WORST_CASE(Omega(0),?)

Initial ITS
Start location: __init
   0: f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1
   1: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg1'=arg1P1, arg2'=arg2P1, (arg1-x50 > 0 /\ -1+arg1 > 0 /\ arg1-arg1P1 == 0 /\ arg1-2*x60 == 0), cost: 1
   3: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg1'=arg1P3, arg2'=arg2P3, (-1+arg1 > 0 /\ -1+arg1-2*x110 == 0 /\ 3*arg1 > 0 /\ arg1-arg1P3 == 0), cost: 1
   2: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ -1+arg1 > 0 /\ -2+arg1-2*arg1P2 < 0 /\ arg1-arg1P2 > 0 /\ -2+arg1-2*x90 < 0 /\ arg1-2*x90 >= 0 /\ arg1-2*x90 == 0), cost: 1
   4: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P4, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0 /\ arg1-2*x130 >= 0 /\ -2+arg1-2*x130 < 0 /\ 1+3*arg1-arg1P4 == 0 /\ 3*arg1 > 0), cost: 1
   5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1


Applied preprocessing
Original rule:
f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ -arg1P0+arg2 == 0 /\ 1+arg2 > 0), cost: 1
New rule:
f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1

Applied preprocessing
Original rule:
f57_0_collatz_LE -> f57_0_collatz_LE\' : arg1'=arg1P1, arg2'=arg2P1, (arg1-x50 > 0 /\ -1+arg1 > 0 /\ arg1-arg1P1 == 0 /\ arg1-2*x60 == 0), cost: 1
New rule:
f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P1, (-1+arg1 > 0 /\ arg1-2*x60 == 0), cost: 1

Applied preprocessing
Original rule:
f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ -1+arg1 > 0 /\ -2+arg1-2*arg1P2 < 0 /\ arg1-arg1P2 > 0 /\ -2+arg1-2*x90 < 0 /\ arg1-2*x90 >= 0 /\ arg1-2*x90 == 0), cost: 1
New rule:
f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 1

Applied preprocessing
Original rule:
f57_0_collatz_LE -> f57_0_collatz_LE\' : arg1'=arg1P3, arg2'=arg2P3, (-1+arg1 > 0 /\ -1+arg1-2*x110 == 0 /\ 3*arg1 > 0 /\ arg1-arg1P3 == 0), cost: 1
New rule:
f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P3, (-1+arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1

Applied preprocessing
Original rule:
f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P4, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0 /\ arg1-2*x130 >= 0 /\ -2+arg1-2*x130 < 0 /\ 1+3*arg1-arg1P4 == 0 /\ 3*arg1 > 0), cost: 1
New rule:
f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0), cost: 1

Simplified rules
Start location: __init
   6: f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1
   7: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P1, (-1+arg1 > 0 /\ arg1-2*x60 == 0), cost: 1
   9: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P3, (-1+arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1
   8: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 1
  10: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0), cost: 1
   5: __init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1


Eliminating location f1_0_main_Load by chaining:

Applied chaining
First rule:
__init -> f1_0_main_Load : arg1'=arg1P5, arg2'=arg2P5, TRUE, cost: 1
Second rule:
f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg2, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2 > 0), cost: 1
New rule:
__init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2

Applied deletion
Removed the following rules: 5 6

Eliminated locations on linear paths
Start location: __init
   7: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P1, (-1+arg1 > 0 /\ arg1-2*x60 == 0), cost: 1
   9: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P3, (-1+arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1
   8: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 1
  10: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0), cost: 1
  11: __init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2


Eliminating location f57_0_collatz_LE\' by chaining:

Applied chaining
First rule:
f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P1, (-1+arg1 > 0 /\ arg1-2*x60 == 0), cost: 1
Second rule:
f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 1
New rule:
f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ -1+arg1 > 0 /\ arg1-2*x60 == 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 2

Applied simplification
Original rule:
f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ -1+arg1 > 0 /\ arg1-2*x60 == 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 2
New rule:
f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-2*x60 == 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 2

Applied chaining
First rule:
f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P3, (-1+arg1 > 0 /\ -1+arg1-2*x110 == 0), cost: 1
Second rule:
f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0), cost: 1
New rule:
f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0 /\ -1+arg1-2*x110 == 0), cost: 2

Applied deletion
Removed the following rules: 7 8 9 10

Eliminated locations on tree-shaped paths
Start location: __init
  12: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-2*x60 == 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 2
  13: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0 /\ -1+arg1-2*x110 == 0), cost: 2
  11: __init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2


Accelerated simple loops
Start location: __init
  12: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-2*x60 == 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 2
  13: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0 /\ -1+arg1-2*x110 == 0), cost: 2
  11: __init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2


Applied chaining
First rule:
__init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2
Second rule:
f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (arg1-2*arg1P2 >= 0 /\ arg1-2*x60 == 0 /\ arg1-arg1P2 > 0 /\ 2-arg1+2*arg1P2 > 0 /\ arg1-2*x90 == 0), cost: 2
New rule:
__init -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (-2*arg1P2+2*x90 >= 0 /\ -arg1P2+2*x90 > 0 /\ 2+2*arg1P2-2*x90 > 0), cost: 4

Applied chaining
First rule:
__init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2
Second rule:
f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P4, (-1+arg1 > 0 /\ -1+arg1-2*x130 == 0 /\ -1+arg1-2*x110 == 0), cost: 2
New rule:
__init -> f57_0_collatz_LE : arg1'=4+6*x130, arg2'=arg2P4, 2*x130 > 0, cost: 4

Applied deletion
Removed the following rules: 12 13

Chained accelerated rules with incoming rules
Start location: __init
  11: __init -> f57_0_collatz_LE : arg1'=arg2P5, arg2'=arg2P0, (arg1P5 > 0 /\ 1+arg2P5 > 0), cost: 2
  14: __init -> f57_0_collatz_LE : arg1'=arg1P2, arg2'=arg2P2, (-2*arg1P2+2*x90 >= 0 /\ -arg1P2+2*x90 > 0 /\ 2+2*arg1P2-2*x90 > 0), cost: 4
  15: __init -> f57_0_collatz_LE : arg1'=4+6*x130, arg2'=arg2P4, 2*x130 > 0, cost: 4


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