WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : i4^0'=i4^post_1, i7^0'=i7^post_1, tmp^0'=tmp^post_1, [ 10<=i4^0 && i7^post_1==0 && i4^0==i4^post_1 && tmp^0==tmp^post_1 ], cost: 1
      1: l0 -> l2 : i4^0'=i4^post_2, i7^0'=i7^post_2, tmp^0'=tmp^post_2, [ 1+i4^0<=10 && i4^post_2==1+i4^0 && i7^0==i7^post_2 && tmp^0==tmp^post_2 ], cost: 1
      3: l1 -> l3 : i4^0'=i4^post_4, i7^0'=i7^post_4, tmp^0'=tmp^post_4, [ i4^0==i4^post_4 && i7^0==i7^post_4 && tmp^0==tmp^post_4 ], cost: 1
      2: l2 -> l0 : i4^0'=i4^post_3, i7^0'=i7^post_3, tmp^0'=tmp^post_3, [ i4^0==i4^post_3 && i7^0==i7^post_3 && tmp^0==tmp^post_3 ], cost: 1
      4: l3 -> l4 : i4^0'=i4^post_5, i7^0'=i7^post_5, tmp^0'=tmp^post_5, [ 10<=i7^0 && i4^0==i4^post_5 && i7^0==i7^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l3 -> l1 : i4^0'=i4^post_6, i7^0'=i7^post_6, tmp^0'=tmp^post_6, [ 1+i7^0<=10 && i7^post_6==1+i7^0 && i4^0==i4^post_6 && tmp^0==tmp^post_6 ], cost: 1
      6: l5 -> l2 : i4^0'=i4^post_7, i7^0'=i7^post_7, tmp^0'=tmp^post_7, [ tmp^post_7==tmp^post_7 && i4^post_7==0 && i7^0==i7^post_7 ], cost: 1
      7: l6 -> l5 : i4^0'=i4^post_8, i7^0'=i7^post_8, tmp^0'=tmp^post_8, [ i4^0==i4^post_8 && i7^0==i7^post_8 && tmp^0==tmp^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : i4^0'=i4^post_8, i7^0'=i7^post_8, tmp^0'=tmp^post_8, [ i4^0==i4^post_8 && i7^0==i7^post_8 && tmp^0==tmp^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      0: l0 -> l1 : i4^0'=i4^post_1, i7^0'=i7^post_1, tmp^0'=tmp^post_1, [ 10<=i4^0 && i7^post_1==0 && i4^0==i4^post_1 && tmp^0==tmp^post_1 ], cost: 1
      1: l0 -> l2 : i4^0'=i4^post_2, i7^0'=i7^post_2, tmp^0'=tmp^post_2, [ 1+i4^0<=10 && i4^post_2==1+i4^0 && i7^0==i7^post_2 && tmp^0==tmp^post_2 ], cost: 1
      3: l1 -> l3 : i4^0'=i4^post_4, i7^0'=i7^post_4, tmp^0'=tmp^post_4, [ i4^0==i4^post_4 && i7^0==i7^post_4 && tmp^0==tmp^post_4 ], cost: 1
      2: l2 -> l0 : i4^0'=i4^post_3, i7^0'=i7^post_3, tmp^0'=tmp^post_3, [ i4^0==i4^post_3 && i7^0==i7^post_3 && tmp^0==tmp^post_3 ], cost: 1
      5: l3 -> l1 : i4^0'=i4^post_6, i7^0'=i7^post_6, tmp^0'=tmp^post_6, [ 1+i7^0<=10 && i7^post_6==1+i7^0 && i4^0==i4^post_6 && tmp^0==tmp^post_6 ], cost: 1
      6: l5 -> l2 : i4^0'=i4^post_7, i7^0'=i7^post_7, tmp^0'=tmp^post_7, [ tmp^post_7==tmp^post_7 && i4^post_7==0 && i7^0==i7^post_7 ], cost: 1
      7: l6 -> l5 : i4^0'=i4^post_8, i7^0'=i7^post_8, tmp^0'=tmp^post_8, [ i4^0==i4^post_8 && i7^0==i7^post_8 && tmp^0==tmp^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : i7^0'=0, [ 10<=i4^0 ], cost: 1
      1: l0 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], cost: 1
      3: l1 -> l3 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      5: l3 -> l1 : i7^0'=1+i7^0, [ 1+i7^0<=10 ], cost: 1
      6: l5 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      0: l0 -> l1 : i7^0'=0, [ 10<=i4^0 ], cost: 1
      1: l0 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], cost: 1
      9: l1 -> l1 : i7^0'=1+i7^0, [ 1+i7^0<=10 ], cost: 2
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      9: l1 -> l1 : i7^0'=1+i7^0, [ 1+i7^0<=10 ], cost: 2

   Accelerated rule 9 with backward acceleration, yielding the new rule 10.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
      0: l0 -> l1 : i7^0'=0, [ 10<=i4^0 ], cost: 1
      1: l0 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], cost: 1
     10: l1 -> l1 : i7^0'=10, [ 10-i7^0>=0 ], cost: 20-2*i7^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      0: l0 -> l1 : i7^0'=0, [ 10<=i4^0 ], cost: 1
      1: l0 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], cost: 1
     11: l0 -> l1 : i7^0'=10, [ 10<=i4^0 ], cost: 21
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
      1: l0 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Eliminated locations (on linear paths):
   Start location: l6
     12: l2 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], cost: 2
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     12: l2 -> l2 : i4^0'=1+i4^0, [ 1+i4^0<=10 ], 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: l6
     13: l2 -> l2 : i4^0'=10, [ 10-i4^0>=0 ], cost: 20-2*i4^0
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      8: l6 -> l2 : i4^0'=0, tmp^0'=tmp^post_7, [], cost: 2
     14: l6 -> l2 : i4^0'=10, tmp^0'=tmp^post_7, [], cost: 22

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     <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:  [ i4^0==i4^post_8 && i7^0==i7^post_8 && tmp^0==tmp^post_8 ]

WORST_CASE(Omega(1),?)