WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : a_20^0'=a_20^post_1, i_13^0'=i_13^post_1, i_21^0'=i_21^post_1, rt_11^0'=rt_11^post_1, st_14^0'=st_14^post_1, [ i_13^post_1==0 && 0<=i_13^post_1 && i_13^post_1<=0 && a_20^0==a_20^post_1 && i_21^0==i_21^post_1 && rt_11^0==rt_11^post_1 && st_14^0==st_14^post_1 ], cost: 1
      3: l1 -> l4 : a_20^0'=a_20^post_4, i_13^0'=i_13^post_4, i_21^0'=i_21^post_4, rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, [ 10<=i_13^0 && rt_11^post_4==st_14^0 && a_20^0==a_20^post_4 && i_13^0==i_13^post_4 && i_21^0==i_21^post_4 && st_14^0==st_14^post_4 ], cost: 1
      4: l1 -> l5 : a_20^0'=a_20^post_5, i_13^0'=i_13^post_5, i_21^0'=i_21^post_5, rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, [ i_21^post_5==i_21^post_5 && 1+i_13^0<=10 && i_13^post_5==1+i_13^0 && i_13^post_5<=1+i_21^post_5 && 1+i_21^post_5<=i_13^post_5 && 1+i_21^post_5<=10 && a_20^0==a_20^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 ], cost: 1
      1: l2 -> l1 : a_20^0'=a_20^post_2, i_13^0'=i_13^post_2, i_21^0'=i_21^post_2, rt_11^0'=rt_11^post_2, st_14^0'=st_14^post_2, [ 1+i_13^0<=10 && i_13^1_1==1+i_13^0 && i_13^post_2==i_13^post_2 && 2<=i_13^post_2 && i_13^post_2<=2 && a_20^post_2==a_20^post_2 && a_20^post_2<=i_13^post_2 && i_13^post_2<=a_20^post_2 && i_21^0==i_21^post_2 && rt_11^0==rt_11^post_2 && st_14^0==st_14^post_2 ], cost: 1
      2: l3 -> l1 : a_20^0'=a_20^post_3, i_13^0'=i_13^post_3, i_21^0'=i_21^post_3, rt_11^0'=rt_11^post_3, st_14^0'=st_14^post_3, [ 1+i_13^0<=10 && i_13^post_3==1+i_13^0 && 1<=i_13^post_3 && i_13^post_3<=1 && a_20^0==a_20^post_3 && i_21^0==i_21^post_3 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 ], cost: 1
      5: l5 -> l1 : a_20^0'=a_20^post_6, i_13^0'=i_13^post_6, i_21^0'=i_21^post_6, rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, [ a_20^0==a_20^post_6 && i_13^0==i_13^post_6 && i_21^0==i_21^post_6 && rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 ], cost: 1
      6: l6 -> l0 : a_20^0'=a_20^post_7, i_13^0'=i_13^post_7, i_21^0'=i_21^post_7, rt_11^0'=rt_11^post_7, st_14^0'=st_14^post_7, [ a_20^0==a_20^post_7 && i_13^0==i_13^post_7 && i_21^0==i_21^post_7 && rt_11^0==rt_11^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: l6 -> l0 : a_20^0'=a_20^post_7, i_13^0'=i_13^post_7, i_21^0'=i_21^post_7, rt_11^0'=rt_11^post_7, st_14^0'=st_14^post_7, [ a_20^0==a_20^post_7 && i_13^0==i_13^post_7 && i_21^0==i_21^post_7 && rt_11^0==rt_11^post_7 && st_14^0==st_14^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      0: l0 -> l1 : a_20^0'=a_20^post_1, i_13^0'=i_13^post_1, i_21^0'=i_21^post_1, rt_11^0'=rt_11^post_1, st_14^0'=st_14^post_1, [ i_13^post_1==0 && 0<=i_13^post_1 && i_13^post_1<=0 && a_20^0==a_20^post_1 && i_21^0==i_21^post_1 && rt_11^0==rt_11^post_1 && st_14^0==st_14^post_1 ], cost: 1
      4: l1 -> l5 : a_20^0'=a_20^post_5, i_13^0'=i_13^post_5, i_21^0'=i_21^post_5, rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, [ i_21^post_5==i_21^post_5 && 1+i_13^0<=10 && i_13^post_5==1+i_13^0 && i_13^post_5<=1+i_21^post_5 && 1+i_21^post_5<=i_13^post_5 && 1+i_21^post_5<=10 && a_20^0==a_20^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 ], cost: 1
      5: l5 -> l1 : a_20^0'=a_20^post_6, i_13^0'=i_13^post_6, i_21^0'=i_21^post_6, rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, [ a_20^0==a_20^post_6 && i_13^0==i_13^post_6 && i_21^0==i_21^post_6 && rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 ], cost: 1
      6: l6 -> l0 : a_20^0'=a_20^post_7, i_13^0'=i_13^post_7, i_21^0'=i_21^post_7, rt_11^0'=rt_11^post_7, st_14^0'=st_14^post_7, [ a_20^0==a_20^post_7 && i_13^0==i_13^post_7 && i_21^0==i_21^post_7 && rt_11^0==rt_11^post_7 && st_14^0==st_14^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : i_13^0'=0, [], cost: 1
      4: l1 -> l5 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, [ 1+i_13^0<=10 ], cost: 1
      5: l5 -> l1 : [], cost: 1
      6: l6 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      8: l1 -> l1 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, [ 1+i_13^0<=10 ], cost: 2
      7: l6 -> l1 : i_13^0'=0, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      8: l1 -> l1 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, [ 1+i_13^0<=10 ], cost: 2

   Accelerated rule 8 with backward acceleration, yielding the new rule 9.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 8.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
      9: l1 -> l1 : i_13^0'=10, i_21^0'=9, [ 10-i_13^0>=1 ], cost: 20-2*i_13^0
      7: l6 -> l1 : i_13^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      7: l6 -> l1 : i_13^0'=0, [], cost: 2
     10: l6 -> l1 : i_13^0'=10, i_21^0'=9, [], cost: 22

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     <empty>

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:  [ a_20^0==a_20^post_7 && i_13^0==i_13^post_7 && i_21^0==i_21^post_7 && rt_11^0==rt_11^post_7 && st_14^0==st_14^post_7 ]

WORST_CASE(Omega(1),?)