WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ 0==arg1P_1 && 0==arg2P_1 && 0==arg3P_1 ], cost: 1
      1: f108_0_add_GT -> f108_0_add_GT : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 && arg2+arg1==arg1P_2 && 1+arg2==arg2P_2 && 1+arg2==arg3P_2 ], cost: 1
      2: f108_0_add_GT -> f208_0_add_GT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg2>1000 && arg2==arg3 && 0==arg1P_3 && 0==arg2P_3 && 0==arg3P_3 ], cost: 1
      3: f208_0_add_GT -> f208_0_add_GT : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 && arg2+arg1==arg1P_4 && 2+arg2==arg2P_4 && 2+arg2==arg3P_4 ], cost: 1
      4: f208_0_add_GT -> f311_0_add_GT : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2>1000 && arg2==arg3 && 0==arg1P_5 && 0==arg2P_5 && 0==arg3P_5 ], cost: 1
      5: f311_0_add_GT -> f311_0_add_GT : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 && arg2+arg1==arg1P_6 && 3+arg2==arg2P_6 && 3+arg2==arg3P_6 ], cost: 1
      6: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [], cost: 1
      1: f108_0_add_GT -> f108_0_add_GT : arg1'=arg2+arg1, arg2'=1+arg2, arg3'=1+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1
      2: f108_0_add_GT -> f208_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
      3: f208_0_add_GT -> f208_0_add_GT : arg1'=arg2+arg1, arg2'=2+arg2, arg3'=2+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1
      4: f208_0_add_GT -> f311_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
      5: f311_0_add_GT -> f311_0_add_GT : arg1'=arg2+arg1, arg2'=3+arg2, arg3'=3+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1
      6: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      1: f108_0_add_GT -> f108_0_add_GT : arg1'=arg2+arg1, arg2'=1+arg2, arg3'=1+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1

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

Accelerating simple loops of location 2.
   Accelerating the following rules:
      3: f208_0_add_GT -> f208_0_add_GT : arg1'=arg2+arg1, arg2'=2+arg2, arg3'=2+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1

   Accelerated rule 3 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 3.

Accelerating simple loops of location 3.
   Accelerating the following rules:
      5: f311_0_add_GT -> f311_0_add_GT : arg1'=arg2+arg1, arg2'=3+arg2, arg3'=3+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1

   Accelerated rule 5 with backward acceleration, yielding the new rule 9.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 5.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [], cost: 1
      2: f108_0_add_GT -> f208_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
      7: f108_0_add_GT -> f108_0_add_GT : arg1'=-1001/2+1/2*arg2-arg2*(-1001+arg2)+1/2*(-1001+arg2)^2+arg1, arg2'=1001, arg3'=1001, [ arg2>-1 && arg1>-1 && arg2==arg3 && 1001-arg2>=1 ], cost: 1001-arg2
      4: f208_0_add_GT -> f311_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
      8: f208_0_add_GT -> f208_0_add_GT : arg1'=-k_1+arg2*k_1+k_1^2+arg1, arg2'=arg2+2*k_1, arg3'=arg2+2*k_1, [ arg2>-1 && arg1>-1 && arg2==arg3 && k_1>=1 && -2+arg2+2*k_1<1001 ], cost: k_1
      9: f311_0_add_GT -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2+arg2*k_2+arg1, arg2'=arg2+3*k_2, arg3'=arg2+3*k_2, [ arg2>-1 && arg1>-1 && arg2==arg3 && k_2>=1 && -3+arg2+3*k_2<1001 ], cost: k_2
      6: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [], cost: 1
     10: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=500500, arg2'=1001, arg3'=1001, [], cost: 1002
      2: f108_0_add_GT -> f208_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
     11: f108_0_add_GT -> f208_0_add_GT : arg1'=-k_1+k_1^2, arg2'=2*k_1, arg3'=2*k_1, [ arg2>1000 && arg2==arg3 && k_1>=1 && -2+2*k_1<1001 ], cost: 1+k_1
      4: f208_0_add_GT -> f311_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
     12: f208_0_add_GT -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2, arg2'=3*k_2, arg3'=3*k_2, [ arg2>1000 && arg2==arg3 && k_2>=1 && -3+3*k_2<1001 ], cost: 1+k_2
      6: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
      0: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [], cost: 1
     10: f1_0_main_ConstantStackPush -> f108_0_add_GT : arg1'=500500, arg2'=1001, arg3'=1001, [], cost: 1002
      2: f108_0_add_GT -> f208_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
     11: f108_0_add_GT -> f208_0_add_GT : arg1'=-k_1+k_1^2, arg2'=2*k_1, arg3'=2*k_1, [ arg2>1000 && arg2==arg3 && k_1>=1 && -2+2*k_1<1001 ], cost: 1+k_1
     12: f208_0_add_GT -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2, arg2'=3*k_2, arg3'=3*k_2, [ arg2>1000 && arg2==arg3 && k_2>=1 && -3+3*k_2<1001 ], cost: 1+k_2
      6: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     15: f108_0_add_GT -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2, arg2'=3*k_2, arg3'=3*k_2, [ arg2>1000 && arg2==arg3 && k_1>=1 && -2+2*k_1<1001 && 2*k_1>1000 && k_2>=1 && -3+3*k_2<1001 ], cost: 2+k_2+k_1
     13: __init -> f108_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [], cost: 2
     14: __init -> f108_0_add_GT : arg1'=500500, arg2'=1001, arg3'=1001, [], cost: 1003

Eliminated locations (on tree-shaped paths):
   Start location: __init
     16: __init -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2, arg2'=3*k_2, arg3'=3*k_2, [ k_1>=1 && -2+2*k_1<1001 && 2*k_1>1000 && k_2>=1 && -3+3*k_2<1001 ], cost: 1005+k_2+k_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     16: __init -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2, arg2'=3*k_2, arg3'=3*k_2, [ k_1>=1 && -2+2*k_1<1001 && 2*k_1>1000 && k_2>=1 && -3+3*k_2<1001 ], cost: 1005+k_2+k_1

Computing asymptotic complexity for rule 16
   Simplified the guard:
     16: __init -> f311_0_add_GT : arg1'=-3/2*k_2+3/2*k_2^2, arg2'=3*k_2, arg3'=3*k_2, [ -2+2*k_1<1001 && 2*k_1>1000 && k_2>=1 && -3+3*k_2<1001 ], cost: 1005+k_2+k_1
   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:  []

WORST_CASE(Omega(1),?)