WORST_CASE(Omega(0),?)

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


Applied preprocessing
Original rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=arg2P1, arg1'=arg1P1, (1+arg1 > 0 /\ arg1-arg1P1 == 0 /\ 1-arg2P1 == 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 : arg2'=arg2P2, arg1'=arg1P2, (-1+arg1-arg1P2 == 0 /\ arg2-arg1 >= 0), cost: 1
New rule:
f212_0_main_LE -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, arg2-arg1 >= 0, cost: 1

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

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


Accelerated simple loops
Start location: __init
   0: f1_0_main_Load -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 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 : arg2'=arg2P2, arg1'=-1+arg1, arg2-arg1 >= 0, cost: 1
   7: f212_0_main_LE -> f212_0_main_LE : arg2'=2*arg2, (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, 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*arg2, (arg2 > 0 /\ -arg2+arg1 > 0), cost: 1
New rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=2, -1+arg1 > 0, cost: 2

Applied deletion
Removed the following rules: 7

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


Eliminating location f1_0_main_Load by chaining:

Applied chaining
First rule:
__init -> f1_0_main_Load : arg2'=arg2P4, arg1'=arg1P4, TRUE, cost: 1
Second rule:
f1_0_main_Load -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2 > 0 /\ arg1 > 0 /\ 1+arg1P0 > 0), cost: 1
New rule:
__init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (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
   8: f161_0_main_LT -> f212_0_main_LE : arg2'=2, -1+arg1 > 0, cost: 2
   6: f212_0_main_LE -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, arg2-arg1 >= 0, cost: 1
   9: __init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (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 : arg2'=arg2P2, arg1'=-1+arg1, arg2-arg1 >= 0, cost: 1
New rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (1+arg1 > 0 /\ 1-arg1 >= 0), cost: 2

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

Applied chaining
First rule:
f161_0_main_LT -> f212_0_main_LE : arg2'=2, -1+arg1 > 0, cost: 2
Second rule:
f212_0_main_LE -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, arg2-arg1 >= 0, cost: 1
New rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (2-arg1 >= 0 /\ -1+arg1 > 0), cost: 3

Applied simplification
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (2-arg1 >= 0 /\ -1+arg1 > 0), cost: 3
New rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (-2+arg1 <= 0 /\ -1+arg1 > 0), cost: 3

Applied deletion
Removed the following rules: 5 6 8

Eliminated locations on tree-shaped paths
Start location: __init
  10: f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (1+arg1 > 0 /\ -1+arg1 <= 0), cost: 2
  11: f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (-2+arg1 <= 0 /\ -1+arg1 > 0), cost: 3
   9: __init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied simplification
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (-2+arg1 <= 0 /\ -1+arg1 > 0), cost: 3
New rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, -2+arg1 == 0, cost: 3

Simplified simple loops
Start location: __init
  10: f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (1+arg1 > 0 /\ -1+arg1 <= 0), cost: 2
  12: f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, -2+arg1 == 0, cost: 3
   9: __init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied acceleration
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, (1+arg1 > 0 /\ -1+arg1 <= 0), cost: 2
New rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-n0+arg1, (2-n0+arg1 > 0 /\ -1+n0 >= 0 /\ 1-arg1 >= 0), cost: 2*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_iMjKjh.txt

Applied instantiation
Original rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-n0+arg1, (2-n0+arg1 > 0 /\ -1+n0 >= 0 /\ 1-arg1 >= 0), cost: 2*n0
New rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1, (1 > 0 /\ arg1 >= 0 /\ 1-arg1 >= 0), cost: 2+2*arg1

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

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: __init
  12: f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, -2+arg1 == 0, cost: 3
  14: f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1, (arg1 >= 0 /\ -1+arg1 <= 0), cost: 2+2*arg1
   9: __init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied chaining
First rule:
__init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1+arg1, -2+arg1 == 0, cost: 3
New rule:
__init -> f161_0_main_LT : arg2'=arg2P2, arg1'=1, 3 > 0, cost: 5

Applied chaining
First rule:
__init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f161_0_main_LT -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1, (arg1 >= 0 /\ -1+arg1 <= 0), cost: 2+2*arg1
New rule:
__init -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1, (-1+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
   9: __init -> f161_0_main_LT : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
  15: __init -> f161_0_main_LT : arg2'=arg2P2, arg1'=1, 3 > 0, cost: 5
  16: __init -> f161_0_main_LT : arg2'=arg2P2, arg1'=-1, (-1+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