WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : __const_10^0'=__const_10^post_1, i^0'=i^post_1, j^0'=j^post_1, x^0'=x^post_1, [ x^0<=i^0 && __const_10^0==__const_10^post_1 && i^0==i^post_1 && j^0==j^post_1 && x^0==x^post_1 ], cost: 1
      1: l0 -> l2 : __const_10^0'=__const_10^post_2, i^0'=i^post_2, j^0'=j^post_2, x^0'=x^post_2, [ 1+i^0<=x^0 && j^post_2==2+j^0 && i^post_2==1+i^0 && __const_10^0==__const_10^post_2 && x^0==x^post_2 ], cost: 1
      6: l1 -> l5 : __const_10^0'=__const_10^post_7, i^0'=i^post_7, j^0'=j^post_7, x^0'=x^post_7, [ 1+j^0<=2*x^0 && __const_10^0==__const_10^post_7 && i^0==i^post_7 && j^0==j^post_7 && x^0==x^post_7 ], cost: 1
      7: l1 -> l5 : __const_10^0'=__const_10^post_8, i^0'=i^post_8, j^0'=j^post_8, x^0'=x^post_8, [ 2*x^0<=j^0 && __const_10^0==__const_10^post_8 && i^0==i^post_8 && j^0==j^post_8 && x^0==x^post_8 ], cost: 1
      4: l2 -> l0 : __const_10^0'=__const_10^post_5, i^0'=i^post_5, j^0'=j^post_5, x^0'=x^post_5, [ __const_10^0==__const_10^post_5 && i^0==i^post_5 && j^0==j^post_5 && x^0==x^post_5 ], cost: 1
      2: l3 -> l2 : __const_10^0'=__const_10^post_3, i^0'=i^post_3, j^0'=j^post_3, x^0'=x^post_3, [ 2<=x^0 && i^post_3==0 && __const_10^0==__const_10^post_3 && j^0==j^post_3 && x^0==x^post_3 ], cost: 1
      3: l3 -> l4 : __const_10^0'=__const_10^post_4, i^0'=i^post_4, j^0'=j^post_4, x^0'=x^post_4, [ x^0<=1 && __const_10^0==__const_10^post_4 && i^0==i^post_4 && j^0==j^post_4 && x^0==x^post_4 ], cost: 1
      5: l5 -> l4 : __const_10^0'=__const_10^post_6, i^0'=i^post_6, j^0'=j^post_6, x^0'=x^post_6, [ __const_10^0==__const_10^post_6 && i^0==i^post_6 && j^0==j^post_6 && x^0==x^post_6 ], cost: 1
      8: l6 -> l3 : __const_10^0'=__const_10^post_9, i^0'=i^post_9, j^0'=j^post_9, x^0'=x^post_9, [ j^post_9==0 && x^post_9==__const_10^0 && __const_10^0==__const_10^post_9 && i^0==i^post_9 ], cost: 1
      9: l7 -> l6 : __const_10^0'=__const_10^post_10, i^0'=i^post_10, j^0'=j^post_10, x^0'=x^post_10, [ __const_10^0==__const_10^post_10 && i^0==i^post_10 && j^0==j^post_10 && x^0==x^post_10 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: l7 -> l6 : __const_10^0'=__const_10^post_10, i^0'=i^post_10, j^0'=j^post_10, x^0'=x^post_10, [ __const_10^0==__const_10^post_10 && i^0==i^post_10 && j^0==j^post_10 && x^0==x^post_10 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      1: l0 -> l2 : __const_10^0'=__const_10^post_2, i^0'=i^post_2, j^0'=j^post_2, x^0'=x^post_2, [ 1+i^0<=x^0 && j^post_2==2+j^0 && i^post_2==1+i^0 && __const_10^0==__const_10^post_2 && x^0==x^post_2 ], cost: 1
      4: l2 -> l0 : __const_10^0'=__const_10^post_5, i^0'=i^post_5, j^0'=j^post_5, x^0'=x^post_5, [ __const_10^0==__const_10^post_5 && i^0==i^post_5 && j^0==j^post_5 && x^0==x^post_5 ], cost: 1
      2: l3 -> l2 : __const_10^0'=__const_10^post_3, i^0'=i^post_3, j^0'=j^post_3, x^0'=x^post_3, [ 2<=x^0 && i^post_3==0 && __const_10^0==__const_10^post_3 && j^0==j^post_3 && x^0==x^post_3 ], cost: 1
      8: l6 -> l3 : __const_10^0'=__const_10^post_9, i^0'=i^post_9, j^0'=j^post_9, x^0'=x^post_9, [ j^post_9==0 && x^post_9==__const_10^0 && __const_10^0==__const_10^post_9 && i^0==i^post_9 ], cost: 1
      9: l7 -> l6 : __const_10^0'=__const_10^post_10, i^0'=i^post_10, j^0'=j^post_10, x^0'=x^post_10, [ __const_10^0==__const_10^post_10 && i^0==i^post_10 && j^0==j^post_10 && x^0==x^post_10 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      1: l0 -> l2 : i^0'=1+i^0, j^0'=2+j^0, [ 1+i^0<=x^0 ], cost: 1
      4: l2 -> l0 : [], cost: 1
      2: l3 -> l2 : i^0'=0, [ 2<=x^0 ], cost: 1
      8: l6 -> l3 : j^0'=0, x^0'=__const_10^0, [], cost: 1
      9: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
     12: l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, [ 1+i^0<=x^0 ], cost: 2
     11: l7 -> l2 : i^0'=0, j^0'=0, x^0'=__const_10^0, [ 2<=__const_10^0 ], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     12: l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, [ 1+i^0<=x^0 ], 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: l7
     13: l2 -> l2 : i^0'=x^0, j^0'=-2*i^0+j^0+2*x^0, [ -i^0+x^0>=0 ], cost: -2*i^0+2*x^0
     11: l7 -> l2 : i^0'=0, j^0'=0, x^0'=__const_10^0, [ 2<=__const_10^0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l7
     11: l7 -> l2 : i^0'=0, j^0'=0, x^0'=__const_10^0, [ 2<=__const_10^0 ], cost: 3
     14: l7 -> l2 : i^0'=__const_10^0, j^0'=2*__const_10^0, x^0'=__const_10^0, [ 2<=__const_10^0 ], cost: 3+2*__const_10^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     14: l7 -> l2 : i^0'=__const_10^0, j^0'=2*__const_10^0, x^0'=__const_10^0, [ 2<=__const_10^0 ], cost: 3+2*__const_10^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     14: l7 -> l2 : i^0'=__const_10^0, j^0'=2*__const_10^0, x^0'=__const_10^0, [ 2<=__const_10^0 ], cost: 3+2*__const_10^0

Computing asymptotic complexity for rule 14
   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_10^0==__const_10^post_10 && i^0==i^post_10 && j^0==j^post_10 && x^0==x^post_10 ]

WORST_CASE(Omega(1),?)