WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : result_11^0'=result_11^post_1, t_16^0'=t_16^post_1, t_22^0'=t_22^post_1, temp0_14^0'=temp0_14^post_1, x_13^0'=x_13^post_1, y_15^0'=y_15^post_1, y_21^0'=y_21^post_1, [ result_11^0==result_11^post_1 && t_16^0==t_16^post_1 && t_22^0==t_22^post_1 && temp0_14^0==temp0_14^post_1 && x_13^0==x_13^post_1 && y_15^0==y_15^post_1 && y_21^0==y_21^post_1 ], cost: 1
      1: l1 -> l2 : result_11^0'=result_11^post_2, t_16^0'=t_16^post_2, t_22^0'=t_22^post_2, temp0_14^0'=temp0_14^post_2, x_13^0'=x_13^post_2, y_15^0'=y_15^post_2, y_21^0'=y_21^post_2, [ 1<=x_13^0 && y_15^0<=0 && result_11^post_2==temp0_14^0 && t_16^0==t_16^post_2 && t_22^0==t_22^post_2 && temp0_14^0==temp0_14^post_2 && x_13^0==x_13^post_2 && y_15^0==y_15^post_2 && y_21^0==y_21^post_2 ], cost: 1
      2: l1 -> l2 : result_11^0'=result_11^post_3, t_16^0'=t_16^post_3, t_22^0'=t_22^post_3, temp0_14^0'=temp0_14^post_3, x_13^0'=x_13^post_3, y_15^0'=y_15^post_3, y_21^0'=y_21^post_3, [ x_13^0<=0 && x_13^post_3==x_13^post_3 && result_11^post_3==temp0_14^0 && x_13^post_3<=0 && t_16^0==t_16^post_3 && t_22^0==t_22^post_3 && temp0_14^0==temp0_14^post_3 && y_15^0==y_15^post_3 && y_21^0==y_21^post_3 ], cost: 1
      3: l1 -> l3 : result_11^0'=result_11^post_4, t_16^0'=t_16^post_4, t_22^0'=t_22^post_4, temp0_14^0'=temp0_14^post_4, x_13^0'=x_13^post_4, y_15^0'=y_15^post_4, y_21^0'=y_21^post_4, [ y_21^post_4==y_21^post_4 && t_22^post_4==t_22^post_4 && 1<=x_13^0 && 1<=y_15^0 && t_16^1_1==x_13^0 && x_13^1_1==-2+y_15^0 && y_15^1_1==1+t_16^1_1 && t_16^post_4==x_13^1_1 && x_13^post_4==-2+y_15^1_1 && y_15^post_4==1+t_16^post_4 && x_13^post_4<=-1+t_22^post_4 && -1+t_22^post_4<=x_13^post_4 && y_15^post_4<=1+t_16^post_4 && 1+t_16^post_4<=y_15^post_4 && t_16^post_4<=-2+y_21^post_4 && -2+y_21^post_4<=t_16^post_4 && 1<=y_21^post_4 && 1<=t_22^post_4 && result_11^0==result_11^post_4 && temp0_14^0==temp0_14^post_4 ], cost: 1
      4: l3 -> l1 : result_11^0'=result_11^post_5, t_16^0'=t_16^post_5, t_22^0'=t_22^post_5, temp0_14^0'=temp0_14^post_5, x_13^0'=x_13^post_5, y_15^0'=y_15^post_5, y_21^0'=y_21^post_5, [ result_11^0==result_11^post_5 && t_16^0==t_16^post_5 && t_22^0==t_22^post_5 && temp0_14^0==temp0_14^post_5 && x_13^0==x_13^post_5 && y_15^0==y_15^post_5 && y_21^0==y_21^post_5 ], cost: 1
      5: l4 -> l0 : result_11^0'=result_11^post_6, t_16^0'=t_16^post_6, t_22^0'=t_22^post_6, temp0_14^0'=temp0_14^post_6, x_13^0'=x_13^post_6, y_15^0'=y_15^post_6, y_21^0'=y_21^post_6, [ result_11^0==result_11^post_6 && t_16^0==t_16^post_6 && t_22^0==t_22^post_6 && temp0_14^0==temp0_14^post_6 && x_13^0==x_13^post_6 && y_15^0==y_15^post_6 && y_21^0==y_21^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l0 : result_11^0'=result_11^post_6, t_16^0'=t_16^post_6, t_22^0'=t_22^post_6, temp0_14^0'=temp0_14^post_6, x_13^0'=x_13^post_6, y_15^0'=y_15^post_6, y_21^0'=y_21^post_6, [ result_11^0==result_11^post_6 && t_16^0==t_16^post_6 && t_22^0==t_22^post_6 && temp0_14^0==temp0_14^post_6 && x_13^0==x_13^post_6 && y_15^0==y_15^post_6 && y_21^0==y_21^post_6 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      0: l0 -> l1 : result_11^0'=result_11^post_1, t_16^0'=t_16^post_1, t_22^0'=t_22^post_1, temp0_14^0'=temp0_14^post_1, x_13^0'=x_13^post_1, y_15^0'=y_15^post_1, y_21^0'=y_21^post_1, [ result_11^0==result_11^post_1 && t_16^0==t_16^post_1 && t_22^0==t_22^post_1 && temp0_14^0==temp0_14^post_1 && x_13^0==x_13^post_1 && y_15^0==y_15^post_1 && y_21^0==y_21^post_1 ], cost: 1
      3: l1 -> l3 : result_11^0'=result_11^post_4, t_16^0'=t_16^post_4, t_22^0'=t_22^post_4, temp0_14^0'=temp0_14^post_4, x_13^0'=x_13^post_4, y_15^0'=y_15^post_4, y_21^0'=y_21^post_4, [ y_21^post_4==y_21^post_4 && t_22^post_4==t_22^post_4 && 1<=x_13^0 && 1<=y_15^0 && t_16^1_1==x_13^0 && x_13^1_1==-2+y_15^0 && y_15^1_1==1+t_16^1_1 && t_16^post_4==x_13^1_1 && x_13^post_4==-2+y_15^1_1 && y_15^post_4==1+t_16^post_4 && x_13^post_4<=-1+t_22^post_4 && -1+t_22^post_4<=x_13^post_4 && y_15^post_4<=1+t_16^post_4 && 1+t_16^post_4<=y_15^post_4 && t_16^post_4<=-2+y_21^post_4 && -2+y_21^post_4<=t_16^post_4 && 1<=y_21^post_4 && 1<=t_22^post_4 && result_11^0==result_11^post_4 && temp0_14^0==temp0_14^post_4 ], cost: 1
      4: l3 -> l1 : result_11^0'=result_11^post_5, t_16^0'=t_16^post_5, t_22^0'=t_22^post_5, temp0_14^0'=temp0_14^post_5, x_13^0'=x_13^post_5, y_15^0'=y_15^post_5, y_21^0'=y_21^post_5, [ result_11^0==result_11^post_5 && t_16^0==t_16^post_5 && t_22^0==t_22^post_5 && temp0_14^0==temp0_14^post_5 && x_13^0==x_13^post_5 && y_15^0==y_15^post_5 && y_21^0==y_21^post_5 ], cost: 1
      5: l4 -> l0 : result_11^0'=result_11^post_6, t_16^0'=t_16^post_6, t_22^0'=t_22^post_6, temp0_14^0'=temp0_14^post_6, x_13^0'=x_13^post_6, y_15^0'=y_15^post_6, y_21^0'=y_21^post_6, [ result_11^0==result_11^post_6 && t_16^0==t_16^post_6 && t_22^0==t_22^post_6 && temp0_14^0==temp0_14^post_6 && x_13^0==x_13^post_6 && y_15^0==y_15^post_6 && y_21^0==y_21^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : [], cost: 1
      3: l1 -> l3 : t_16^0'=-2+y_15^0, t_22^0'=x_13^0, x_13^0'=-1+x_13^0, y_15^0'=-1+y_15^0, y_21^0'=y_15^0, [ 1<=x_13^0 && 1<=y_15^0 ], cost: 1
      4: l3 -> l1 : [], cost: 1
      5: l4 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      7: l1 -> l1 : t_16^0'=-2+y_15^0, t_22^0'=x_13^0, x_13^0'=-1+x_13^0, y_15^0'=-1+y_15^0, y_21^0'=y_15^0, [ 1<=x_13^0 && 1<=y_15^0 ], cost: 2
      6: l4 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      7: l1 -> l1 : t_16^0'=-2+y_15^0, t_22^0'=x_13^0, x_13^0'=-1+x_13^0, y_15^0'=-1+y_15^0, y_21^0'=y_15^0, [ 1<=x_13^0 && 1<=y_15^0 ], cost: 2

   Accelerated rule 7 with backward acceleration, yielding the new rule 8.
   Accelerated rule 7 with backward acceleration, yielding the new rule 9.
[accelerate] Nesting with 2 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 : t_16^0'=-1-x_13^0+y_15^0, t_22^0'=1, x_13^0'=0, y_15^0'=-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, [ x_13^0>=1 && 1<=1-x_13^0+y_15^0 ], cost: 2*x_13^0
      9: l1 -> l1 : t_16^0'=-1, t_22^0'=1+x_13^0-y_15^0, x_13^0'=x_13^0-y_15^0, y_15^0'=0, y_21^0'=1, [ y_15^0>=1 && 1<=1+x_13^0-y_15^0 ], cost: 2*y_15^0
      6: l4 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l1 : [], cost: 2
     10: l4 -> l1 : t_16^0'=-1-x_13^0+y_15^0, t_22^0'=1, x_13^0'=0, y_15^0'=-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, [ x_13^0>=1 && 1<=1-x_13^0+y_15^0 ], cost: 2+2*x_13^0
     11: l4 -> l1 : t_16^0'=-1, t_22^0'=1+x_13^0-y_15^0, x_13^0'=x_13^0-y_15^0, y_15^0'=0, y_21^0'=1, [ y_15^0>=1 && 1<=1+x_13^0-y_15^0 ], cost: 2+2*y_15^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     10: l4 -> l1 : t_16^0'=-1-x_13^0+y_15^0, t_22^0'=1, x_13^0'=0, y_15^0'=-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, [ x_13^0>=1 && 1<=1-x_13^0+y_15^0 ], cost: 2+2*x_13^0
     11: l4 -> l1 : t_16^0'=-1, t_22^0'=1+x_13^0-y_15^0, x_13^0'=x_13^0-y_15^0, y_15^0'=0, y_21^0'=1, [ y_15^0>=1 && 1<=1+x_13^0-y_15^0 ], cost: 2+2*y_15^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     10: l4 -> l1 : t_16^0'=-1-x_13^0+y_15^0, t_22^0'=1, x_13^0'=0, y_15^0'=-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, [ x_13^0>=1 && 1<=1-x_13^0+y_15^0 ], cost: 2+2*x_13^0
     11: l4 -> l1 : t_16^0'=-1, t_22^0'=1+x_13^0-y_15^0, x_13^0'=x_13^0-y_15^0, y_15^0'=0, y_21^0'=1, [ y_15^0>=1 && 1<=1+x_13^0-y_15^0 ], cost: 2+2*y_15^0

Computing asymptotic complexity for rule 10
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 11
   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_11^0==result_11^post_6 && t_16^0==t_16^post_6 && t_22^0==t_22^post_6 && temp0_14^0==temp0_14^post_6 && x_13^0==x_13^post_6 && y_15^0==y_15^post_6 && y_21^0==y_21^post_6 ]

WORST_CASE(Omega(1),?)