WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l12
      0: l0 -> l1 : __const_100^0'=__const_100^post_1, __const_200^0'=__const_200^post_1, i^0'=i^post_1, j^0'=j^post_1, y4^0'=y4^post_1, y6^0'=y6^post_1, y8^0'=y8^post_1, [ __const_100^0==__const_100^post_1 && __const_200^0==__const_200^post_1 && i^0==i^post_1 && j^0==j^post_1 && y4^0==y4^post_1 && y6^0==y6^post_1 && y8^0==y8^post_1 ], cost: 1
     11: l1 -> l10 : __const_100^0'=__const_100^post_12, __const_200^0'=__const_200^post_12, i^0'=i^post_12, j^0'=j^post_12, y4^0'=y4^post_12, y6^0'=y6^post_12, y8^0'=y8^post_12, [ y6^post_12==i^0 && __const_100^0==__const_100^post_12 && __const_200^0==__const_200^post_12 && i^0==i^post_12 && j^0==j^post_12 && y4^0==y4^post_12 && y8^0==y8^post_12 ], cost: 1
      1: l2 -> l3 : __const_100^0'=__const_100^post_2, __const_200^0'=__const_200^post_2, i^0'=i^post_2, j^0'=j^post_2, y4^0'=y4^post_2, y6^0'=y6^post_2, y8^0'=y8^post_2, [ __const_100^0<=i^0 && j^post_2==__const_100^0 && __const_100^0==__const_100^post_2 && __const_200^0==__const_200^post_2 && i^0==i^post_2 && y4^0==y4^post_2 && y6^0==y6^post_2 && y8^0==y8^post_2 ], cost: 1
      2: l2 -> l0 : __const_100^0'=__const_100^post_3, __const_200^0'=__const_200^post_3, i^0'=i^post_3, j^0'=j^post_3, y4^0'=y4^post_3, y6^0'=y6^post_3, y8^0'=y8^post_3, [ 1+i^0<=__const_100^0 && y4^post_3==i^0 && __const_100^0==__const_100^post_3 && __const_200^0==__const_200^post_3 && i^0==i^post_3 && j^0==j^post_3 && y6^0==y6^post_3 && y8^0==y8^post_3 ], cost: 1
      8: l3 -> l7 : __const_100^0'=__const_100^post_9, __const_200^0'=__const_200^post_9, i^0'=i^post_9, j^0'=j^post_9, y4^0'=y4^post_9, y6^0'=y6^post_9, y8^0'=y8^post_9, [ __const_100^0==__const_100^post_9 && __const_200^0==__const_200^post_9 && i^0==i^post_9 && j^0==j^post_9 && y4^0==y4^post_9 && y6^0==y6^post_9 && y8^0==y8^post_9 ], cost: 1
      3: l4 -> l3 : __const_100^0'=__const_100^post_4, __const_200^0'=__const_200^post_4, i^0'=i^post_4, j^0'=j^post_4, y4^0'=y4^post_4, y6^0'=y6^post_4, y8^0'=y8^post_4, [ j^post_4==1+j^0 && __const_100^0==__const_100^post_4 && __const_200^0==__const_200^post_4 && i^0==i^post_4 && y4^0==y4^post_4 && y6^0==y6^post_4 && y8^0==y8^post_4 ], cost: 1
      4: l5 -> l2 : __const_100^0'=__const_100^post_5, __const_200^0'=__const_200^post_5, i^0'=i^post_5, j^0'=j^post_5, y4^0'=y4^post_5, y6^0'=y6^post_5, y8^0'=y8^post_5, [ __const_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && i^0==i^post_5 && j^0==j^post_5 && y4^0==y4^post_5 && y6^0==y6^post_5 && y8^0==y8^post_5 ], cost: 1
      5: l6 -> l4 : __const_100^0'=__const_100^post_6, __const_200^0'=__const_200^post_6, i^0'=i^post_6, j^0'=j^post_6, y4^0'=y4^post_6, y6^0'=y6^post_6, y8^0'=y8^post_6, [ __const_100^0==__const_100^post_6 && __const_200^0==__const_200^post_6 && i^0==i^post_6 && j^0==j^post_6 && y4^0==y4^post_6 && y6^0==y6^post_6 && y8^0==y8^post_6 ], cost: 1
      6: l7 -> l8 : __const_100^0'=__const_100^post_7, __const_200^0'=__const_200^post_7, i^0'=i^post_7, j^0'=j^post_7, y4^0'=y4^post_7, y6^0'=y6^post_7, y8^0'=y8^post_7, [ __const_200^0<=j^0 && __const_100^0==__const_100^post_7 && __const_200^0==__const_200^post_7 && i^0==i^post_7 && j^0==j^post_7 && y4^0==y4^post_7 && y6^0==y6^post_7 && y8^0==y8^post_7 ], cost: 1
      7: l7 -> l6 : __const_100^0'=__const_100^post_8, __const_200^0'=__const_200^post_8, i^0'=i^post_8, j^0'=j^post_8, y4^0'=y4^post_8, y6^0'=y6^post_8, y8^0'=y8^post_8, [ 1+j^0<=__const_200^0 && y8^post_8==j^0 && __const_100^0==__const_100^post_8 && __const_200^0==__const_200^post_8 && i^0==i^post_8 && j^0==j^post_8 && y4^0==y4^post_8 && y6^0==y6^post_8 ], cost: 1
      9: l9 -> l5 : __const_100^0'=__const_100^post_10, __const_200^0'=__const_200^post_10, i^0'=i^post_10, j^0'=j^post_10, y4^0'=y4^post_10, y6^0'=y6^post_10, y8^0'=y8^post_10, [ i^post_10==1+i^0 && __const_100^0==__const_100^post_10 && __const_200^0==__const_200^post_10 && j^0==j^post_10 && y4^0==y4^post_10 && y6^0==y6^post_10 && y8^0==y8^post_10 ], cost: 1
     10: l10 -> l9 : __const_100^0'=__const_100^post_11, __const_200^0'=__const_200^post_11, i^0'=i^post_11, j^0'=j^post_11, y4^0'=y4^post_11, y6^0'=y6^post_11, y8^0'=y8^post_11, [ __const_100^0==__const_100^post_11 && __const_200^0==__const_200^post_11 && i^0==i^post_11 && j^0==j^post_11 && y4^0==y4^post_11 && y6^0==y6^post_11 && y8^0==y8^post_11 ], cost: 1
     12: l11 -> l5 : __const_100^0'=__const_100^post_13, __const_200^0'=__const_200^post_13, i^0'=i^post_13, j^0'=j^post_13, y4^0'=y4^post_13, y6^0'=y6^post_13, y8^0'=y8^post_13, [ i^post_13==0 && __const_100^0==__const_100^post_13 && __const_200^0==__const_200^post_13 && j^0==j^post_13 && y4^0==y4^post_13 && y6^0==y6^post_13 && y8^0==y8^post_13 ], cost: 1
     13: l12 -> l11 : __const_100^0'=__const_100^post_14, __const_200^0'=__const_200^post_14, i^0'=i^post_14, j^0'=j^post_14, y4^0'=y4^post_14, y6^0'=y6^post_14, y8^0'=y8^post_14, [ __const_100^0==__const_100^post_14 && __const_200^0==__const_200^post_14 && i^0==i^post_14 && j^0==j^post_14 && y4^0==y4^post_14 && y6^0==y6^post_14 && y8^0==y8^post_14 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     13: l12 -> l11 : __const_100^0'=__const_100^post_14, __const_200^0'=__const_200^post_14, i^0'=i^post_14, j^0'=j^post_14, y4^0'=y4^post_14, y6^0'=y6^post_14, y8^0'=y8^post_14, [ __const_100^0==__const_100^post_14 && __const_200^0==__const_200^post_14 && i^0==i^post_14 && j^0==j^post_14 && y4^0==y4^post_14 && y6^0==y6^post_14 && y8^0==y8^post_14 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l12
      0: l0 -> l1 : __const_100^0'=__const_100^post_1, __const_200^0'=__const_200^post_1, i^0'=i^post_1, j^0'=j^post_1, y4^0'=y4^post_1, y6^0'=y6^post_1, y8^0'=y8^post_1, [ __const_100^0==__const_100^post_1 && __const_200^0==__const_200^post_1 && i^0==i^post_1 && j^0==j^post_1 && y4^0==y4^post_1 && y6^0==y6^post_1 && y8^0==y8^post_1 ], cost: 1
     11: l1 -> l10 : __const_100^0'=__const_100^post_12, __const_200^0'=__const_200^post_12, i^0'=i^post_12, j^0'=j^post_12, y4^0'=y4^post_12, y6^0'=y6^post_12, y8^0'=y8^post_12, [ y6^post_12==i^0 && __const_100^0==__const_100^post_12 && __const_200^0==__const_200^post_12 && i^0==i^post_12 && j^0==j^post_12 && y4^0==y4^post_12 && y8^0==y8^post_12 ], cost: 1
      1: l2 -> l3 : __const_100^0'=__const_100^post_2, __const_200^0'=__const_200^post_2, i^0'=i^post_2, j^0'=j^post_2, y4^0'=y4^post_2, y6^0'=y6^post_2, y8^0'=y8^post_2, [ __const_100^0<=i^0 && j^post_2==__const_100^0 && __const_100^0==__const_100^post_2 && __const_200^0==__const_200^post_2 && i^0==i^post_2 && y4^0==y4^post_2 && y6^0==y6^post_2 && y8^0==y8^post_2 ], cost: 1
      2: l2 -> l0 : __const_100^0'=__const_100^post_3, __const_200^0'=__const_200^post_3, i^0'=i^post_3, j^0'=j^post_3, y4^0'=y4^post_3, y6^0'=y6^post_3, y8^0'=y8^post_3, [ 1+i^0<=__const_100^0 && y4^post_3==i^0 && __const_100^0==__const_100^post_3 && __const_200^0==__const_200^post_3 && i^0==i^post_3 && j^0==j^post_3 && y6^0==y6^post_3 && y8^0==y8^post_3 ], cost: 1
      8: l3 -> l7 : __const_100^0'=__const_100^post_9, __const_200^0'=__const_200^post_9, i^0'=i^post_9, j^0'=j^post_9, y4^0'=y4^post_9, y6^0'=y6^post_9, y8^0'=y8^post_9, [ __const_100^0==__const_100^post_9 && __const_200^0==__const_200^post_9 && i^0==i^post_9 && j^0==j^post_9 && y4^0==y4^post_9 && y6^0==y6^post_9 && y8^0==y8^post_9 ], cost: 1
      3: l4 -> l3 : __const_100^0'=__const_100^post_4, __const_200^0'=__const_200^post_4, i^0'=i^post_4, j^0'=j^post_4, y4^0'=y4^post_4, y6^0'=y6^post_4, y8^0'=y8^post_4, [ j^post_4==1+j^0 && __const_100^0==__const_100^post_4 && __const_200^0==__const_200^post_4 && i^0==i^post_4 && y4^0==y4^post_4 && y6^0==y6^post_4 && y8^0==y8^post_4 ], cost: 1
      4: l5 -> l2 : __const_100^0'=__const_100^post_5, __const_200^0'=__const_200^post_5, i^0'=i^post_5, j^0'=j^post_5, y4^0'=y4^post_5, y6^0'=y6^post_5, y8^0'=y8^post_5, [ __const_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && i^0==i^post_5 && j^0==j^post_5 && y4^0==y4^post_5 && y6^0==y6^post_5 && y8^0==y8^post_5 ], cost: 1
      5: l6 -> l4 : __const_100^0'=__const_100^post_6, __const_200^0'=__const_200^post_6, i^0'=i^post_6, j^0'=j^post_6, y4^0'=y4^post_6, y6^0'=y6^post_6, y8^0'=y8^post_6, [ __const_100^0==__const_100^post_6 && __const_200^0==__const_200^post_6 && i^0==i^post_6 && j^0==j^post_6 && y4^0==y4^post_6 && y6^0==y6^post_6 && y8^0==y8^post_6 ], cost: 1
      7: l7 -> l6 : __const_100^0'=__const_100^post_8, __const_200^0'=__const_200^post_8, i^0'=i^post_8, j^0'=j^post_8, y4^0'=y4^post_8, y6^0'=y6^post_8, y8^0'=y8^post_8, [ 1+j^0<=__const_200^0 && y8^post_8==j^0 && __const_100^0==__const_100^post_8 && __const_200^0==__const_200^post_8 && i^0==i^post_8 && j^0==j^post_8 && y4^0==y4^post_8 && y6^0==y6^post_8 ], cost: 1
      9: l9 -> l5 : __const_100^0'=__const_100^post_10, __const_200^0'=__const_200^post_10, i^0'=i^post_10, j^0'=j^post_10, y4^0'=y4^post_10, y6^0'=y6^post_10, y8^0'=y8^post_10, [ i^post_10==1+i^0 && __const_100^0==__const_100^post_10 && __const_200^0==__const_200^post_10 && j^0==j^post_10 && y4^0==y4^post_10 && y6^0==y6^post_10 && y8^0==y8^post_10 ], cost: 1
     10: l10 -> l9 : __const_100^0'=__const_100^post_11, __const_200^0'=__const_200^post_11, i^0'=i^post_11, j^0'=j^post_11, y4^0'=y4^post_11, y6^0'=y6^post_11, y8^0'=y8^post_11, [ __const_100^0==__const_100^post_11 && __const_200^0==__const_200^post_11 && i^0==i^post_11 && j^0==j^post_11 && y4^0==y4^post_11 && y6^0==y6^post_11 && y8^0==y8^post_11 ], cost: 1
     12: l11 -> l5 : __const_100^0'=__const_100^post_13, __const_200^0'=__const_200^post_13, i^0'=i^post_13, j^0'=j^post_13, y4^0'=y4^post_13, y6^0'=y6^post_13, y8^0'=y8^post_13, [ i^post_13==0 && __const_100^0==__const_100^post_13 && __const_200^0==__const_200^post_13 && j^0==j^post_13 && y4^0==y4^post_13 && y6^0==y6^post_13 && y8^0==y8^post_13 ], cost: 1
     13: l12 -> l11 : __const_100^0'=__const_100^post_14, __const_200^0'=__const_200^post_14, i^0'=i^post_14, j^0'=j^post_14, y4^0'=y4^post_14, y6^0'=y6^post_14, y8^0'=y8^post_14, [ __const_100^0==__const_100^post_14 && __const_200^0==__const_200^post_14 && i^0==i^post_14 && j^0==j^post_14 && y4^0==y4^post_14 && y6^0==y6^post_14 && y8^0==y8^post_14 ], cost: 1

Simplified all rules, resulting in:
   Start location: l12
      0: l0 -> l1 : [], cost: 1
     11: l1 -> l10 : y6^0'=i^0, [], cost: 1
      1: l2 -> l3 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
      2: l2 -> l0 : y4^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 1
      8: l3 -> l7 : [], cost: 1
      3: l4 -> l3 : j^0'=1+j^0, [], cost: 1
      4: l5 -> l2 : [], cost: 1
      5: l6 -> l4 : [], cost: 1
      7: l7 -> l6 : y8^0'=j^0, [ 1+j^0<=__const_200^0 ], cost: 1
      9: l9 -> l5 : i^0'=1+i^0, [], cost: 1
     10: l10 -> l9 : [], cost: 1
     12: l11 -> l5 : i^0'=0, [], cost: 1
     13: l12 -> l11 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l12
      1: l2 -> l3 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
     18: l2 -> l5 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 5
     21: l3 -> l3 : j^0'=1+j^0, y8^0'=j^0, [ 1+j^0<=__const_200^0 ], cost: 4
      4: l5 -> l2 : [], cost: 1
     14: l12 -> l5 : i^0'=0, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     21: l3 -> l3 : j^0'=1+j^0, y8^0'=j^0, [ 1+j^0<=__const_200^0 ], cost: 4

   Accelerated rule 21 with backward acceleration, yielding the new rule 22.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 21.

Accelerated all simple loops using metering functions (where possible):
   Start location: l12
      1: l2 -> l3 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
     18: l2 -> l5 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 5
     22: l3 -> l3 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_200^0-j^0>=1 ], cost: 4*__const_200^0-4*j^0
      4: l5 -> l2 : [], cost: 1
     14: l12 -> l5 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l12
      1: l2 -> l3 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
     18: l2 -> l5 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 5
     23: l2 -> l3 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=i^0 && __const_200^0-__const_100^0>=1 ], cost: 1+4*__const_200^0-4*__const_100^0
      4: l5 -> l2 : [], cost: 1
     14: l12 -> l5 : i^0'=0, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l12
     18: l2 -> l5 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 5
     23: l2 -> l3 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=i^0 && __const_200^0-__const_100^0>=1 ], cost: 1+4*__const_200^0-4*__const_100^0
      4: l5 -> l2 : [], cost: 1
     14: l12 -> l5 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l12
     24: l5 -> l5 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 6
     25: l5 -> l3 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=i^0 && __const_200^0-__const_100^0>=1 ], cost: 2+4*__const_200^0-4*__const_100^0
     14: l12 -> l5 : i^0'=0, [], cost: 2

Accelerating simple loops of location 5.
   Accelerating the following rules:
     24: l5 -> l5 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 6

   Accelerated rule 24 with backward acceleration, yielding the new rule 26.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 24.

Accelerated all simple loops using metering functions (where possible):
   Start location: l12
     25: l5 -> l3 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=i^0 && __const_200^0-__const_100^0>=1 ], cost: 2+4*__const_200^0-4*__const_100^0
     26: l5 -> l5 : i^0'=__const_100^0, y4^0'=-1+__const_100^0, y6^0'=-1+__const_100^0, [ -i^0+__const_100^0>=1 ], cost: -6*i^0+6*__const_100^0
     14: l12 -> l5 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l12
     25: l5 -> l3 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=i^0 && __const_200^0-__const_100^0>=1 ], cost: 2+4*__const_200^0-4*__const_100^0
     14: l12 -> l5 : i^0'=0, [], cost: 2
     27: l12 -> l5 : i^0'=__const_100^0, y4^0'=-1+__const_100^0, y6^0'=-1+__const_100^0, [ __const_100^0>=1 ], cost: 2+6*__const_100^0

Eliminated locations (on tree-shaped paths):
   Start location: l12
     28: l12 -> l3 : i^0'=0, j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=0 && __const_200^0-__const_100^0>=1 ], cost: 4+4*__const_200^0-4*__const_100^0
     29: l12 -> l3 : i^0'=__const_100^0, j^0'=__const_200^0, y4^0'=-1+__const_100^0, y6^0'=-1+__const_100^0, y8^0'=-1+__const_200^0, [ __const_100^0>=1 && __const_200^0-__const_100^0>=1 ], cost: 4+4*__const_200^0+2*__const_100^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l12
     28: l12 -> l3 : i^0'=0, j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_100^0<=0 && __const_200^0-__const_100^0>=1 ], cost: 4+4*__const_200^0-4*__const_100^0
     29: l12 -> l3 : i^0'=__const_100^0, j^0'=__const_200^0, y4^0'=-1+__const_100^0, y6^0'=-1+__const_100^0, y8^0'=-1+__const_200^0, [ __const_100^0>=1 && __const_200^0-__const_100^0>=1 ], cost: 4+4*__const_200^0+2*__const_100^0

Computing asymptotic complexity for rule 28
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 29
   Resulting cost 0 has complexity: Unknown

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:  [ __const_100^0==__const_100^post_14 && __const_200^0==__const_200^post_14 && i^0==i^post_14 && j^0==j^post_14 && y4^0==y4^post_14 && y6^0==y6^post_14 && y8^0==y8^post_14 ]

WORST_CASE(Omega(1),?)