WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      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<=i^0 && j^post_1==__const_100^0 && __const_100^0==__const_100^post_1 && __const_200^0==__const_200^post_1 && i^0==i^post_1 && y4^0==y4^post_1 && y6^0==y6^post_1 && y8^0==y8^post_1 ], cost: 1
      1: l0 -> l2 : __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, [ 1+i^0<=__const_100^0 && y4^post_2==i^0 && y6^post_2==i^0 && i^post_2==1+i^0 && __const_100^0==__const_100^post_2 && __const_200^0==__const_200^post_2 && j^0==j^post_2 && y8^0==y8^post_2 ], cost: 1
      5: l1 -> l3 : __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
      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, [ __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 ], cost: 1
      3: l3 -> l4 : __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, [ __const_200^0<=j^0 && __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 ], cost: 1
      4: l3 -> l1 : __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, [ 1+j^0<=__const_200^0 && y8^post_5==j^0 && j^post_5==1+j^0 && __const_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && i^0==i^post_5 && y4^0==y4^post_5 && y6^0==y6^post_5 ], cost: 1
      6: l5 -> l2 : __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, [ i^post_7==0 && __const_100^0==__const_100^post_7 && __const_200^0==__const_200^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: l6 -> l5 : __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, [ __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 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : __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, [ __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 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      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<=i^0 && j^post_1==__const_100^0 && __const_100^0==__const_100^post_1 && __const_200^0==__const_200^post_1 && i^0==i^post_1 && y4^0==y4^post_1 && y6^0==y6^post_1 && y8^0==y8^post_1 ], cost: 1
      1: l0 -> l2 : __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, [ 1+i^0<=__const_100^0 && y4^post_2==i^0 && y6^post_2==i^0 && i^post_2==1+i^0 && __const_100^0==__const_100^post_2 && __const_200^0==__const_200^post_2 && j^0==j^post_2 && y8^0==y8^post_2 ], cost: 1
      5: l1 -> l3 : __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
      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, [ __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 ], cost: 1
      4: l3 -> l1 : __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, [ 1+j^0<=__const_200^0 && y8^post_5==j^0 && j^post_5==1+j^0 && __const_100^0==__const_100^post_5 && __const_200^0==__const_200^post_5 && i^0==i^post_5 && y4^0==y4^post_5 && y6^0==y6^post_5 ], cost: 1
      6: l5 -> l2 : __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, [ i^post_7==0 && __const_100^0==__const_100^post_7 && __const_200^0==__const_200^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: l6 -> l5 : __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, [ __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 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 1
      5: l1 -> l3 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      4: l3 -> l1 : j^0'=1+j^0, y8^0'=j^0, [ 1+j^0<=__const_200^0 ], cost: 1
      6: l5 -> l2 : i^0'=0, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      0: l0 -> l1 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 1
      9: l1 -> l1 : j^0'=1+j^0, y8^0'=j^0, [ 1+j^0<=__const_200^0 ], cost: 2
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i^0'=0, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      9: l1 -> l1 : j^0'=1+j^0, y8^0'=j^0, [ 1+j^0<=__const_200^0 ], 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 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 1
     10: l1 -> l1 : j^0'=__const_200^0, y8^0'=-1+__const_200^0, [ __const_200^0-j^0>=1 ], cost: 2*__const_200^0-2*j^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      0: l0 -> l1 : j^0'=__const_100^0, [ __const_100^0<=i^0 ], cost: 1
      1: l0 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 1
     11: l0 -> l1 : 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+2*__const_200^0-2*__const_100^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i^0'=0, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
      1: l0 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 1
     11: l0 -> l1 : 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+2*__const_200^0-2*__const_100^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
     12: l2 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 2
     13: l2 -> l1 : 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+2*__const_200^0-2*__const_100^0
      8: l6 -> l2 : i^0'=0, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     12: l2 -> l2 : i^0'=1+i^0, y4^0'=i^0, y6^0'=i^0, [ 1+i^0<=__const_100^0 ], cost: 2

   Accelerated rule 12 with backward acceleration, yielding the new rule 14.
[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 -> l1 : 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+2*__const_200^0-2*__const_100^0
     14: l2 -> l2 : i^0'=__const_100^0, y4^0'=-1+__const_100^0, y6^0'=-1+__const_100^0, [ -i^0+__const_100^0>=1 ], cost: -2*i^0+2*__const_100^0
      8: l6 -> l2 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
     13: l2 -> l1 : 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+2*__const_200^0-2*__const_100^0
      8: l6 -> l2 : i^0'=0, [], cost: 2
     15: l6 -> l2 : i^0'=__const_100^0, y4^0'=-1+__const_100^0, y6^0'=-1+__const_100^0, [ __const_100^0>=1 ], cost: 2+2*__const_100^0

Eliminated locations (on tree-shaped paths):
   Start location: l6
     16: l6 -> l1 : 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+2*__const_200^0-2*__const_100^0
     17: l6 -> l1 : 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+2*__const_200^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     16: l6 -> l1 : 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+2*__const_200^0-2*__const_100^0
     17: l6 -> l1 : 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+2*__const_200^0

Computing asymptotic complexity for rule 16
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 17
   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_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 ]

WORST_CASE(Omega(1),?)