && x1^0==x1^post_9 && y2^0==y2^post_9 ], cost: 1
      3: l2 -> l0 : j^0'=j^post_4, tmp3^0'=tmp3^post_4, x1^0'=x1^post_4, y2^0'=y2^post_4, [ 1+j^0<=4 && j^0==j^post_4 && tmp3^0==tmp3^post_4 && x1^0==x1^post_4 && y2^0==y2^post_4 ], cost: 1
      5: l6 -> l2 : j^0'=j^post_6, tmp3^0'=tmp3^post_6, x1^0'=x1^post_6, y2^0'=y2^post_6, [ j^0==j^post_6 && tmp3^0==tmp3^post_6 && x1^0==x1^post_6 && y2^0==y2^post_6 ], cost: 1
      9: l7 -> l6 : j^0'=j^post_10, tmp3^0'=tmp3^post_10, x1^0'=x1^post_10, y2^0'=y2^post_10, [ j^post_10==0 && tmp3^0==tmp3^post_10 && x1^0==x1^post_10 && y2^0==y2^post_10 ], cost: 1
     10: l8 -> l7 : j^0'=j^post_11, tmp3^0'=tmp3^post_11, x1^0'=x1^post_11, y2^0'=y2^post_11, [ j^0==j^post_11 && tmp3^0==tmp3^post_11 && x1^0==x1^post_11 && y2^0==y2^post_11 ], cost: 1

Simplified all rules, resulting in:
   Start location: l8
      0: l0 -> l1 : tmp3^0'=tmp3^post_1, x1^0'=j^0, y2^0'=1+j^0, [], cost: 1
      1: l0 -> l1 : [], cost: 1
      8: l1 -> l6 : j^0'=1+j^0, [], cost: 1
      3: l2 -> l0 : [ 1+j^0<=4 ], cost: 1
      5: l6 -> l2 : [], cost: 1
      9: l7 -> l6 : j^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 : tmp3^0'=tmp3^post_1, x1^0'=j^0, y2^0'=1+j^0, [], cost: 1
      1: l0 -> l1 : [], cost: 1
      8: l1 -> l6 : j^0'=1+j^0, [], cost: 1
     12: l6 -> l0 : [ 1+j^0<=4 ], cost: 2
     11: l8 -> l6 : j^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l8
      8: l1 -> l6 : j^0'=1+j^0, [], cost: 1
     13: l6 -> l1 : tmp3^0'=tmp3^post_1, x1^0'=j^0, y2^0'=1+j^0, [ 1+j^0<=4 ], cost: 3
     14: l6 -> l1 : [ 1+j^0<=4 ], cost: 3
     11: l8 -> l6 : j^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l8
     15: l6 -> l6 : j^0'=1+j^0, tmp3^0'=tmp3^post_1, x1^0'=j^0, y2^0'=1+j^0, [ 1+j^0<=4 ], cost: 4
     16: l6 -> l6 : j^0'=1+j^0, [ 1+j^0<=4 ], cost: 4
     11: l8 -> l6 : j^0'=0, [], cost: 2

Accelerating simple loops of location 6.
   Accelerating the following rules:
     15: l6 -> l6 : j^0'=1+j^0, tmp3^0'=tmp3^post_1, x1^0'=j^0, y2^0'=1+j^0, [ 1+j^0<=4 ], cost: 4
     16: l6 -> l6 : j^0'=1+j^0, [ 1+j^0<=4 ], cost: 4

   Accelerated rule 15 with backward acceleration, yielding the new rule 17.
   Accelerated rule 16 with backward acceleration, yielding the new rule 18.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 15 16.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     17: l6 -> l6 : j^0'=4, tmp3^0'=tmp3^post_1, x1^0'=3, y2^0'=4, [ 4-j^0>=1 ], cost: 16-4*j^0
     18: l6 -> l6 : j^0'=4, [ 4-j^0>=0 ], cost: 16-4*j^0
     11: l8 -> l6 : j^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
     11: l8 -> l6 : j^0'=0, [], cost: 2
     19: l8 -> l6 : j^0'=4, tmp3^0'=tmp3^post_1, x1^0'=3, y2^0'=4, [], cost: 18
     20: l8 -> l6 : j^0'=4, [], cost: 18

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:  [ j^0==j^post_11 && tmp3^0==tmp3^post_11 && x1^0==x1^post_11 && y2^0==y2^post_11 ]

WORST_CASE(Omega(1),?)