WORST_CASE(Omega(0),?)

Initial ITS
Start location: __init
   0: f1_0_main_Load -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   1: f151_0_main_LT -> f192_0_main_LT : arg1'=arg1P1, arg2'=arg2P1, (1-arg2P1 == 0 /\ 1+arg1 > 0 /\ 1+arg1-arg1P1 == 0), cost: 1
   2: f192_0_main_LT -> f192_0_main_LT : arg1'=arg1P2, arg2'=arg2P2, (arg1-arg1P2 == 0 /\ 1-arg2P2+arg2 == 0 /\ -arg1+arg2 <= 0), cost: 1
   3: f192_0_main_LT -> f151_0_main_LT : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -2+arg1-arg1P3 == 0 /\ -arg1+arg2 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied preprocessing
Original rule:
f151_0_main_LT -> f192_0_main_LT : arg1'=arg1P1, arg2'=arg2P1, (1-arg2P1 == 0 /\ 1+arg1 > 0 /\ 1+arg1-arg1P1 == 0), cost: 1
New rule:
f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=1, 1+arg1 > 0, cost: 1

Applied preprocessing
Original rule:
f192_0_main_LT -> f192_0_main_LT : arg1'=arg1P2, arg2'=arg2P2, (arg1-arg1P2 == 0 /\ 1-arg2P2+arg2 == 0 /\ -arg1+arg2 <= 0), cost: 1
New rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg2, -arg1+arg2 <= 0, cost: 1

Applied preprocessing
Original rule:
f192_0_main_LT -> f151_0_main_LT : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -2+arg1-arg1P3 == 0 /\ -arg1+arg2 > 0), cost: 1
New rule:
f192_0_main_LT -> f151_0_main_LT : arg1'=-2+arg1, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1

Simplified rules
Start location: __init
   0: f1_0_main_Load -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=1, 1+arg1 > 0, cost: 1
   6: f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg2, -arg1+arg2 <= 0, cost: 1
   7: f192_0_main_LT -> f151_0_main_LT : arg1'=-2+arg1, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied acceleration
Original rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg2, -arg1+arg2 <= 0, cost: 1
New rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=n0+arg2, (n0 >= 0 /\ 1+arg1-n0-arg2 >= 0), cost: n0

Applied instantiation
Original rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=n0+arg2, (n0 >= 0 /\ 1+arg1-n0-arg2 >= 0), cost: n0
New rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg1, (0 >= 0 /\ 1+arg1-arg2 >= 0), cost: 1+arg1-arg2

Applied simplification
Original rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg1, (0 >= 0 /\ 1+arg1-arg2 >= 0), cost: 1+arg1-arg2
New rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg1, 1+arg1-arg2 >= 0, cost: 1+arg1-arg2

Applied deletion
Removed the following rules: 6

Accelerated simple loops
Start location: __init
   0: f1_0_main_Load -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=1, 1+arg1 > 0, cost: 1
   7: f192_0_main_LT -> f151_0_main_LT : arg1'=-2+arg1, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1
   9: f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg1, 1+arg1-arg2 >= 0, cost: 1+arg1-arg2
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied chaining
First rule:
f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=1, 1+arg1 > 0, cost: 1
Second rule:
f192_0_main_LT -> f192_0_main_LT : arg2'=1+arg1, 1+arg1-arg2 >= 0, cost: 1+arg1-arg2
New rule:
f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=2+arg1, 1+arg1 > 0, cost: 2+arg1

Applied deletion
Removed the following rules: 9

Chained accelerated rules with incoming rules
Start location: __init
   0: f1_0_main_Load -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=1, 1+arg1 > 0, cost: 1
  10: f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=2+arg1, 1+arg1 > 0, cost: 2+arg1
   7: f192_0_main_LT -> f151_0_main_LT : arg1'=-2+arg1, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Eliminating location f1_0_main_Load by chaining:

Applied chaining
First rule:
__init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1
Second rule:
f1_0_main_Load -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
New rule:
__init -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2

Applied deletion
Removed the following rules: 0 4

Eliminated locations on linear paths
Start location: __init
   5: f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=1, 1+arg1 > 0, cost: 1
  10: f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=2+arg1, 1+arg1 > 0, cost: 2+arg1
   7: f192_0_main_LT -> f151_0_main_LT : arg1'=-2+arg1, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1
  11: __init -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Eliminating location f192_0_main_LT by chaining:

Applied chaining
First rule:
f151_0_main_LT -> f192_0_main_LT : arg1'=1+arg1, arg2'=2+arg1, 1+arg1 > 0, cost: 2+arg1
Second rule:
f192_0_main_LT -> f151_0_main_LT : arg1'=-2+arg1, arg2'=arg2P3, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 1
New rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1+arg1, arg2'=arg2P3, (1 > 0 /\ 1+arg1 > 0), cost: 3+arg1

Applied simplification
Original rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1+arg1, arg2'=arg2P3, (1 > 0 /\ 1+arg1 > 0), cost: 3+arg1
New rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1+arg1, arg2'=arg2P3, 1+arg1 > 0, cost: 3+arg1

Applied deletion
Removed the following rules: 5 7 10

Eliminated locations on tree-shaped paths
Start location: __init
  12: f151_0_main_LT -> f151_0_main_LT : arg1'=-1+arg1, arg2'=arg2P3, 1+arg1 > 0, cost: 3+arg1
  11: __init -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied acceleration
Original rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1+arg1, arg2'=arg2P3, 1+arg1 > 0, cost: 3+arg1
New rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=arg1-n3, arg2'=arg2P3, (2+arg1-n3 > 0 /\ -1+n3 >= 0), cost: -1/2*n3^2+arg1*n3+7/2*n3

Applied instantiation
Original rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=arg1-n3, arg2'=arg2P3, (2+arg1-n3 > 0 /\ -1+n3 >= 0), cost: -1/2*n3^2+arg1*n3+7/2*n3
New rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, (arg1 >= 0 /\ 1 > 0), cost: 7/2+7/2*arg1+arg1*(1+arg1)-1/2*(1+arg1)^2

Applied simplification
Original rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, (arg1 >= 0 /\ 1 > 0), cost: 7/2+7/2*arg1+arg1*(1+arg1)-1/2*(1+arg1)^2
New rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, arg1 >= 0, cost: 7/2+7/2*arg1+arg1*(1+arg1)-1/2*(1+arg1)^2

Applied deletion
Removed the following rules: 12

Accelerated simple loops
Start location: __init
  14: f151_0_main_LT -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, arg1 >= 0, cost: 7/2+7/2*arg1+arg1*(1+arg1)-1/2*(1+arg1)^2
  11: __init -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied chaining
First rule:
__init -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f151_0_main_LT -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, arg1 >= 0, cost: 7/2+7/2*arg1+arg1*(1+arg1)-1/2*(1+arg1)^2
New rule:
__init -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, arg1P0 >= 0, cost: 11/2+(1+arg1P0)*arg1P0-1/2*(1+arg1P0)^2+7/2*arg1P0

Applied deletion
Removed the following rules: 14

Chained accelerated rules with incoming rules
Start location: __init
  11: __init -> f151_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
  15: __init -> f151_0_main_LT : arg1'=-1, arg2'=arg2P3, arg1P0 >= 0, cost: 11/2+(1+arg1P0)*arg1P0-1/2*(1+arg1P0)^2+7/2*arg1P0


Removed unreachable locations and irrelevant leafs
Start location: __init
  <empty>


Computing asymptotic complexity

Proved the following lower bound
Complexity:  Unknown
Cpx degree: ?

Solved cost: 0
Rule cost:   0