WORST_CASE(Omega(0),?)

Initial ITS
Start location: l5
   0: l0 -> l1 : op1^0'=op1^post0, op2^0'=op2^post0, (op2^0-op2^post0 == 0 /\ op1^0-op1^post0 == 0 /\ -op1^0 <= 0 /\ -op2^0 <= 0 /\ op2^0 <= 0), cost: 1
   6: l1 -> l4 : op1^0'=op1^post6, op2^0'=op2^post6, (1-op1^0 <= 0 /\ 1-op1^0+op1^post6 == 0 /\ -1+op2^post6-op2^0 == 0), cost: 1
   1: l2 -> l3 : op1^0'=op1^post1, op2^0'=op2^post1, (-1-op1^0+op1^post1 == 0 /\ 1+op2^post1-op2^0 == 0 /\ 1-op2^0 <= 0), cost: 1
   3: l2 -> l4 : op1^0'=op1^post3, op2^0'=op2^post3, (1-op1^0+op1^post3 == 0 /\ -1-op2^0+op2^post3 == 0 /\ 1-op1^0 <= 0), cost: 1
   2: l3 -> l2 : op1^0'=op1^post2, op2^0'=op2^post2, (-op2^post2+op2^0 == 0 /\ op1^0-op1^post2 == 0), cost: 1
   4: l4 -> l2 : op1^0'=op1^post4, op2^0'=op2^post4, (op1^0-op1^post4 == 0 /\ 1-op2^0 <= 0 /\ 1+op2^post4-op2^0 == 0), cost: 1
   5: l4 -> l1 : op1^0'=op1^post5, op2^0'=op2^post5, (op2^0-op2^post5 == 0 /\ op1^0-op1^post5 == 0), cost: 1
   7: l5 -> l0 : op1^0'=op1^post7, op2^0'=op2^post7, (op1^0-op1^post7 == 0 /\ -op2^post7+op2^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : op1^0'=op1^post0, op2^0'=op2^post0, (op2^0-op2^post0 == 0 /\ op1^0-op1^post0 == 0 /\ -op1^0 <= 0 /\ -op2^0 <= 0 /\ op2^0 <= 0), cost: 1
New rule:
l0 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : op1^0'=op1^post1, op2^0'=op2^post1, (-1-op1^0+op1^post1 == 0 /\ 1+op2^post1-op2^0 == 0 /\ 1-op2^0 <= 0), cost: 1
New rule:
l2 -> l3 : op1^0'=1+op1^0, op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : op1^0'=op1^post2, op2^0'=op2^post2, (-op2^post2+op2^0 == 0 /\ op1^0-op1^post2 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l4 : op1^0'=op1^post3, op2^0'=op2^post3, (1-op1^0+op1^post3 == 0 /\ -1-op2^0+op2^post3 == 0 /\ 1-op1^0 <= 0), cost: 1
New rule:
l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : op1^0'=op1^post4, op2^0'=op2^post4, (op1^0-op1^post4 == 0 /\ 1-op2^0 <= 0 /\ 1+op2^post4-op2^0 == 0), cost: 1
New rule:
l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l1 : op1^0'=op1^post5, op2^0'=op2^post5, (op2^0-op2^post5 == 0 /\ op1^0-op1^post5 == 0), cost: 1
New rule:
l4 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l4 : op1^0'=op1^post6, op2^0'=op2^post6, (1-op1^0 <= 0 /\ 1-op1^0+op1^post6 == 0 /\ -1+op2^post6-op2^0 == 0), cost: 1
New rule:
l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l0 : op1^0'=op1^post7, op2^0'=op2^post7, (op1^0-op1^post7 == 0 /\ -op2^post7+op2^0 == 0), cost: 1
New rule:
l5 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l5
   8: l0 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 1
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
   9: l2 -> l3 : op1^0'=1+op1^0, op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
  11: l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  10: l3 -> l2 : TRUE, cost: 1
  12: l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  15: l5 -> l0 : TRUE, cost: 1


Eliminating location l0 by chaining:

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 1
New rule:
l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2

Applied deletion
Removed the following rules: 8 15

Eliminating location l3 by chaining:

Applied chaining
First rule:
l2 -> l3 : op1^0'=1+op1^0, op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
Second rule:
l3 -> l2 : TRUE, cost: 1
New rule:
l2 -> l2 : op1^0'=1+op1^0, op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 9 10

Eliminated locations on linear paths
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  11: l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  17: l2 -> l2 : op1^0'=1+op1^0, op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 2
  12: l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied acceleration
Original rule:
l2 -> l2 : op1^0'=1+op1^0, op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 2
New rule:
l2 -> l2 : op1^0'=op1^0+n0, op2^0'=-n0+op2^0, (n0 >= 0 /\ -n0+op2^0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l2 -> l2 : op1^0'=op1^0+n0, op2^0'=-n0+op2^0, (n0 >= 0 /\ -n0+op2^0 >= 0), cost: 2*n0
New rule:
l2 -> l2 : op1^0'=op1^0+op2^0, op2^0'=0, (0 >= 0 /\ op2^0 >= 0), cost: 2*op2^0

Applied simplification
Original rule:
l2 -> l2 : op1^0'=op1^0+op2^0, op2^0'=0, (0 >= 0 /\ op2^0 >= 0), cost: 2*op2^0
New rule:
l2 -> l2 : op1^0'=op1^0+op2^0, op2^0'=0, op2^0 >= 0, cost: 2*op2^0

Applied deletion
Removed the following rules: 17

Accelerated simple loops
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  11: l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  19: l2 -> l2 : op1^0'=op1^0+op2^0, op2^0'=0, op2^0 >= 0, cost: 2*op2^0
  12: l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied chaining
First rule:
l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
Second rule:
l2 -> l2 : op1^0'=op1^0+op2^0, op2^0'=0, op2^0 >= 0, cost: 2*op2^0
New rule:
l4 -> l2 : op1^0'=-1+op1^0+op2^0, op2^0'=0, -1+op2^0 >= 0, cost: -1+2*op2^0

Applied deletion
Removed the following rules: 19

Chained accelerated rules with incoming rules
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  11: l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  12: l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  20: l4 -> l2 : op1^0'=-1+op1^0+op2^0, op2^0'=0, -1+op2^0 >= 0, cost: -1+2*op2^0
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l4 -> l2 : op2^0'=-1+op2^0, -1+op2^0 >= 0, cost: 1
Second rule:
l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
New rule:
l4 -> l4 : op1^0'=-1+op1^0, op2^0'=op2^0, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2

Applied chaining
First rule:
l4 -> l2 : op1^0'=-1+op1^0+op2^0, op2^0'=0, -1+op2^0 >= 0, cost: -1+2*op2^0
Second rule:
l2 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
New rule:
l4 -> l4 : op1^0'=-2+op1^0+op2^0, op2^0'=1, (-2+op1^0+op2^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op2^0

Applied deletion
Removed the following rules: 11 12 20

Eliminated locations on tree-shaped paths
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  21: l4 -> l4 : op1^0'=-1+op1^0, op2^0'=op2^0, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2
  22: l4 -> l4 : op1^0'=-2+op1^0+op2^0, op2^0'=1, (-2+op1^0+op2^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op2^0
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied simplification
Original rule:
l4 -> l4 : op1^0'=-1+op1^0, op2^0'=op2^0, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2
New rule:
l4 -> l4 : op1^0'=-1+op1^0, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2

Simplified simple loops
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  22: l4 -> l4 : op1^0'=-2+op1^0+op2^0, op2^0'=1, (-2+op1^0+op2^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op2^0
  23: l4 -> l4 : op1^0'=-1+op1^0, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied acceleration
Original rule:
l4 -> l4 : op1^0'=-2+op1^0+op2^0, op2^0'=1, (-2+op1^0+op2^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op2^0
New rule:
l4 -> l4 : op1^0'=op1^0-n4, op2^0'=1, (-1+n4 >= 0 /\ -1+op2^0 >= 0 /\ op1^0-n4 >= 0), cost: 2*n4

Applied instantiation
Original rule:
l4 -> l4 : op1^0'=op1^0-n4, op2^0'=1, (-1+n4 >= 0 /\ -1+op2^0 >= 0 /\ op1^0-n4 >= 0), cost: 2*n4
New rule:
l4 -> l4 : op1^0'=0, op2^0'=1, (0 >= 0 /\ -1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0

Applied acceleration
Original rule:
l4 -> l4 : op1^0'=-1+op1^0, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2
New rule:
l4 -> l4 : op1^0'=op1^0-n6, (op1^0-n6 >= 0 /\ n6 >= 0 /\ -1+op2^0 >= 0), cost: 2*n6

Applied instantiation
Original rule:
l4 -> l4 : op1^0'=op1^0-n6, (op1^0-n6 >= 0 /\ n6 >= 0 /\ -1+op2^0 >= 0), cost: 2*n6
New rule:
l4 -> l4 : op1^0'=0, (0 >= 0 /\ op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0

Applied simplification
Original rule:
l4 -> l4 : op1^0'=0, op2^0'=1, (0 >= 0 /\ -1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0
New rule:
l4 -> l4 : op1^0'=0, op2^0'=1, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0

Applied simplification
Original rule:
l4 -> l4 : op1^0'=0, (0 >= 0 /\ op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0
New rule:
l4 -> l4 : op1^0'=0, (op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0

Applied deletion
Removed the following rules: 22 23

Accelerated simple loops
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  13: l4 -> l1 : TRUE, cost: 1
  26: l4 -> l4 : op1^0'=0, op2^0'=1, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0
  27: l4 -> l4 : op1^0'=0, (op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied chaining
First rule:
l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
Second rule:
l4 -> l4 : op1^0'=0, op2^0'=1, (-1+op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0
New rule:
l1 -> l4 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: -1+2*op1^0

Applied chaining
First rule:
l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
Second rule:
l4 -> l4 : op1^0'=0, (op1^0 >= 0 /\ -1+op2^0 >= 0), cost: 2*op1^0
New rule:
l1 -> l4 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: -1+2*op1^0

Applied deletion
Removed the following rules: 26 27

Chained accelerated rules with incoming rules
Start location: l5
  14: l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
  28: l1 -> l4 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: -1+2*op1^0
  29: l1 -> l4 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: -1+2*op1^0
  13: l4 -> l1 : TRUE, cost: 1
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Eliminating location l4 by chaining:

Applied chaining
First rule:
l1 -> l4 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 1
Second rule:
l4 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 2

Applied chaining
First rule:
l1 -> l4 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: -1+2*op1^0
Second rule:
l4 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: 2*op1^0

Applied chaining
First rule:
l1 -> l4 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: -1+2*op1^0
Second rule:
l4 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: 2*op1^0

Applied deletion
Removed the following rules: 13 14 28 29

Eliminated locations on tree-shaped paths
Start location: l5
  30: l1 -> l1 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 2
  31: l1 -> l1 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: 2*op1^0
  32: l1 -> l1 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: 2*op1^0
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied acceleration
Original rule:
l1 -> l1 : op1^0'=-1+op1^0, op2^0'=1+op2^0, -1+op1^0 >= 0, cost: 2
New rule:
l1 -> l1 : op1^0'=op1^0-n18, op2^0'=n18+op2^0, (n18 >= 0 /\ op1^0-n18 >= 0), cost: 2*n18

Applied instantiation
Original rule:
l1 -> l1 : op1^0'=op1^0-n18, op2^0'=n18+op2^0, (n18 >= 0 /\ op1^0-n18 >= 0), cost: 2*n18
New rule:
l1 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, (0 >= 0 /\ op1^0 >= 0), cost: 2*op1^0

Applied simplification
Original rule:
l1 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, (0 >= 0 /\ op1^0 >= 0), cost: 2*op1^0
New rule:
l1 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, op1^0 >= 0, cost: 2*op1^0

Applied deletion
Removed the following rules: 30

Accelerated simple loops
Start location: l5
  31: l1 -> l1 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: 2*op1^0
  32: l1 -> l1 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: 2*op1^0
  34: l1 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, op1^0 >= 0, cost: 2*op1^0
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2


Applied chaining
First rule:
l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2
Second rule:
l1 -> l1 : op1^0'=0, op2^0'=1, (op2^0 >= 0 /\ -2+op1^0 >= 0), cost: 2*op1^0
New rule:
l5 -> l1 : op1^0'=0, op2^0'=1, (op2^0 == 0 /\ -2+op1^0 >= 0), cost: 2+2*op1^0

Applied chaining
First rule:
l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2
Second rule:
l1 -> l1 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 >= 0), cost: 2*op1^0
New rule:
l5 -> l1 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 == 0), cost: 2+2*op1^0

Applied chaining
First rule:
l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2
Second rule:
l1 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, op1^0 >= 0, cost: 2*op1^0
New rule:
l5 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, (op1^0 >= 0 /\ op2^0 == 0), cost: 2+2*op1^0

Applied deletion
Removed the following rules: 31 32 34

Chained accelerated rules with incoming rules
Start location: l5
  16: l5 -> l1 : (op1^0 >= 0 /\ op2^0 == 0), cost: 2
  35: l5 -> l1 : op1^0'=0, op2^0'=1, (op2^0 == 0 /\ -2+op1^0 >= 0), cost: 2+2*op1^0
  36: l5 -> l1 : op1^0'=0, op2^0'=1+op2^0, (-1+op1^0 >= 0 /\ op2^0 == 0), cost: 2+2*op1^0
  37: l5 -> l1 : op1^0'=0, op2^0'=op1^0+op2^0, (op1^0 >= 0 /\ op2^0 == 0), cost: 2+2*op1^0


Removed unreachable locations and irrelevant leafs
Start location: l5
  <empty>


Computing asymptotic complexity

Proved the following lower bound
Complexity:  Unknown
Cpx degree: ?

Solved cost: 0
Rule cost:   0