WORST_CASE(Omega(0),?)

Initial ITS
Start location: __init
   0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   1: f161_0_main_LT -> f212_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (1-arg2P1 == 0 /\ 1+arg1 > 0 /\ arg1-arg1P1 == 0), cost: 1
   2: f212_0_main_LE -> f161_0_main_LT : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1-arg1P2 == 0 /\ -arg1+arg2 >= 0), cost: 1
   3: f212_0_main_LE -> f212_0_main_LE : arg1'=arg1P3, arg2'=arg2P3, (2*arg2-arg2P3 == 0 /\ arg1-arg1P3 == 0 /\ -arg1+arg2 < 0 /\ arg2 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied preprocessing
Original rule:
f161_0_main_LT -> f212_0_main_LE : arg1'=arg1P1, arg2'=arg2P1, (1-arg2P1 == 0 /\ 1+arg1 > 0 /\ arg1-arg1P1 == 0), cost: 1
New rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1

Applied preprocessing
Original rule:
f212_0_main_LE -> f161_0_main_LT : arg1'=arg1P2, arg2'=arg2P2, (-1+arg1-arg1P2 == 0 /\ -arg1+arg2 >= 0), cost: 1
New rule:
f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -arg1+arg2 >= 0, cost: 1

Applied preprocessing
Original rule:
f212_0_main_LE -> f212_0_main_LE : arg1'=arg1P3, arg2'=arg2P3, (2*arg2-arg2P3 == 0 /\ arg1-arg1P3 == 0 /\ -arg1+arg2 < 0 /\ arg2 > 0), cost: 1
New rule:
f212_0_main_LE -> f212_0_main_LE : arg2'=2*arg2, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1

Simplified rules
Start location: __init
   0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1
   6: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -arg1+arg2 >= 0, cost: 1
   7: f212_0_main_LE -> f212_0_main_LE : arg2'=2*arg2, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied acceleration
Original rule:
f212_0_main_LE -> f212_0_main_LE : arg2'=2*arg2, (arg2 > 0 /\ arg1-arg2 > 0), cost: 1
New rule:
f212_0_main_LE -> f212_0_main_LE : arg2'=2^n0*arg2, (n0 >= 0 /\ arg1-2^(-1+n0)*arg2 > 0 /\ arg2 > 0), cost: n0

Applied deletion
Removed the following rules: 7

Accelerated simple loops
Start location: __init
   0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1
   6: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -arg1+arg2 >= 0, cost: 1
   8: f212_0_main_LE -> f212_0_main_LE : arg2'=2^n0*arg2, (n0 >= 0 /\ arg1-2^(-1+n0)*arg2 > 0 /\ arg2 > 0), cost: n0
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied chaining
First rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1
Second rule:
f212_0_main_LE -> f212_0_main_LE : arg2'=2^n0*arg2, (n0 >= 0 /\ arg1-2^(-1+n0)*arg2 > 0 /\ arg2 > 0), cost: n0
New rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=2^n0, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0), cost: 1+n0

Applied deletion
Removed the following rules: 8

Chained accelerated rules with incoming rules
Start location: __init
   0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1
   9: f161_0_main_LT -> f212_0_main_LE : arg2'=2^n0, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0), cost: 1+n0
   6: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -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 -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
New rule:
__init -> f161_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: f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1
   9: f161_0_main_LT -> f212_0_main_LE : arg2'=2^n0, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0), cost: 1+n0
   6: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -arg1+arg2 >= 0, cost: 1
  10: __init -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Eliminating location f212_0_main_LE by chaining:

Applied chaining
First rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=1, 1+arg1 > 0, cost: 1
Second rule:
f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -arg1+arg2 >= 0, cost: 1
New rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (1-arg1 >= 0 /\ 1+arg1 > 0), cost: 2

Applied simplification
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (1-arg1 >= 0 /\ 1+arg1 > 0), cost: 2
New rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (-1+arg1 <= 0 /\ 1+arg1 > 0), cost: 2

Applied chaining
First rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=2^n0, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0), cost: 1+n0
Second rule:
f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, -arg1+arg2 >= 0, cost: 1
New rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0 /\ -arg1+2^n0 >= 0), cost: 2+n0

Applied deletion
Removed the following rules: 5 6 9

Eliminated locations on tree-shaped paths
Start location: __init
  11: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (-1+arg1 <= 0 /\ 1+arg1 > 0), cost: 2
  12: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0 /\ -arg1+2^n0 >= 0), cost: 2+n0
  10: __init -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied acceleration
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (-1+arg1 <= 0 /\ 1+arg1 > 0), cost: 2
New rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=arg1-n4, arg2'=arg2P2, (2+arg1-n4 > 0 /\ 1-arg1 >= 0 /\ -1+n4 >= 0), cost: 2*n4

Applied instantiation
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=arg1-n4, arg2'=arg2P2, (2+arg1-n4 > 0 /\ 1-arg1 >= 0 /\ -1+n4 >= 0), cost: 2*n4
New rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1 >= 0 /\ 1 > 0 /\ 1-arg1 >= 0), cost: 2+2*arg1

Applied simplification
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1 >= 0 /\ 1 > 0 /\ 1-arg1 >= 0), cost: 2+2*arg1
New rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1 >= 0 /\ -1+arg1 <= 0), cost: 2+2*arg1

Applied deletion
Removed the following rules: 11

Accelerated simple loops
Start location: __init
  12: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0 /\ -arg1+2^n0 >= 0), cost: 2+n0
  14: f161_0_main_LT -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1 >= 0 /\ -1+arg1 <= 0), cost: 2+2*arg1
  10: __init -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied chaining
First rule:
__init -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P2, (n0 >= 0 /\ arg1-2^(-1+n0) > 0 /\ 1+arg1 > 0 /\ -arg1+2^n0 >= 0), cost: 2+n0
New rule:
__init -> f161_0_main_LT : arg1'=-1+arg1P0, arg2'=arg2P2, (n0 >= 0 /\ -2^(-1+n0)+arg1P0 > 0 /\ 1+arg1P0 > 0 /\ 2^n0-arg1P0 >= 0), cost: 4+n0

Applied chaining
First rule:
__init -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f161_0_main_LT -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1 >= 0 /\ -1+arg1 <= 0), cost: 2+2*arg1
New rule:
__init -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1P0 >= 0 /\ -1+arg1P0 <= 0), cost: 4+2*arg1P0

Applied deletion
Removed the following rules: 12 14

Chained accelerated rules with incoming rules
Start location: __init
  10: __init -> f161_0_main_LT : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
  15: __init -> f161_0_main_LT : arg1'=-1+arg1P0, arg2'=arg2P2, (n0 >= 0 /\ -2^(-1+n0)+arg1P0 > 0 /\ 1+arg1P0 > 0 /\ 2^n0-arg1P0 >= 0), cost: 4+n0
  16: __init -> f161_0_main_LT : arg1'=-1, arg2'=arg2P2, (arg1P0 >= 0 /\ -1+arg1P0 <= 0), cost: 4+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