WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l18
      0: l0 -> l1 : i2^0'=i2^post_1, i^0'=i^post_1, r^0'=r^post_1, [ 1000<=i^0 && i^post_1==0 && i2^0==i2^post_1 && r^0==r^post_1 ], cost: 1
      1: l0 -> l2 : i2^0'=i2^post_2, i^0'=i^post_2, r^0'=r^post_2, [ 1+i^0<=1000 && i2^post_2==i^0 && i^0==i^post_2 && r^0==r^post_2 ], cost: 1
     16: l1 -> l10 : i2^0'=i2^post_17, i^0'=i^post_17, r^0'=r^post_17, [ i^0==i^post_17 && i2^0==i2^post_17 && r^0==r^post_17 ], cost: 1
     23: l2 -> l16 : i2^0'=i2^post_24, i^0'=i^post_24, r^0'=r^post_24, [ i^0==i^post_24 && i2^0==i2^post_24 && r^0==r^post_24 ], cost: 1
     24: l2 -> l12 : i2^0'=i2^post_25, i^0'=i^post_25, r^0'=r^post_25, [ i^0==i^post_25 && i2^0==i2^post_25 && r^0==r^post_25 ], cost: 1
     25: l2 -> l16 : i2^0'=i2^post_26, i^0'=i^post_26, r^0'=r^post_26, [ i^0==i^post_26 && i2^0==i2^post_26 && r^0==r^post_26 ], cost: 1
      2: l3 -> l1 : i2^0'=i2^post_3, i^0'=i^post_3, r^0'=r^post_3, [ i^post_3==1+i^0 && i2^0==i2^post_3 && r^0==r^post_3 ], cost: 1
      3: l4 -> l5 : i2^0'=i2^post_4, i^0'=i^post_4, r^0'=r^post_4, [ i^0==i^post_4 && i2^0==i2^post_4 && r^0==r^post_4 ], cost: 1
      4: l5 -> l3 : i2^0'=i2^post_5, i^0'=i^post_5, r^0'=r^post_5, [ i^0==i^post_5 && i2^0==i2^post_5 && r^0==r^post_5 ], cost: 1
      5: l6 -> l0 : i2^0'=i2^post_6, i^0'=i^post_6, r^0'=r^post_6, [ i^0==i^post_6 && i2^0==i2^post_6 && r^0==r^post_6 ], cost: 1
      6: l7 -> l4 : i2^0'=i2^post_7, i^0'=i^post_7, r^0'=r^post_7, [ i^0==i^post_7 && i2^0==i2^post_7 && r^0==r^post_7 ], cost: 1
      7: l7 -> l4 : i2^0'=i2^post_8, i^0'=i^post_8, r^0'=r^post_8, [ i^0==i^post_8 && i2^0==i2^post_8 && r^0==r^post_8 ], cost: 1
      8: l7 -> l5 : i2^0'=i2^post_9, i^0'=i^post_9, r^0'=r^post_9, [ i^0==i^post_9 && i2^0==i2^post_9 && r^0==r^post_9 ], cost: 1
      9: l8 -> l7 : i2^0'=i2^post_10, i^0'=i^post_10, r^0'=r^post_10, [ r^post_10==r^post_10 && i^0==i^post_10 && i2^0==i2^post_10 ], cost: 1
     10: l9 -> l8 : i2^0'=i2^post_11, i^0'=i^post_11, r^0'=r^post_11, [ i^0==i^post_11 && i2^0==i2^post_11 && r^0==r^post_11 ], cost: 1
     11: l9 -> l3 : i2^0'=i2^post_12, i^0'=i^post_12, r^0'=r^post_12, [ i^0==i^post_12 && i2^0==i2^post_12 && r^0==r^post_12 ], cost: 1
     12: l9 -> l8 : i2^0'=i2^post_13, i^0'=i^post_13, r^0'=r^post_13, [ i^0==i^post_13 && i2^0==i2^post_13 && r^0==r^post_13 ], cost: 1
     13: l10 -> l11 : i2^0'=i2^post_14, i^0'=i^post_14, r^0'=r^post_14, [ 1000<=i^0 && i^0==i^post_14 && i2^0==i2^post_14 && r^0==r^post_14 ], cost: 1
     14: l10 -> l9 : i2^0'=i2^post_15, i^0'=i^post_15, r^0'=r^post_15, [ 1+i^0<=1000 && i^0==i^post_15 && i2^0==i2^post_15 && r^0==r^post_15 ], cost: 1
     15: l12 -> l6 : i2^0'=i2^post_16, i^0'=i^post_16, r^0'=r^post_16, [ i^post_16==1+i^0 && i2^0==i2^post_16 && r^0==r^post_16 ], cost: 1
     17: l13 -> l14 : i2^0'=i2^post_18, i^0'=i^post_18, r^0'=r^post_18, [ i^0==i^post_18 && i2^0==i2^post_18 && r^0==r^post_18 ], cost: 1
     18: l14 -> l12 : i2^0'=i2^post_19, i^0'=i^post_19, r^0'=r^post_19, [ i^0==i^post_19 && i2^0==i2^post_19 && r^0==r^post_19 ], cost: 1
     19: l15 -> l13 : i2^0'=i2^post_20, i^0'=i^post_20, r^0'=r^post_20, [ i^0==i^post_20 && i2^0==i2^post_20 && r^0==r^post_20 ], cost: 1
     20: l15 -> l13 : i2^0'=i2^post_21, i^0'=i^post_21, r^0'=r^post_21, [ i^0==i^post_21 && i2^0==i2^post_21 && r^0==r^post_21 ], cost: 1
     21: l15 -> l14 : i2^0'=i2^post_22, i^0'=i^post_22, r^0'=r^post_22, [ i^0==i^post_22 && i2^0==i2^post_22 && r^0==r^post_22 ], cost: 1
     22: l16 -> l15 : i2^0'=i2^post_23, i^0'=i^post_23, r^0'=r^post_23, [ i^0==i^post_23 && i2^0==i2^post_23 && r^0==r^post_23 ], cost: 1
     26: l17 -> l6 : i2^0'=i2^post_27, i^0'=i^post_27, r^0'=r^post_27, [ i^1_1==0 && i^post_27==0 && i2^0==i2^post_27 && r^0==r^post_27 ], cost: 1
     27: l18 -> l17 : i2^0'=i2^post_28, i^0'=i^post_28, r^0'=r^post_28, [ i^0==i^post_28 && i2^0==i2^post_28 && r^0==r^post_28 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     27: l18 -> l17 : i2^0'=i2^post_28, i^0'=i^post_28, r^0'=r^post_28, [ i^0==i^post_28 && i2^0==i2^post_28 && r^0==r^post_28 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l18
      0: l0 -> l1 : i2^0'=i2^post_1, i^0'=i^post_1, r^0'=r^post_1, [ 1000<=i^0 && i^post_1==0 && i2^0==i2^post_1 && r^0==r^post_1 ], cost: 1
      1: l0 -> l2 : i2^0'=i2^post_2, i^0'=i^post_2, r^0'=r^post_2, [ 1+i^0<=1000 && i2^post_2==i^0 && i^0==i^post_2 && r^0==r^post_2 ], cost: 1
     16: l1 -> l10 : i2^0'=i2^post_17, i^0'=i^post_17, r^0'=r^post_17, [ i^0==i^post_17 && i2^0==i2^post_17 && r^0==r^post_17 ], cost: 1
     23: l2 -> l16 : i2^0'=i2^post_24, i^0'=i^post_24, r^0'=r^post_24, [ i^0==i^post_24 && i2^0==i2^post_24 && r^0==r^post_24 ], cost: 1
     24: l2 -> l12 : i2^0'=i2^post_25, i^0'=i^post_25, r^0'=r^post_25, [ i^0==i^post_25 && i2^0==i2^post_25 && r^0==r^post_25 ], cost: 1
     25: l2 -> l16 : i2^0'=i2^post_26, i^0'=i^post_26, r^0'=r^post_26, [ i^0==i^post_26 && i2^0==i2^post_26 && r^0==r^post_26 ], cost: 1
      2: l3 -> l1 : i2^0'=i2^post_3, i^0'=i^post_3, r^0'=r^post_3, [ i^post_3==1+i^0 && i2^0==i2^post_3 && r^0==r^post_3 ], cost: 1
      3: l4 -> l5 : i2^0'=i2^post_4, i^0'=i^post_4, r^0'=r^post_4, [ i^0==i^post_4 && i2^0==i2^post_4 && r^0==r^post_4 ], cost: 1
      4: l5 -> l3 : i2^0'=i2^post_5, i^0'=i^post_5, r^0'=r^post_5, [ i^0==i^post_5 && i2^0==i2^post_5 && r^0==r^post_5 ], cost: 1
      5: l6 -> l0 : i2^0'=i2^post_6, i^0'=i^post_6, r^0'=r^post_6, [ i^0==i^post_6 && i2^0==i2^post_6 && r^0==r^post_6 ], cost: 1
      6: l7 -> l4 : i2^0'=i2^post_7, i^0'=i^post_7, r^0'=r^post_7, [ i^0==i^post_7 && i2^0==i2^post_7 && r^0==r^post_7 ], cost: 1
      7: l7 -> l4 : i2^0'=i2^post_8, i^0'=i^post_8, r^0'=r^post_8, [ i^0==i^post_8 && i2^0==i2^post_8 && r^0==r^post_8 ], cost: 1
      8: l7 -> l5 : i2^0'=i2^post_9, i^0'=i^post_9, r^0'=r^post_9, [ i^0==i^post_9 && i2^0==i2^post_9 && r^0==r^post_9 ], cost: 1
      9: l8 -> l7 : i2^0'=i2^post_10, i^0'=i^post_10, r^0'=r^post_10, [ r^post_10==r^post_10 && i^0==i^post_10 && i2^0==i2^post_10 ], cost: 1
     10: l9 -> l8 : i2^0'=i2^post_11, i^0'=i^post_11, r^0'=r^post_11, [ i^0==i^post_11 && i2^0==i2^post_11 && r^0==r^post_11 ], cost: 1
     11: l9 -> l3 : i2^0'=i2^post_12, i^0'=i^post_12, r^0'=r^post_12, [ i^0==i^post_12 && i2^0==i2^post_12 && r^0==r^post_12 ], cost: 1
     12: l9 -> l8 : i2^0'=i2^post_13, i^0'=i^post_13, r^0'=r^post_13, [ i^0==i^post_13 && i2^0==i2^post_13 && r^0==r^post_13 ], cost: 1
     14: l10 -> l9 : i2^0'=i2^post_15, i^0'=i^post_15, r^0'=r^post_15, [ 1+i^0<=1000 && i^0==i^post_15 && i2^0==i2^post_15 && r^0==r^post_15 ], cost: 1
     15: l12 -> l6 : i2^0'=i2^post_16, i^0'=i^post_16, r^0'=r^post_16, [ i^post_16==1+i^0 && i2^0==i2^post_16 && r^0==r^post_16 ], cost: 1
     17: l13 -> l14 : i2^0'=i2^post_18, i^0'=i^post_18, r^0'=r^post_18, [ i^0==i^post_18 && i2^0==i2^post_18 && r^0==r^post_18 ], cost: 1
     18: l14 -> l12 : i2^0'=i2^post_19, i^0'=i^post_19, r^0'=r^post_19, [ i^0==i^post_19 && i2^0==i2^post_19 && r^0==r^post_19 ], cost: 1
     19: l15 -> l13 : i2^0'=i2^post_20, i^0'=i^post_20, r^0'=r^post_20, [ i^0==i^post_20 && i2^0==i2^post_20 && r^0==r^post_20 ], cost: 1
     20: l15 -> l13 : i2^0'=i2^post_21, i^0'=i^post_21, r^0'=r^post_21, [ i^0==i^post_21 && i2^0==i2^post_21 && r^0==r^post_21 ], cost: 1
     21: l15 -> l14 : i2^0'=i2^post_22, i^0'=i^post_22, r^0'=r^post_22, [ i^0==i^post_22 && i2^0==i2^post_22 && r^0==r^post_22 ], cost: 1
     22: l16 -> l15 : i2^0'=i2^post_23, i^0'=i^post_23, r^0'=r^post_23, [ i^0==i^post_23 && i2^0==i2^post_23 && r^0==r^post_23 ], cost: 1
     26: l17 -> l6 : i2^0'=i2^post_27, i^0'=i^post_27, r^0'=r^post_27, [ i^1_1==0 && i^post_27==0 && i2^0==i2^post_27 && r^0==r^post_27 ], cost: 1
     27: l18 -> l17 : i2^0'=i2^post_28, i^0'=i^post_28, r^0'=r^post_28, [ i^0==i^post_28 && i2^0==i2^post_28 && r^0==r^post_28 ], cost: 1

Simplified all rules, resulting in:
   Start location: l18
      0: l0 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 1
      1: l0 -> l2 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 1
     16: l1 -> l10 : [], cost: 1
     24: l2 -> l12 : [], cost: 1
     25: l2 -> l16 : [], cost: 1
      2: l3 -> l1 : i^0'=1+i^0, [], cost: 1
      3: l4 -> l5 : [], cost: 1
      4: l5 -> l3 : [], cost: 1
      5: l6 -> l0 : [], cost: 1
      7: l7 -> l4 : [], cost: 1
      8: l7 -> l5 : [], cost: 1
      9: l8 -> l7 : r^0'=r^post_10, [], cost: 1
     11: l9 -> l3 : [], cost: 1
     12: l9 -> l8 : [], cost: 1
     14: l10 -> l9 : [ 1+i^0<=1000 ], cost: 1
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     17: l13 -> l14 : [], cost: 1
     18: l14 -> l12 : [], cost: 1
     20: l15 -> l13 : [], cost: 1
     21: l15 -> l14 : [], cost: 1
     22: l16 -> l15 : [], cost: 1
     26: l17 -> l6 : i^0'=0, [], cost: 1
     27: l18 -> l17 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l18
      0: l0 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 1
      1: l0 -> l2 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 1
     29: l1 -> l9 : [ 1+i^0<=1000 ], cost: 2
     24: l2 -> l12 : [], cost: 1
     32: l2 -> l15 : [], cost: 2
      2: l3 -> l1 : i^0'=1+i^0, [], cost: 1
      4: l5 -> l3 : [], cost: 1
      5: l6 -> l0 : [], cost: 1
      8: l7 -> l5 : [], cost: 1
     31: l7 -> l5 : [], cost: 2
     11: l9 -> l3 : [], cost: 1
     30: l9 -> l7 : r^0'=r^post_10, [], cost: 2
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     18: l14 -> l12 : [], cost: 1
     21: l15 -> l14 : [], cost: 1
     33: l15 -> l14 : [], cost: 2
     28: l18 -> l6 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l18
     36: l1 -> l3 : [ 1+i^0<=1000 ], cost: 3
     37: l1 -> l7 : r^0'=r^post_10, [ 1+i^0<=1000 ], cost: 4
     24: l2 -> l12 : [], cost: 1
     40: l2 -> l14 : [], cost: 3
     41: l2 -> l14 : [], cost: 4
      2: l3 -> l1 : i^0'=1+i^0, [], cost: 1
     34: l6 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 2
     35: l6 -> l2 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 2
     38: l7 -> l3 : [], cost: 2
     39: l7 -> l3 : [], cost: 3
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     18: l14 -> l12 : [], cost: 1
     28: l18 -> l6 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l18
     36: l1 -> l3 : [ 1+i^0<=1000 ], cost: 3
     45: l1 -> l3 : r^0'=r^post_10, [ 1+i^0<=1000 ], cost: 6
     46: l1 -> l3 : r^0'=r^post_10, [ 1+i^0<=1000 ], cost: 7
      2: l3 -> l1 : i^0'=1+i^0, [], cost: 1
     34: l6 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 2
     42: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 3
     43: l6 -> l14 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 5
     44: l6 -> l14 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 6
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     18: l14 -> l12 : [], cost: 1
     28: l18 -> l6 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l18
     49: l1 -> l1 : i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 4
     50: l1 -> l1 : i^0'=1+i^0, r^0'=r^post_10, [ 1+i^0<=1000 ], cost: 7
     51: l1 -> l1 : i^0'=1+i^0, r^0'=r^post_10, [ 1+i^0<=1000 ], cost: 8
     34: l6 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 2
     42: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 3
     47: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 6
     48: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 7
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     28: l18 -> l6 : i^0'=0, [], cost: 2

Accelerating simple loops of location 1.
[accelerate] Removed some duplicate simple loops
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     49: l1 -> l1 : i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 4
     51: l1 -> l1 : i^0'=1+i^0, r^0'=r^post_10, [ 1+i^0<=1000 ], cost: 8

   Accelerated rule 49 with backward acceleration, yielding the new rule 52.
   Accelerated rule 51 with backward acceleration, yielding the new rule 53.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 49 51.

Accelerated all simple loops using metering functions (where possible):
   Start location: l18
     52: l1 -> l1 : i^0'=1000, [ 1000-i^0>=0 ], cost: 4000-4*i^0
     53: l1 -> l1 : i^0'=1000, r^0'=r^post_10, [ 1000-i^0>=1 ], cost: 8000-8*i^0
     34: l6 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 2
     42: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 3
     47: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 6
     48: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 7
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     28: l18 -> l6 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l18
     34: l6 -> l1 : i^0'=0, [ 1000<=i^0 ], cost: 2
     42: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 3
     47: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 6
     48: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 7
     54: l6 -> l1 : i^0'=1000, [ 1000<=i^0 ], cost: 4002
     55: l6 -> l1 : i^0'=1000, r^0'=r^post_10, [ 1000<=i^0 ], cost: 8002
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     28: l18 -> l6 : i^0'=0, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l18
     42: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 3
     47: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 6
     48: l6 -> l12 : i2^0'=i^0, [ 1+i^0<=1000 ], cost: 7
     15: l12 -> l6 : i^0'=1+i^0, [], cost: 1
     28: l18 -> l6 : i^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l18
     56: l6 -> l6 : i2^0'=i^0, i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 4
     57: l6 -> l6 : i2^0'=i^0, i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 7
     58: l6 -> l6 : i2^0'=i^0, i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 8
     28: l18 -> l6 : i^0'=0, [], cost: 2

Merged rules:
   Start location: l18
     60: l6 -> l6 : i2^0'=i^0, i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 8
     28: l18 -> l6 : i^0'=0, [], cost: 2

Accelerating simple loops of location 6.
   Accelerating the following rules:
     60: l6 -> l6 : i2^0'=i^0, i^0'=1+i^0, [ 1+i^0<=1000 ], cost: 8

   Accelerated rule 60 with backward acceleration, yielding the new rule 61.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 60.

Accelerated all simple loops using metering functions (where possible):
   Start location: l18
     61: l6 -> l6 : i2^0'=999, i^0'=1000, [ 1000-i^0>=1 ], cost: 8000-8*i^0
     28: l18 -> l6 : i^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l18
     28: l18 -> l6 : i^0'=0, [], cost: 2
     62: l18 -> l6 : i2^0'=999, i^0'=1000, [], cost: 8002

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l18
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l18
     <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:  [ i^0==i^post_28 && i2^0==i2^post_28 && r^0==r^post_28 ]

WORST_CASE(Omega(1),?)