WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : i1^0'=i1^post_1, [ i1^post_1==1+i1^0 ], cost: 1
      7: l1 -> l4 : i1^0'=i1^post_8, [ i1^0==i1^post_8 ], cost: 1
      1: l2 -> l0 : i1^0'=i1^post_2, [ i1^0==i1^post_2 ], cost: 1
      2: l3 -> l2 : i1^0'=i1^post_3, [ i1^0==i1^post_3 ], cost: 1
      3: l3 -> l0 : i1^0'=i1^post_4, [ i1^0==i1^post_4 ], cost: 1
      4: l3 -> l2 : i1^0'=i1^post_5, [ i1^0==i1^post_5 ], cost: 1
      5: l4 -> l5 : i1^0'=i1^post_6, [ 42<=i1^0 && i1^0==i1^post_6 ], cost: 1
      6: l4 -> l3 : i1^0'=i1^post_7, [ 1+i1^0<=42 && i1^0==i1^post_7 ], cost: 1
      8: l6 -> l1 : i1^0'=i1^post_9, [ i1^post_9==0 ], cost: 1
      9: l7 -> l6 : i1^0'=i1^post_10, [ i1^0==i1^post_10 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: l7 -> l6 : i1^0'=i1^post_10, [ i1^0==i1^post_10 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      0: l0 -> l1 : i1^0'=i1^post_1, [ i1^post_1==1+i1^0 ], cost: 1
      7: l1 -> l4 : i1^0'=i1^post_8, [ i1^0==i1^post_8 ], cost: 1
      1: l2 -> l0 : i1^0'=i1^post_2, [ i1^0==i1^post_2 ], cost: 1
      2: l3 -> l2 : i1^0'=i1^post_3, [ i1^0==i1^post_3 ], cost: 1
      3: l3 -> l0 : i1^0'=i1^post_4, [ i1^0==i1^post_4 ], cost: 1
      4: l3 -> l2 : i1^0'=i1^post_5, [ i1^0==i1^post_5 ], cost: 1
      6: l4 -> l3 : i1^0'=i1^post_7, [ 1+i1^0<=42 && i1^0==i1^post_7 ], cost: 1
      8: l6 -> l1 : i1^0'=i1^post_9, [ i1^post_9==0 ], cost: 1
      9: l7 -> l6 : i1^0'=i1^post_10, [ i1^0==i1^post_10 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      0: l0 -> l1 : i1^0'=1+i1^0, [], cost: 1
      7: l1 -> l4 : [], cost: 1
      1: l2 -> l0 : [], cost: 1
      3: l3 -> l0 : [], cost: 1
      4: l3 -> l2 : [], cost: 1
      6: l4 -> l3 : [ 1+i1^0<=42 ], cost: 1
      8: l6 -> l1 : i1^0'=0, [], cost: 1
      9: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
      0: l0 -> l1 : i1^0'=1+i1^0, [], cost: 1
     11: l1 -> l3 : [ 1+i1^0<=42 ], cost: 2
      3: l3 -> l0 : [], cost: 1
     12: l3 -> l0 : [], cost: 2
     10: l7 -> l1 : i1^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l7
      0: l0 -> l1 : i1^0'=1+i1^0, [], cost: 1
     13: l1 -> l0 : [ 1+i1^0<=42 ], cost: 3
     14: l1 -> l0 : [ 1+i1^0<=42 ], cost: 4
     10: l7 -> l1 : i1^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l7
     15: l1 -> l1 : i1^0'=1+i1^0, [ 1+i1^0<=42 ], cost: 4
     16: l1 -> l1 : i1^0'=1+i1^0, [ 1+i1^0<=42 ], cost: 5
     10: l7 -> l1 : i1^0'=0, [], cost: 2

Accelerating simple loops of location 1.
[accelerate] Removed some duplicate simple loops
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     16: l1 -> l1 : i1^0'=1+i1^0, [ 1+i1^0<=42 ], cost: 5

   Accelerated rule 16 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 16.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     17: l1 -> l1 : i1^0'=42, [ 42-i1^0>=0 ], cost: 210-5*i1^0
     10: l7 -> l1 : i1^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
     10: l7 -> l1 : i1^0'=0, [], cost: 2
     18: l7 -> l1 : i1^0'=42, [], cost: 212

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     <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:  [ i1^0==i1^post_10 ]

WORST_CASE(Omega(1),?)