WORST_CASE(Omega(0),?)

Initial ITS
Start location: __init
   0: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=arg1P0, arg2'=arg2P0, (10-arg2P0 == 0 /\ 12-arg1P0 == 0), cost: 1
   1: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1 < 0 /\ 1-arg1P1 == 0 /\ arg2 > 0 /\ -1-arg2P1+arg2 == 0), cost: 1
   2: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -1+arg1-arg1P2 == 0 /\ -arg2P2+arg2 == 0 /\ arg2 > 0 /\ -1 < 0), cost: 1
   3: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -1+arg2-arg2P3 == 0 /\ arg2 > 0 /\ -1 < 0), cost: 1
   4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied preprocessing
Original rule:
f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=arg1P0, arg2'=arg2P0, (10-arg2P0 == 0 /\ 12-arg1P0 == 0), cost: 1
New rule:
f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, TRUE, cost: 1

Applied preprocessing
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P1, arg2'=arg2P1, (-1+arg1 < 0 /\ 1-arg1P1 == 0 /\ arg2 > 0 /\ -1-arg2P1+arg2 == 0), cost: 1
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2, (1-arg1 > 0 /\ arg2 > 0), cost: 1

Applied preprocessing
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P2, arg2'=arg2P2, (arg1 > 0 /\ -1+arg1-arg1P2 == 0 /\ -arg2P2+arg2 == 0 /\ arg2 > 0 /\ -1 < 0), cost: 1
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=-1+arg1, (arg1 > 0 /\ arg2 > 0), cost: 1

Applied preprocessing
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=arg2P3, (arg1 > 0 /\ -1+arg2-arg2P3 == 0 /\ arg2 > 0 /\ -1 < 0), cost: 1
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=-1+arg2, (arg1 > 0 /\ arg2 > 0), cost: 1

Simplified rules
Start location: __init
   5: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, TRUE, cost: 1
   6: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2, (1-arg1 > 0 /\ arg2 > 0), cost: 1
   7: f138_0_ack_GT -> f138_0_ack_GT : arg1'=-1+arg1, (arg1 > 0 /\ arg2 > 0), cost: 1
   8: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=-1+arg2, (arg1 > 0 /\ arg2 > 0), cost: 1
   4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied acceleration
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=-1+arg1, (arg1 > 0 /\ arg2 > 0), cost: 1
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1-n3, (1+arg1-n3 > 0 /\ arg2 > 0 /\ n3 >= 0), cost: n3

Applied instantiation
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1-n3, (1+arg1-n3 > 0 /\ arg2 > 0 /\ n3 >= 0), cost: n3
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, (arg1 >= 0 /\ 1 > 0 /\ arg2 > 0), cost: arg1

Applied acceleration
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=-1+arg2, (arg1 > 0 /\ arg2 > 0), cost: 1
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=-n5+arg2, (arg1 > 0 /\ -1+n5 >= 0 /\ arg1P3 > 0 /\ 1-n5+arg2 > 0), cost: n5

Applied instantiation
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=-n5+arg2, (arg1 > 0 /\ -1+n5 >= 0 /\ arg1P3 > 0 /\ 1-n5+arg2 > 0), cost: n5
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, (arg1 > 0 /\ 1 > 0 /\ arg1P3 > 0 /\ -1+arg2 >= 0), cost: arg2

Applied simplification
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, (arg1 >= 0 /\ 1 > 0 /\ arg2 > 0), cost: arg1
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, (arg1 >= 0 /\ arg2 > 0), cost: arg1

Applied simplification
Original rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, (arg1 > 0 /\ 1 > 0 /\ arg1P3 > 0 /\ -1+arg2 >= 0), cost: arg2
New rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, (arg1 > 0 /\ arg1P3 > 0 /\ -1+arg2 >= 0), cost: arg2

Applied deletion
Removed the following rules: 7 8

Accelerated simple loops
Start location: __init
   5: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, TRUE, cost: 1
   6: f138_0_ack_GT -> f138_0_ack_GT : arg1'=1, arg2'=-1+arg2, (1-arg1 > 0 /\ arg2 > 0), cost: 1
  11: f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, (arg1 >= 0 /\ arg2 > 0), cost: arg1
  12: f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, (arg1 > 0 /\ arg1P3 > 0 /\ -1+arg2 >= 0), cost: arg2
   4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


Applied chaining
First rule:
f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, TRUE, cost: 1
Second rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=0, (arg1 >= 0 /\ arg2 > 0), cost: arg1
New rule:
f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=0, arg2'=10, (12 >= 0 /\ 10 > 0), cost: 13

Applied chaining
First rule:
f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, TRUE, cost: 1
Second rule:
f138_0_ack_GT -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, (arg1 > 0 /\ arg1P3 > 0 /\ -1+arg2 >= 0), cost: arg2
New rule:
f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, arg1P3 > 0, cost: 11

Applied deletion
Removed the following rules: 6 11 12

Chained accelerated rules with incoming rules
Start location: __init
   5: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=12, arg2'=10, TRUE, cost: 1
  13: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=0, arg2'=10, (12 >= 0 /\ 10 > 0), cost: 13
  14: f1_0_main_ConstantStackPush -> f138_0_ack_GT : arg1'=arg1P3, arg2'=0, arg1P3 > 0, cost: 11
   4: __init -> f1_0_main_ConstantStackPush : arg1'=arg1P4, arg2'=arg2P4, TRUE, cost: 1


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