WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, b_7^0'=b_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-1-x_5^0+y_6^0 && 1-b_7^0<=0 && b_7^post_1==0 && y_6^post_1==-1+y_6^0 && Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1
      1: l0 -> l2 : Result_4^0'=Result_4^post_2, b_7^0'=b_7^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ -x_5^0+y_6^0<=0 && Result_4^post_2==Result_4^post_2 && b_7^0==b_7^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      3: l1 -> l0 : Result_4^0'=Result_4^post_4, b_7^0'=b_7^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 0<=-1-x_5^0+y_6^0 && 0<=-b_7^0 && b_7^post_4==1 && x_5^post_4==1+x_5^0 && Result_4^0==Result_4^post_4 && y_6^0==y_6^post_4 ], cost: 1
      4: l1 -> l2 : Result_4^0'=Result_4^post_5, b_7^0'=b_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ -x_5^0+y_6^0<=0 && Result_4^post_5==Result_4^post_5 && b_7^0==b_7^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      2: l3 -> l1 : Result_4^0'=Result_4^post_3, b_7^0'=b_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ b_7^post_3==0 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && b_7^0==b_7^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && b_7^0==b_7^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, b_7^0'=b_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-1-x_5^0+y_6^0 && 1-b_7^0<=0 && b_7^post_1==0 && y_6^post_1==-1+y_6^0 && Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1
      3: l1 -> l0 : Result_4^0'=Result_4^post_4, b_7^0'=b_7^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 0<=-1-x_5^0+y_6^0 && 0<=-b_7^0 && b_7^post_4==1 && x_5^post_4==1+x_5^0 && Result_4^0==Result_4^post_4 && y_6^0==y_6^post_4 ], cost: 1
      2: l3 -> l1 : Result_4^0'=Result_4^post_3, b_7^0'=b_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ b_7^post_3==0 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && b_7^0==b_7^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : b_7^0'=0, y_6^0'=-1+y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1-b_7^0<=0 ], cost: 1
      3: l1 -> l0 : b_7^0'=1, x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && 0<=-b_7^0 ], cost: 1
      2: l3 -> l1 : b_7^0'=0, [], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      7: l1 -> l1 : b_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=-1+y_6^0, [ 0<=-b_7^0 && 0<=-2-x_5^0+y_6^0 ], cost: 2
      6: l4 -> l1 : b_7^0'=0, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      7: l1 -> l1 : b_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=-1+y_6^0, [ 0<=-b_7^0 && 0<=-2-x_5^0+y_6^0 ], cost: 2

   Accelerated rule 7 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 7.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      8: l1 -> l1 : b_7^0'=0, x_5^0'=k+x_5^0, y_6^0'=-k+y_6^0, [ 0<=-b_7^0 && k>=1 && 0<=-2*k-x_5^0+y_6^0 ], cost: 2*k
      6: l4 -> l1 : b_7^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l1 : b_7^0'=0, [], cost: 2
      9: l4 -> l1 : b_7^0'=0, x_5^0'=k+x_5^0, y_6^0'=-k+y_6^0, [ k>=1 && 0<=-2*k-x_5^0+y_6^0 ], cost: 2+2*k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
      9: l4 -> l1 : b_7^0'=0, x_5^0'=k+x_5^0, y_6^0'=-k+y_6^0, [ k>=1 && 0<=-2*k-x_5^0+y_6^0 ], cost: 2+2*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
      9: l4 -> l1 : b_7^0'=0, x_5^0'=k+x_5^0, y_6^0'=-k+y_6^0, [ k>=1 && 0<=-2*k-x_5^0+y_6^0 ], cost: 2+2*k

Computing asymptotic complexity for rule 9
   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:  [ Result_4^0==Result_4^post_6 && b_7^0==b_7^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ]

WORST_CASE(Omega(1),?)