WORST_CASE(Omega(0),?)

Initial ITS
Start location: __init
   0: f1_0_main_Load -> f223_0_main_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1-arg2 == 0 /\ -arg1P0 == 0), cost: 1
   1: f1_0_main_Load -> f259_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2P1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P1 > 0), cost: 1
   2: f223_0_main_LE -> f223_0_main_LE : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1-arg1P2 == 0 /\ arg2 > 0 /\ arg1-arg2P2+arg2 == 0), cost: 1
   3: f259_0_main_LE -> f259_0_main_LE : arg1'=arg1P3, arg2'=arg2P3, (-1+arg1-arg1P3 == 0 /\ arg2 > 0 /\ arg1+arg2-arg2P3 == 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied preprocessing
Original rule:
f1_0_main_Load -> f223_0_main_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1-arg2 == 0 /\ -arg1P0 == 0), cost: 1
New rule:
f1_0_main_Load -> f223_0_main_LE : arg1'=0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 == 0), cost: 1

Applied preprocessing
Original rule:
f223_0_main_LE -> f223_0_main_LE : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1-arg1P2 == 0 /\ arg2 > 0 /\ arg1-arg2P2+arg2 == 0), cost: 1
New rule:
f223_0_main_LE -> f223_0_main_LE : arg1'=-1+arg1, arg2'=arg1+arg2, arg2 > 0, cost: 1

Applied preprocessing
Original rule:
f259_0_main_LE -> f259_0_main_LE : arg1'=arg1P3, arg2'=arg2P3, (-1+arg1-arg1P3 == 0 /\ arg2 > 0 /\ arg1+arg2-arg2P3 == 0), cost: 1
New rule:
f259_0_main_LE -> f259_0_main_LE : arg1'=-1+arg1, arg2'=arg1+arg2, arg2 > 0, cost: 1

Simplified rules
Start location: __init
   1: f1_0_main_Load -> f259_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2P1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P1 > 0), cost: 1
   5: f1_0_main_Load -> f223_0_main_LE : arg1'=0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 == 0), cost: 1
   6: f223_0_main_LE -> f223_0_main_LE : arg1'=-1+arg1, arg2'=arg1+arg2, arg2 > 0, cost: 1
   7: f259_0_main_LE -> f259_0_main_LE : arg1'=-1+arg1, arg2'=arg1+arg2, arg2 > 0, cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied acceleration
Original rule:
f223_0_main_LE -> f223_0_main_LE : arg1'=-1+arg1, arg2'=arg1+arg2, arg2 > 0, cost: 1
New rule:
f223_0_main_LE -> f223_0_main_LE : arg1'=arg1-n0, arg2'=-1/2*n0^2+1/2*n0+arg2+arg1*n0, (-1/2+arg1*(-1+n0)+1/2*n0+arg2-1/2*(-1+n0)^2 > 0 /\ n0 >= 0 /\ arg2 > 0), cost: n0

Applied deletion
Removed the following rules: 6

Applied acceleration
Original rule:
f259_0_main_LE -> f259_0_main_LE : arg1'=-1+arg1, arg2'=arg1+arg2, arg2 > 0, cost: 1
New rule:
f259_0_main_LE -> f259_0_main_LE : arg1'=arg1-n3, arg2'=1/2*n3+arg1*n3-1/2*n3^2+arg2, (n3 >= 0 /\ arg2 > 0 /\ -1/2-1/2*(-1+n3)^2+1/2*n3+arg1*(-1+n3)+arg2 > 0), cost: n3

Applied deletion
Removed the following rules: 7

Accelerated simple loops
Start location: __init
   1: f1_0_main_Load -> f259_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2P1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P1 > 0), cost: 1
   5: f1_0_main_Load -> f223_0_main_LE : arg1'=0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 == 0), cost: 1
   8: f223_0_main_LE -> f223_0_main_LE : arg1'=arg1-n0, arg2'=-1/2*n0^2+1/2*n0+arg2+arg1*n0, (-1/2+arg1*(-1+n0)+1/2*n0+arg2-1/2*(-1+n0)^2 > 0 /\ n0 >= 0 /\ arg2 > 0), cost: n0
   9: f259_0_main_LE -> f259_0_main_LE : arg1'=arg1-n3, arg2'=1/2*n3+arg1*n3-1/2*n3^2+arg2, (n3 >= 0 /\ arg2 > 0 /\ -1/2-1/2*(-1+n3)^2+1/2*n3+arg1*(-1+n3)+arg2 > 0), cost: n3
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied chaining
First rule:
f1_0_main_Load -> f223_0_main_LE : arg1'=0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 == 0), cost: 1
Second rule:
f223_0_main_LE -> f223_0_main_LE : arg1'=arg1-n0, arg2'=-1/2*n0^2+1/2*n0+arg2+arg1*n0, (-1/2+arg1*(-1+n0)+1/2*n0+arg2-1/2*(-1+n0)^2 > 0 /\ n0 >= 0 /\ arg2 > 0), cost: n0
New rule:
f1_0_main_Load -> f223_0_main_LE : arg1'=-n0, arg2'=-1/2*n0^2+1/2*n0+arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1/2+1/2*n0+arg2P0-1/2*(-1+n0)^2 > 0 /\ -1+arg2 == 0 /\ n0 >= 0 /\ arg2P0 > 0), cost: 1+n0

Applied deletion
Removed the following rules: 8

Applied chaining
First rule:
f1_0_main_Load -> f259_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2P1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P1 > 0), cost: 1
Second rule:
f259_0_main_LE -> f259_0_main_LE : arg1'=arg1-n3, arg2'=1/2*n3+arg1*n3-1/2*n3^2+arg2, (n3 >= 0 /\ arg2 > 0 /\ -1/2-1/2*(-1+n3)^2+1/2*n3+arg1*(-1+n3)+arg2 > 0), cost: n3
New rule:
f1_0_main_Load -> f259_0_main_LE : arg1'=-n3+arg1P1, arg2'=1/2*n3+n3*arg1P1+arg2P1-1/2*n3^2, (arg1 > 0 /\ n3 >= 0 /\ arg2P1 > 0 /\ -1+arg2 > 0 /\ -1/2-1/2*(-1+n3)^2+1/2*n3+arg2P1+arg1P1*(-1+n3) > 0 /\ 1+arg1P1 > 0), cost: 1+n3

Applied deletion
Removed the following rules: 9

Chained accelerated rules with incoming rules
Start location: __init
   1: f1_0_main_Load -> f259_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ 1+arg2P1 > 0 /\ -1+arg2 > 0 /\ 1+arg1P1 > 0), cost: 1
   5: f1_0_main_Load -> f223_0_main_LE : arg1'=0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1+arg2 == 0), cost: 1
  10: f1_0_main_Load -> f223_0_main_LE : arg1'=-n0, arg2'=-1/2*n0^2+1/2*n0+arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ -1/2+1/2*n0+arg2P0-1/2*(-1+n0)^2 > 0 /\ -1+arg2 == 0 /\ n0 >= 0 /\ arg2P0 > 0), cost: 1+n0
  11: f1_0_main_Load -> f259_0_main_LE : arg1'=-n3+arg1P1, arg2'=1/2*n3+n3*arg1P1+arg2P1-1/2*n3^2, (arg1 > 0 /\ n3 >= 0 /\ arg2P1 > 0 /\ -1+arg2 > 0 /\ -1/2-1/2*(-1+n3)^2+1/2*n3+arg2P1+arg1P1*(-1+n3) > 0 /\ 1+arg1P1 > 0), cost: 1+n3
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


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