WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l12
      0: l0 -> l1 : i4^0'=i4^post_1, j5^0'=j5^post_1, k6^0'=k6^post_1, [ i4^0==i4^post_1 && j5^0==j5^post_1 && k6^0==k6^post_1 ], cost: 1
     13: l1 -> l4 : i4^0'=i4^post_14, j5^0'=j5^post_14, k6^0'=k6^post_14, [ 6<=i4^0 && i4^post_14==1 && j5^0==j5^post_14 && k6^0==k6^post_14 ], cost: 1
     14: l1 -> l2 : i4^0'=i4^post_15, j5^0'=j5^post_15, k6^0'=k6^post_15, [ i4^0<=5 && j5^post_15==1 && i4^0==i4^post_15 && k6^0==k6^post_15 ], cost: 1
      1: l2 -> l3 : i4^0'=i4^post_2, j5^0'=j5^post_2, k6^0'=k6^post_2, [ i4^0==i4^post_2 && j5^0==j5^post_2 && k6^0==k6^post_2 ], cost: 1
     11: l3 -> l0 : i4^0'=i4^post_12, j5^0'=j5^post_12, k6^0'=k6^post_12, [ 6<=j5^0 && i4^post_12==1+i4^0 && j5^0==j5^post_12 && k6^0==k6^post_12 ], cost: 1
     12: l3 -> l2 : i4^0'=i4^post_13, j5^0'=j5^post_13, k6^0'=k6^post_13, [ j5^0<=5 && j5^post_13==1+j5^0 && i4^0==i4^post_13 && k6^0==k6^post_13 ], cost: 1
      2: l4 -> l5 : i4^0'=i4^post_3, j5^0'=j5^post_3, k6^0'=k6^post_3, [ i4^0==i4^post_3 && j5^0==j5^post_3 && k6^0==k6^post_3 ], cost: 1
      8: l5 -> l10 : i4^0'=i4^post_9, j5^0'=j5^post_9, k6^0'=k6^post_9, [ 6<=i4^0 && i4^0==i4^post_9 && j5^0==j5^post_9 && k6^0==k6^post_9 ], cost: 1
      9: l5 -> l6 : i4^0'=i4^post_10, j5^0'=j5^post_10, k6^0'=k6^post_10, [ i4^0<=5 && j5^post_10==1 && i4^0==i4^post_10 && k6^0==k6^post_10 ], cost: 1
      3: l6 -> l7 : i4^0'=i4^post_4, j5^0'=j5^post_4, k6^0'=k6^post_4, [ i4^0==i4^post_4 && j5^0==j5^post_4 && k6^0==k6^post_4 ], cost: 1
      6: l7 -> l4 : i4^0'=i4^post_7, j5^0'=j5^post_7, k6^0'=k6^post_7, [ 6<=j5^0 && i4^post_7==1+i4^0 && j5^0==j5^post_7 && k6^0==k6^post_7 ], cost: 1
      7: l7 -> l9 : i4^0'=i4^post_8, j5^0'=j5^post_8, k6^0'=k6^post_8, [ j5^0<=5 && k6^post_8==1 && i4^0==i4^post_8 && j5^0==j5^post_8 ], cost: 1
      4: l8 -> l6 : i4^0'=i4^post_5, j5^0'=j5^post_5, k6^0'=k6^post_5, [ 6<=k6^0 && j5^post_5==1+j5^0 && i4^0==i4^post_5 && k6^0==k6^post_5 ], cost: 1
      5: l8 -> l9 : i4^0'=i4^post_6, j5^0'=j5^post_6, k6^0'=k6^post_6, [ k6^0<=5 && k6^post_6==1+k6^0 && i4^0==i4^post_6 && j5^0==j5^post_6 ], cost: 1
     10: l9 -> l8 : i4^0'=i4^post_11, j5^0'=j5^post_11, k6^0'=k6^post_11, [ i4^0==i4^post_11 && j5^0==j5^post_11 && k6^0==k6^post_11 ], cost: 1
     15: l11 -> l0 : i4^0'=i4^post_16, j5^0'=j5^post_16, k6^0'=k6^post_16, [ i4^post_16==1 && j5^0==j5^post_16 && k6^0==k6^post_16 ], cost: 1
     16: l12 -> l11 : i4^0'=i4^post_17, j5^0'=j5^post_17, k6^0'=k6^post_17, [ i4^0==i4^post_17 && j5^0==j5^post_17 && k6^0==k6^post_17 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     16: l12 -> l11 : i4^0'=i4^post_17, j5^0'=j5^post_17, k6^0'=k6^post_17, [ i4^0==i4^post_17 && j5^0==j5^post_17 && k6^0==k6^post_17 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l12
      0: l0 -> l1 : i4^0'=i4^post_1, j5^0'=j5^post_1, k6^0'=k6^post_1, [ i4^0==i4^post_1 && j5^0==j5^post_1 && k6^0==k6^post_1 ], cost: 1
     13: l1 -> l4 : i4^0'=i4^post_14, j5^0'=j5^post_14, k6^0'=k6^post_14, [ 6<=i4^0 && i4^post_14==1 && j5^0==j5^post_14 && k6^0==k6^post_14 ], cost: 1
     14: l1 -> l2 : i4^0'=i4^post_15, j5^0'=j5^post_15, k6^0'=k6^post_15, [ i4^0<=5 && j5^post_15==1 && i4^0==i4^post_15 && k6^0==k6^post_15 ], cost: 1
      1: l2 -> l3 : i4^0'=i4^post_2, j5^0'=j5^post_2, k6^0'=k6^post_2, [ i4^0==i4^post_2 && j5^0==j5^post_2 && k6^0==k6^post_2 ], cost: 1
     11: l3 -> l0 : i4^0'=i4^post_12, j5^0'=j5^post_12, k6^0'=k6^post_12, [ 6<=j5^0 && i4^post_12==1+i4^0 && j5^0==j5^post_12 && k6^0==k6^post_12 ], cost: 1
     12: l3 -> l2 : i4^0'=i4^post_13, j5^0'=j5^post_13, k6^0'=k6^post_13, [ j5^0<=5 && j5^post_13==1+j5^0 && i4^0==i4^post_13 && k6^0==k6^post_13 ], cost: 1
      2: l4 -> l5 : i4^0'=i4^post_3, j5^0'=j5^post_3, k6^0'=k6^post_3, [ i4^0==i4^post_3 && j5^0==j5^post_3 && k6^0==k6^post_3 ], cost: 1
      9: l5 -> l6 : i4^0'=i4^post_10, j5^0'=j5^post_10, k6^0'=k6^post_10, [ i4^0<=5 && j5^post_10==1 && i4^0==i4^post_10 && k6^0==k6^post_10 ], cost: 1
      3: l6 -> l7 : i4^0'=i4^post_4, j5^0'=j5^post_4, k6^0'=k6^post_4, [ i4^0==i4^post_4 && j5^0==j5^post_4 && k6^0==k6^post_4 ], cost: 1
      6: l7 -> l4 : i4^0'=i4^post_7, j5^0'=j5^post_7, k6^0'=k6^post_7, [ 6<=j5^0 && i4^post_7==1+i4^0 && j5^0==j5^post_7 && k6^0==k6^post_7 ], cost: 1
      7: l7 -> l9 : i4^0'=i4^post_8, j5^0'=j5^post_8, k6^0'=k6^post_8, [ j5^0<=5 && k6^post_8==1 && i4^0==i4^post_8 && j5^0==j5^post_8 ], cost: 1
      4: l8 -> l6 : i4^0'=i4^post_5, j5^0'=j5^post_5, k6^0'=k6^post_5, [ 6<=k6^0 && j5^post_5==1+j5^0 && i4^0==i4^post_5 && k6^0==k6^post_5 ], cost: 1
      5: l8 -> l9 : i4^0'=i4^post_6, j5^0'=j5^post_6, k6^0'=k6^post_6, [ k6^0<=5 && k6^post_6==1+k6^0 && i4^0==i4^post_6 && j5^0==j5^post_6 ], cost: 1
     10: l9 -> l8 : i4^0'=i4^post_11, j5^0'=j5^post_11, k6^0'=k6^post_11, [ i4^0==i4^post_11 && j5^0==j5^post_11 && k6^0==k6^post_11 ], cost: 1
     15: l11 -> l0 : i4^0'=i4^post_16, j5^0'=j5^post_16, k6^0'=k6^post_16, [ i4^post_16==1 && j5^0==j5^post_16 && k6^0==k6^post_16 ], cost: 1
     16: l12 -> l11 : i4^0'=i4^post_17, j5^0'=j5^post_17, k6^0'=k6^post_17, [ i4^0==i4^post_17 && j5^0==j5^post_17 && k6^0==k6^post_17 ], cost: 1

Simplified all rules, resulting in:
   Start location: l12
      0: l0 -> l1 : [], cost: 1
     13: l1 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 1
     14: l1 -> l2 : j5^0'=1, [ i4^0<=5 ], cost: 1
      1: l2 -> l3 : [], cost: 1
     11: l3 -> l0 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 1
     12: l3 -> l2 : j5^0'=1+j5^0, [ j5^0<=5 ], cost: 1
      2: l4 -> l5 : [], cost: 1
      9: l5 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 1
      3: l6 -> l7 : [], cost: 1
      6: l7 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 1
      7: l7 -> l9 : k6^0'=1, [ j5^0<=5 ], cost: 1
      4: l8 -> l6 : j5^0'=1+j5^0, [ 6<=k6^0 ], cost: 1
      5: l8 -> l9 : k6^0'=1+k6^0, [ k6^0<=5 ], cost: 1
     10: l9 -> l8 : [], cost: 1
     15: l11 -> l0 : i4^0'=1, [], cost: 1
     16: l12 -> l11 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l12
      0: l0 -> l1 : [], cost: 1
     13: l1 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 1
     14: l1 -> l2 : j5^0'=1, [ i4^0<=5 ], cost: 1
      1: l2 -> l3 : [], cost: 1
     11: l3 -> l0 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 1
     12: l3 -> l2 : j5^0'=1+j5^0, [ j5^0<=5 ], cost: 1
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
      3: l6 -> l7 : [], cost: 1
      6: l7 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 1
      7: l7 -> l9 : k6^0'=1, [ j5^0<=5 ], cost: 1
      4: l8 -> l6 : j5^0'=1+j5^0, [ 6<=k6^0 ], cost: 1
      5: l8 -> l9 : k6^0'=1+k6^0, [ k6^0<=5 ], cost: 1
     10: l9 -> l8 : [], cost: 1
     17: l12 -> l0 : i4^0'=1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l12
     19: l0 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 2
     20: l0 -> l2 : j5^0'=1, [ i4^0<=5 ], cost: 2
     21: l2 -> l0 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     22: l2 -> l2 : j5^0'=1+j5^0, [ j5^0<=5 ], cost: 2
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
     23: l6 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     24: l6 -> l9 : k6^0'=1, [ j5^0<=5 ], cost: 2
     25: l9 -> l6 : j5^0'=1+j5^0, [ 6<=k6^0 ], cost: 2
     26: l9 -> l9 : k6^0'=1+k6^0, [ k6^0<=5 ], cost: 2
     17: l12 -> l0 : i4^0'=1, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     22: l2 -> l2 : j5^0'=1+j5^0, [ j5^0<=5 ], cost: 2

   Accelerated rule 22 with backward acceleration, yielding the new rule 27.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 22.

Accelerating simple loops of location 9.
   Accelerating the following rules:
     26: l9 -> l9 : k6^0'=1+k6^0, [ k6^0<=5 ], cost: 2

   Accelerated rule 26 with backward acceleration, yielding the new rule 28.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 26.

Accelerated all simple loops using metering functions (where possible):
   Start location: l12
     19: l0 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 2
     20: l0 -> l2 : j5^0'=1, [ i4^0<=5 ], cost: 2
     21: l2 -> l0 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     27: l2 -> l2 : j5^0'=6, [ 6-j5^0>=0 ], cost: 12-2*j5^0
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
     23: l6 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     24: l6 -> l9 : k6^0'=1, [ j5^0<=5 ], cost: 2
     25: l9 -> l6 : j5^0'=1+j5^0, [ 6<=k6^0 ], cost: 2
     28: l9 -> l9 : k6^0'=6, [ 6-k6^0>=0 ], cost: 12-2*k6^0
     17: l12 -> l0 : i4^0'=1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l12
     19: l0 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 2
     20: l0 -> l2 : j5^0'=1, [ i4^0<=5 ], cost: 2
     29: l0 -> l2 : j5^0'=6, [ i4^0<=5 ], cost: 12
     21: l2 -> l0 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
     23: l6 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     24: l6 -> l9 : k6^0'=1, [ j5^0<=5 ], cost: 2
     30: l6 -> l9 : k6^0'=6, [ j5^0<=5 ], cost: 12
     25: l9 -> l6 : j5^0'=1+j5^0, [ 6<=k6^0 ], cost: 2
     17: l12 -> l0 : i4^0'=1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l12
     19: l0 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 2
     31: l0 -> l0 : i4^0'=1+i4^0, j5^0'=6, [ i4^0<=5 ], cost: 14
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
     23: l6 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     32: l6 -> l6 : j5^0'=1+j5^0, k6^0'=6, [ j5^0<=5 ], cost: 14
     17: l12 -> l0 : i4^0'=1, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     31: l0 -> l0 : i4^0'=1+i4^0, j5^0'=6, [ i4^0<=5 ], cost: 14

   Accelerated rule 31 with backward acceleration, yielding the new rule 33.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 31.

Accelerating simple loops of location 6.
   Accelerating the following rules:
     32: l6 -> l6 : j5^0'=1+j5^0, k6^0'=6, [ j5^0<=5 ], cost: 14

   Accelerated rule 32 with backward acceleration, yielding the new rule 34.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 32.

Accelerated all simple loops using metering functions (where possible):
   Start location: l12
     19: l0 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 2
     33: l0 -> l0 : i4^0'=6, j5^0'=6, [ 6-i4^0>=1 ], cost: 84-14*i4^0
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
     23: l6 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     34: l6 -> l6 : j5^0'=6, k6^0'=6, [ 6-j5^0>=1 ], cost: 84-14*j5^0
     17: l12 -> l0 : i4^0'=1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l12
     19: l0 -> l4 : i4^0'=1, [ 6<=i4^0 ], cost: 2
     18: l4 -> l6 : j5^0'=1, [ i4^0<=5 ], cost: 2
     36: l4 -> l6 : j5^0'=6, k6^0'=6, [ i4^0<=5 ], cost: 72
     23: l6 -> l4 : i4^0'=1+i4^0, [ 6<=j5^0 ], cost: 2
     17: l12 -> l0 : i4^0'=1, [], cost: 2
     35: l12 -> l0 : i4^0'=6, j5^0'=6, [], cost: 72

Eliminated locations (on tree-shaped paths):
   Start location: l12
     38: l4 -> l4 : i4^0'=1+i4^0, j5^0'=6, k6^0'=6, [ i4^0<=5 ], cost: 74
     37: l12 -> l4 : i4^0'=1, j5^0'=6, [], cost: 74

Accelerating simple loops of location 4.
   Accelerating the following rules:
     38: l4 -> l4 : i4^0'=1+i4^0, j5^0'=6, k6^0'=6, [ i4^0<=5 ], cost: 74

   Accelerated rule 38 with backward acceleration, yielding the new rule 39.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 38.

Accelerated all simple loops using metering functions (where possible):
   Start location: l12
     39: l4 -> l4 : i4^0'=6, j5^0'=6, k6^0'=6, [ 6-i4^0>=1 ], cost: 444-74*i4^0
     37: l12 -> l4 : i4^0'=1, j5^0'=6, [], cost: 74

Chained accelerated rules (with incoming rules):
   Start location: l12
     37: l12 -> l4 : i4^0'=1, j5^0'=6, [], cost: 74
     40: l12 -> l4 : i4^0'=6, j5^0'=6, k6^0'=6, [], cost: 444

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l12
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l12
     <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_17 && j5^0==j5^post_17 && k6^0==k6^post_17 ]

WORST_CASE(Omega(1),?)