WORST_CASE(Omega(0),?)

Initial ITS
Start location: __init
   0: f1_0_main_Load -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   1: f152_0_gcd_LE -> f216_0_mod_LT : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -arg2P1+arg2 == 0 /\ arg2 > 0 /\ arg1-arg1P1 == 0), cost: 1
   2: f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg1P2, arg2'=arg2P2, (-arg1+arg2 > 0 /\ arg1-arg2P2 == 0 /\ arg2-arg1P2 == 0), cost: 1
   3: f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-arg1P3-arg2 == 0 /\ -arg1+arg2 <= 0 /\ arg2 > 0 /\ arg2-arg2P3 == 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied preprocessing
Original rule:
f152_0_gcd_LE -> f216_0_mod_LT : arg1'=arg1P1, arg2'=arg2P1, (arg1 > 0 /\ -arg2P1+arg2 == 0 /\ arg2 > 0 /\ arg1-arg1P1 == 0), cost: 1
New rule:
f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1

Applied preprocessing
Original rule:
f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg1P2, arg2'=arg2P2, (-arg1+arg2 > 0 /\ arg1-arg2P2 == 0 /\ arg2-arg1P2 == 0), cost: 1
New rule:
f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -arg1+arg2 > 0, cost: 1

Applied preprocessing
Original rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ arg1-arg1P3-arg2 == 0 /\ -arg1+arg2 <= 0 /\ arg2 > 0 /\ arg2-arg2P3 == 0), cost: 1
New rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-arg2, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1

Simplified rules
Start location: __init
   0: f1_0_main_Load -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1
   6: f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -arg1+arg2 > 0, cost: 1
   7: f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-arg2, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied acceleration
Original rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-arg2, (-arg1+arg2 <= 0 /\ arg2 > 0), cost: 1
New rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: n0

Applied deletion
Removed the following rules: 7

Accelerated simple loops
Start location: __init
   0: f1_0_main_Load -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1
   6: f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -arg1+arg2 > 0, cost: 1
   8: f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: n0
   4: __init -> f1_0_main_Load : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied chaining
First rule:
f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1
Second rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: n0
New rule:
f152_0_gcd_LE -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (arg1 > 0 /\ n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 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 -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
   5: f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1
   9: f152_0_gcd_LE -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (arg1 > 0 /\ n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 1+n0
   6: f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -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 -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (arg1 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ 1+arg2 > 0), cost: 1
New rule:
__init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 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: f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1
   9: f152_0_gcd_LE -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (arg1 > 0 /\ n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 1+n0
   6: f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -arg1+arg2 > 0, cost: 1
  10: __init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Eliminating location f216_0_mod_LT by chaining:

Applied chaining
First rule:
f152_0_gcd_LE -> f216_0_mod_LT : (arg1 > 0 /\ arg2 > 0), cost: 1
Second rule:
f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -arg1+arg2 > 0, cost: 1
New rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ -arg1+arg2 > 0 /\ arg2 > 0), cost: 2

Applied simplification
Original rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ -arg1+arg2 > 0 /\ arg2 > 0), cost: 2
New rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 2

Applied chaining
First rule:
f152_0_gcd_LE -> f216_0_mod_LT : arg1'=arg1-n0*arg2, (arg1 > 0 /\ n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 1+n0
Second rule:
f216_0_mod_LT -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, -arg1+arg2 > 0, cost: 1
New rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1-n0*arg2, (arg1 > 0 /\ -arg1+n0*arg2+arg2 > 0 /\ n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 2+n0

Applied simplification
Original rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1-n0*arg2, (arg1 > 0 /\ -arg1+n0*arg2+arg2 > 0 /\ n0 >= 0 /\ arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 2+n0
New rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1-n0*arg2, (arg1 > 0 /\ -arg1+n0*arg2+arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 2+n0

Applied deletion
Removed the following rules: 5 6 9

Eliminated locations on tree-shaped paths
Start location: __init
  11: f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 2
  12: f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1-n0*arg2, (arg1 > 0 /\ -arg1+n0*arg2+arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 2+n0
  10: __init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Accelerated simple loops
Start location: __init
  11: f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 2
  12: f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1-n0*arg2, (arg1 > 0 /\ -arg1+n0*arg2+arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 2+n0
  10: __init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


Applied chaining
First rule:
__init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1, (arg1 > 0 /\ -arg1+arg2 > 0), cost: 2
New rule:
__init -> f152_0_gcd_LE : arg1'=arg2P0, arg2'=arg1P0, (arg1P0 > 0 /\ -arg1P0+arg2P0 > 0), cost: 4

Applied chaining
First rule:
__init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
Second rule:
f152_0_gcd_LE -> f152_0_gcd_LE : arg1'=arg2, arg2'=arg1-n0*arg2, (arg1 > 0 /\ -arg1+n0*arg2+arg2 > 0 /\ arg1-arg2-(-1+n0)*arg2 >= 0), cost: 2+n0
New rule:
__init -> f152_0_gcd_LE : arg1'=arg2P0, arg2'=arg1P0-n0*arg2P0, (-arg1P0+arg2P0+n0*arg2P0 > 0 /\ arg1P0 > 0 /\ -(-1+n0)*arg2P0+arg1P0-arg2P0 >= 0), cost: 4+n0

Applied deletion
Removed the following rules: 11 12

Chained accelerated rules with incoming rules
Start location: __init
  10: __init -> f152_0_gcd_LE : arg1'=arg1P0, arg2'=arg2P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2
  13: __init -> f152_0_gcd_LE : arg1'=arg2P0, arg2'=arg1P0, (arg1P0 > 0 /\ -arg1P0+arg2P0 > 0), cost: 4
  14: __init -> f152_0_gcd_LE : arg1'=arg2P0, arg2'=arg1P0-n0*arg2P0, (-arg1P0+arg2P0+n0*arg2P0 > 0 /\ arg1P0 > 0 /\ -(-1+n0)*arg2P0+arg1P0-arg2P0 >= 0), cost: 4+n0


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