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, n^0'=n^post_1, [ i^0<=j^0 && i^post_1==1+i^0 && j^0==j^post_1 && n^0==n^post_1 ], cost: 1
      1: l0 -> l2 : i^0'=i^post_2, j^0'=j^post_2, n^0'=n^post_2, [ 1+j^0<=i^0 && j^post_2==1+j^0 && i^0==i^post_2 && n^0==n^post_2 ], cost: 1
      3: l1 -> l0 : i^0'=i^post_4, j^0'=j^post_4, n^0'=n^post_4, [ 1+i^0<=n^0 && j^post_4==0 && i^0==i^post_4 && n^0==n^post_4 ], cost: 1
      2: l2 -> l0 : i^0'=i^post_3, j^0'=j^post_3, n^0'=n^post_3, [ i^0==i^post_3 && j^0==j^post_3 && n^0==n^post_3 ], cost: 1
      4: l3 -> l1 : i^0'=i^post_5, j^0'=j^post_5, n^0'=n^post_5, [ i^post_5==0 && j^0==j^post_5 && n^0==n^post_5 ], cost: 1
      5: l4 -> l3 : i^0'=i^post_6, j^0'=j^post_6, n^0'=n^post_6, [ i^0==i^post_6 && j^0==j^post_6 && n^0==n^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l3 : i^0'=i^post_6, j^0'=j^post_6, n^0'=n^post_6, [ i^0==i^post_6 && j^0==j^post_6 && n^0==n^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : i^0'=1+i^0, [ i^0<=j^0 ], cost: 1
      1: l0 -> l2 : j^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 1
      3: l1 -> l0 : j^0'=0, [ 1+i^0<=n^0 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      4: l3 -> l1 : i^0'=0, [], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      0: l0 -> l1 : i^0'=1+i^0, [ i^0<=j^0 ], cost: 1
      7: l0 -> l0 : j^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 2
      3: l1 -> l0 : j^0'=0, [ 1+i^0<=n^0 ], cost: 1
      6: l4 -> l1 : i^0'=0, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      7: l0 -> l0 : j^0'=1+j^0, [ 1+j^0<=i^0 ], cost: 2

   Accelerated rule 7 with metering function i^0-j^0, yielding the new rule 8.
   Removing the simple loops: 7.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      0: l0 -> l1 : i^0'=1+i^0, [ i^0<=j^0 ], cost: 1
      8: l0 -> l0 : j^0'=i^0, [ 1+j^0<=i^0 ], cost: 2*i^0-2*j^0
      3: l1 -> l0 : j^0'=0, [ 1+i^0<=n^0 ], cost: 1
      6: l4 -> l1 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      0: l0 -> l1 : i^0'=1+i^0, [ i^0<=j^0 ], cost: 1
      3: l1 -> l0 : j^0'=0, [ 1+i^0<=n^0 ], cost: 1
      9: l1 -> l0 : j^0'=i^0, [ 1+i^0<=n^0 && 1<=i^0 ], cost: 1+2*i^0
      6: l4 -> l1 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l4
     10: l1 -> l1 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 && i^0<=0 ], cost: 2
     11: l1 -> l1 : i^0'=1+i^0, j^0'=i^0, [ 1+i^0<=n^0 && 1<=i^0 ], cost: 2+2*i^0
      6: l4 -> l1 : i^0'=0, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     10: l1 -> l1 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 && i^0<=0 ], cost: 2
     11: l1 -> l1 : i^0'=1+i^0, j^0'=i^0, [ 1+i^0<=n^0 && 1<=i^0 ], cost: 2+2*i^0

   Found no metering function for rule 10.
   Accelerated rule 11 with metering function n^0-i^0, yielding the new rule 12.
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
     10: l1 -> l1 : i^0'=1+i^0, j^0'=0, [ 1+i^0<=n^0 && i^0<=0 ], cost: 2
     12: l1 -> l1 : i^0'=n^0, j^0'=-1+n^0, [ 1+i^0<=n^0 && 1<=i^0 ], cost: n^0+(n^0-i^0)^2+2*i^0*(n^0-i^0)-i^0
      6: l4 -> l1 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l1 : i^0'=0, [], cost: 2
     13: l4 -> l1 : i^0'=1, j^0'=0, [ 1<=n^0 ], cost: 4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     <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_6 && j^0==j^post_6 && n^0==n^post_6 ]

WORST_CASE(Omega(1),?)