WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l5
      0: l0 -> l1 : i_13^0'=i_13^post_1, j_15^0'=j_15^post_1, rt_11^0'=rt_11^post_1, s_16^0'=s_16^post_1, s_17^0'=s_17^post_1, st_14^0'=st_14^post_1, [ i_13^1_1==s_17^0 && j_15^post_1==s_16^0 && i_13^post_1==j_15^post_1 && rt_11^0==rt_11^post_1 && s_16^0==s_16^post_1 && s_17^0==s_17^post_1 && st_14^0==st_14^post_1 ], cost: 1
      4: l1 -> l3 : i_13^0'=i_13^post_5, j_15^0'=j_15^post_5, rt_11^0'=rt_11^post_5, s_16^0'=s_16^post_5, s_17^0'=s_17^post_5, st_14^0'=st_14^post_5, [ 500<=i_13^0 && rt_11^post_5==st_14^0 && i_13^0==i_13^post_5 && j_15^0==j_15^post_5 && s_16^0==s_16^post_5 && s_17^0==s_17^post_5 && st_14^0==st_14^post_5 ], cost: 1
      5: l1 -> l2 : i_13^0'=i_13^post_6, j_15^0'=j_15^post_6, rt_11^0'=rt_11^post_6, s_16^0'=s_16^post_6, s_17^0'=s_17^post_6, st_14^0'=st_14^post_6, [ 1+i_13^0<=500 && i_13^post_6==1+i_13^0 && j_15^0==j_15^post_6 && rt_11^0==rt_11^post_6 && s_16^0==s_16^post_6 && s_17^0==s_17^post_6 && st_14^0==st_14^post_6 ], cost: 1
      1: l2 -> l3 : i_13^0'=i_13^post_2, j_15^0'=j_15^post_2, rt_11^0'=rt_11^post_2, s_16^0'=s_16^post_2, s_17^0'=s_17^post_2, st_14^0'=st_14^post_2, [ 500<=i_13^0 && rt_11^post_2==st_14^0 && i_13^0==i_13^post_2 && j_15^0==j_15^post_2 && s_16^0==s_16^post_2 && s_17^0==s_17^post_2 && st_14^0==st_14^post_2 ], cost: 1
      2: l2 -> l4 : i_13^0'=i_13^post_3, j_15^0'=j_15^post_3, rt_11^0'=rt_11^post_3, s_16^0'=s_16^post_3, s_17^0'=s_17^post_3, st_14^0'=st_14^post_3, [ 1+i_13^0<=500 && i_13^post_3==1+i_13^0 && j_15^0==j_15^post_3 && rt_11^0==rt_11^post_3 && s_16^0==s_16^post_3 && s_17^0==s_17^post_3 && st_14^0==st_14^post_3 ], cost: 1
      3: l4 -> l2 : i_13^0'=i_13^post_4, j_15^0'=j_15^post_4, rt_11^0'=rt_11^post_4, s_16^0'=s_16^post_4, s_17^0'=s_17^post_4, st_14^0'=st_14^post_4, [ i_13^0==i_13^post_4 && j_15^0==j_15^post_4 && rt_11^0==rt_11^post_4 && s_16^0==s_16^post_4 && s_17^0==s_17^post_4 && st_14^0==st_14^post_4 ], cost: 1
      6: l5 -> l0 : i_13^0'=i_13^post_7, j_15^0'=j_15^post_7, rt_11^0'=rt_11^post_7, s_16^0'=s_16^post_7, s_17^0'=s_17^post_7, st_14^0'=st_14^post_7, [ i_13^0==i_13^post_7 && j_15^0==j_15^post_7 && rt_11^0==rt_11^post_7 && s_16^0==s_16^post_7 && s_17^0==s_17^post_7 && st_14^0==st_14^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l0 : i_13^0'=i_13^post_7, j_15^0'=j_15^post_7, rt_11^0'=rt_11^post_7, s_16^0'=s_16^post_7, s_17^0'=s_17^post_7, st_14^0'=st_14^post_7, [ i_13^0==i_13^post_7 && j_15^0==j_15^post_7 && rt_11^0==rt_11^post_7 && s_16^0==s_16^post_7 && s_17^0==s_17^post_7 && st_14^0==st_14^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      0: l0 -> l1 : i_13^0'=i_13^post_1, j_15^0'=j_15^post_1, rt_11^0'=rt_11^post_1, s_16^0'=s_16^post_1, s_17^0'=s_17^post_1, st_14^0'=st_14^post_1, [ i_13^1_1==s_17^0 && j_15^post_1==s_16^0 && i_13^post_1==j_15^post_1 && rt_11^0==rt_11^post_1 && s_16^0==s_16^post_1 && s_17^0==s_17^post_1 && st_14^0==st_14^post_1 ], cost: 1
      5: l1 -> l2 : i_13^0'=i_13^post_6, j_15^0'=j_15^post_6, rt_11^0'=rt_11^post_6, s_16^0'=s_16^post_6, s_17^0'=s_17^post_6, st_14^0'=st_14^post_6, [ 1+i_13^0<=500 && i_13^post_6==1+i_13^0 && j_15^0==j_15^post_6 && rt_11^0==rt_11^post_6 && s_16^0==s_16^post_6 && s_17^0==s_17^post_6 && st_14^0==st_14^post_6 ], cost: 1
      2: l2 -> l4 : i_13^0'=i_13^post_3, j_15^0'=j_15^post_3, rt_11^0'=rt_11^post_3, s_16^0'=s_16^post_3, s_17^0'=s_17^post_3, st_14^0'=st_14^post_3, [ 1+i_13^0<=500 && i_13^post_3==1+i_13^0 && j_15^0==j_15^post_3 && rt_11^0==rt_11^post_3 && s_16^0==s_16^post_3 && s_17^0==s_17^post_3 && st_14^0==st_14^post_3 ], cost: 1
      3: l4 -> l2 : i_13^0'=i_13^post_4, j_15^0'=j_15^post_4, rt_11^0'=rt_11^post_4, s_16^0'=s_16^post_4, s_17^0'=s_17^post_4, st_14^0'=st_14^post_4, [ i_13^0==i_13^post_4 && j_15^0==j_15^post_4 && rt_11^0==rt_11^post_4 && s_16^0==s_16^post_4 && s_17^0==s_17^post_4 && st_14^0==st_14^post_4 ], cost: 1
      6: l5 -> l0 : i_13^0'=i_13^post_7, j_15^0'=j_15^post_7, rt_11^0'=rt_11^post_7, s_16^0'=s_16^post_7, s_17^0'=s_17^post_7, st_14^0'=st_14^post_7, [ i_13^0==i_13^post_7 && j_15^0==j_15^post_7 && rt_11^0==rt_11^post_7 && s_16^0==s_16^post_7 && s_17^0==s_17^post_7 && st_14^0==st_14^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      0: l0 -> l1 : i_13^0'=s_16^0, j_15^0'=s_16^0, [], cost: 1
      5: l1 -> l2 : i_13^0'=1+i_13^0, [ 1+i_13^0<=500 ], cost: 1
      2: l2 -> l4 : i_13^0'=1+i_13^0, [ 1+i_13^0<=500 ], cost: 1
      3: l4 -> l2 : [], cost: 1
      6: l5 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      9: l2 -> l2 : i_13^0'=1+i_13^0, [ 1+i_13^0<=500 ], cost: 2
      8: l5 -> l2 : i_13^0'=1+s_16^0, j_15^0'=s_16^0, [ 1+s_16^0<=500 ], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
      9: l2 -> l2 : i_13^0'=1+i_13^0, [ 1+i_13^0<=500 ], 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: l5
     10: l2 -> l2 : i_13^0'=500, [ 500-i_13^0>=0 ], cost: 1000-2*i_13^0
      8: l5 -> l2 : i_13^0'=1+s_16^0, j_15^0'=s_16^0, [ 1+s_16^0<=500 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l5
      8: l5 -> l2 : i_13^0'=1+s_16^0, j_15^0'=s_16^0, [ 1+s_16^0<=500 ], cost: 3
     11: l5 -> l2 : i_13^0'=500, j_15^0'=s_16^0, [ 1+s_16^0<=500 ], cost: 1001-2*s_16^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     11: l5 -> l2 : i_13^0'=500, j_15^0'=s_16^0, [ 1+s_16^0<=500 ], cost: 1001-2*s_16^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     11: l5 -> l2 : i_13^0'=500, j_15^0'=s_16^0, [ 1+s_16^0<=500 ], cost: 1001-2*s_16^0

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:  [ i_13^0==i_13^post_7 && j_15^0==j_15^post_7 && rt_11^0==rt_11^post_7 && s_16^0==s_16^post_7 && s_17^0==s_17^post_7 && st_14^0==st_14^post_7 ]

WORST_CASE(Omega(1),?)