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 && arg1+arg2==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 && arg1+arg2==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 && arg1+arg2==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'=arg1+arg2, 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'=arg1+arg2, 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'=arg1+arg2, 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'=arg1+arg2, arg2'=1+arg2, arg3'=1+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1

   Accelerated rule 1 with metering function 1001-arg2, yielding the new rule 7.
   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'=arg1+arg2, arg2'=2+arg2, arg3'=2+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1

   Accelerated rule 3 with metering function meter (where 2*meter==1000-arg2), yielding the new rule 8.
   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'=arg1+arg2, arg2'=3+arg2, arg3'=3+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], cost: 1

   Accelerated rule 5 with metering function meter_1 (where 3*meter_1==1000-arg2), yielding the new rule 9.
   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*(-1001+arg2)^2-arg2*(-1001+arg2)+arg1+1/2*arg2, arg2'=1001, arg3'=1001, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 ], 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'=-meter+arg1+meter^2+meter*arg2, arg2'=2*meter+arg2, arg3'=2*meter+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 && 2*meter==1000-arg2 && meter>=1 ], cost: meter
      9: f311_0_add_GT -> f311_0_add_GT : arg1'=-3/2*meter_1+meter_1*arg2+arg1+3/2*meter_1^2, arg2'=3*meter_1+arg2, arg3'=3*meter_1+arg2, [ arg2>-1 && arg1>-1 && arg2<1001 && arg2==arg3 && 3*meter_1==1000-arg2 && meter_1>=1 ], cost: meter_1
      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'=249500, arg2'=1000, arg3'=1000, [ arg2>1000 && arg2==arg3 ], cost: 501
      4: f208_0_add_GT -> f311_0_add_GT : arg1'=0, arg2'=0, arg3'=0, [ arg2>1000 && arg2==arg3 ], cost: 1
      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
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     <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:  []

WORST_CASE(Omega(1),?)