WORST_CASE(Omega(0),?)

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


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

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

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

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


Applied acceleration
Original rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=-arg2+arg1, (arg2 > 0 /\ arg2-arg1 <= 0), cost: 1
New rule:
f216_0_mod_LT -> f216_0_mod_LT : arg1'=arg1-arg2*n, (arg2 > 0 /\ n >= 0 /\ -arg2+arg1-arg2*(-1+n) >= 0), cost: n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_bDCpeH.txt

Applied deletion
Removed the following rules: 7

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


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

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

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

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

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

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 : arg2'=arg1, arg1'=arg2, (arg2-arg1 > 0 /\ arg1 > 0), cost: 2
  12: f152_0_gcd_LE -> f152_0_gcd_LE : arg2'=arg1-arg2*n, arg1'=arg2, (-arg2+arg1-arg2*(-1+n) >= 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n > 0), cost: 2+n
  10: __init -> f152_0_gcd_LE : arg2'=arg2P0, arg1'=arg1P0, (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 : arg2'=arg1, arg1'=arg2, (arg2-arg1 > 0 /\ arg1 > 0), cost: 2
  12: f152_0_gcd_LE -> f152_0_gcd_LE : arg2'=arg1-arg2*n, arg1'=arg2, (-arg2+arg1-arg2*(-1+n) >= 0 /\ arg1 > 0 /\ arg2-arg1+arg2*n > 0), cost: 2+n
  10: __init -> f152_0_gcd_LE : arg2'=arg2P0, arg1'=arg1P0, (1+arg2P4 > 0 /\ 1+arg2P0 > 0 /\ 1+arg1P0 > 0 /\ arg1P4 > 0), cost: 2


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

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

Applied deletion
Removed the following rules: 11 12

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


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