WORST_CASE(Omega(0),?)

Initial ITS
Start location: l8
   0: l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=y2^post0, j^0'=j^post0, x1^0'=x1^post0, (0 == 0 /\ -j^0+x1^post0 == 0 /\ -1+y2^post0-j^0 == 0 /\ j^0-j^post0 == 0), cost: 1
   1: l0 -> l1 : tmp3^0'=tmp3^post1, y2^0'=y2^post1, j^0'=j^post1, x1^0'=x1^post1, (j^0-j^post1 == 0 /\ y2^0-y2^post1 == 0 /\ tmp3^0-tmp3^post1 == 0 /\ -x1^post1+x1^0 == 0), cost: 1
   8: l1 -> l6 : tmp3^0'=tmp3^post8, y2^0'=y2^post8, j^0'=j^post8, x1^0'=x1^post8, (x1^0-x1^post8 == 0 /\ -1+j^post8-j^0 == 0 /\ -tmp3^post8+tmp3^0 == 0 /\ y2^0-y2^post8 == 0), cost: 1
   2: l2 -> l3 : tmp3^0'=tmp3^post2, y2^0'=y2^post2, j^0'=j^post2, x1^0'=x1^post2, (-y2^post2+y2^0 == 0 /\ 4-j^0 <= 0 /\ tmp3^0-tmp3^post2 == 0 /\ -j^post2+j^0 == 0 /\ -x1^post2+x1^0 == 0), cost: 1
   3: l2 -> l0 : tmp3^0'=tmp3^post3, y2^0'=y2^post3, j^0'=j^post3, x1^0'=x1^post3, (-j^post3+j^0 == 0 /\ -3+j^0 <= 0 /\ -x1^post3+x1^0 == 0 /\ -y2^post3+y2^0 == 0 /\ tmp3^0-tmp3^post3 == 0), cost: 1
   6: l3 -> l4 : tmp3^0'=tmp3^post6, y2^0'=y2^post6, j^0'=j^post6, x1^0'=x1^post6, (tmp3^0-tmp3^post6 == 0 /\ j^0-j^post6 == 0 /\ y2^0-y2^post6 == 0 /\ -x1^post6+x1^0 == 0), cost: 1
   7: l3 -> l4 : tmp3^0'=tmp3^post7, y2^0'=y2^post7, j^0'=j^post7, x1^0'=x1^post7, (-x1^post7+x1^0 == 0 /\ -j^post7+j^0 == 0 /\ -y2^post7+y2^0 == 0 /\ tmp3^0-tmp3^post7 == 0), cost: 1
   4: l4 -> l5 : tmp3^0'=tmp3^post4, y2^0'=y2^post4, j^0'=j^post4, x1^0'=x1^post4, (-j^post4+j^0 == 0 /\ -x1^post4+x1^0 == 0 /\ -y2^post4+y2^0 == 0 /\ -tmp3^post4+tmp3^0 == 0), cost: 1
   5: l6 -> l2 : tmp3^0'=tmp3^post5, y2^0'=y2^post5, j^0'=j^post5, x1^0'=x1^post5, (y2^0-y2^post5 == 0 /\ x1^0-x1^post5 == 0 /\ tmp3^0-tmp3^post5 == 0 /\ j^0-j^post5 == 0), cost: 1
   9: l7 -> l6 : tmp3^0'=tmp3^post9, y2^0'=y2^post9, j^0'=j^post9, x1^0'=x1^post9, (-x1^post9+x1^0 == 0 /\ y2^0-y2^post9 == 0 /\ tmp3^0-tmp3^post9 == 0 /\ j^post9 == 0), cost: 1
  10: l8 -> l7 : tmp3^0'=tmp3^post10, y2^0'=y2^post10, j^0'=j^post10, x1^0'=x1^post10, (tmp3^0-tmp3^post10 == 0 /\ j^0-j^post10 == 0 /\ -x1^post10+x1^0 == 0 /\ y2^0-y2^post10 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l8
   0: l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=y2^post0, j^0'=j^post0, x1^0'=x1^post0, (0 == 0 /\ -j^0+x1^post0 == 0 /\ -1+y2^post0-j^0 == 0 /\ j^0-j^post0 == 0), cost: 1
   1: l0 -> l1 : tmp3^0'=tmp3^post1, y2^0'=y2^post1, j^0'=j^post1, x1^0'=x1^post1, (j^0-j^post1 == 0 /\ y2^0-y2^post1 == 0 /\ tmp3^0-tmp3^post1 == 0 /\ -x1^post1+x1^0 == 0), cost: 1
   8: l1 -> l6 : tmp3^0'=tmp3^post8, y2^0'=y2^post8, j^0'=j^post8, x1^0'=x1^post8, (x1^0-x1^post8 == 0 /\ -1+j^post8-j^0 == 0 /\ -tmp3^post8+tmp3^0 == 0 /\ y2^0-y2^post8 == 0), cost: 1
   3: l2 -> l0 : tmp3^0'=tmp3^post3, y2^0'=y2^post3, j^0'=j^post3, x1^0'=x1^post3, (-j^post3+j^0 == 0 /\ -3+j^0 <= 0 /\ -x1^post3+x1^0 == 0 /\ -y2^post3+y2^0 == 0 /\ tmp3^0-tmp3^post3 == 0), cost: 1
   5: l6 -> l2 : tmp3^0'=tmp3^post5, y2^0'=y2^post5, j^0'=j^post5, x1^0'=x1^post5, (y2^0-y2^post5 == 0 /\ x1^0-x1^post5 == 0 /\ tmp3^0-tmp3^post5 == 0 /\ j^0-j^post5 == 0), cost: 1
   9: l7 -> l6 : tmp3^0'=tmp3^post9, y2^0'=y2^post9, j^0'=j^post9, x1^0'=x1^post9, (-x1^post9+x1^0 == 0 /\ y2^0-y2^post9 == 0 /\ tmp3^0-tmp3^post9 == 0 /\ j^post9 == 0), cost: 1
  10: l8 -> l7 : tmp3^0'=tmp3^post10, y2^0'=y2^post10, j^0'=j^post10, x1^0'=x1^post10, (tmp3^0-tmp3^post10 == 0 /\ j^0-j^post10 == 0 /\ -x1^post10+x1^0 == 0 /\ y2^0-y2^post10 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=y2^post0, j^0'=j^post0, x1^0'=x1^post0, (0 == 0 /\ -j^0+x1^post0 == 0 /\ -1+y2^post0-j^0 == 0 /\ j^0-j^post0 == 0), cost: 1
New rule:
l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l0 -> l1 : tmp3^0'=tmp3^post1, y2^0'=y2^post1, j^0'=j^post1, x1^0'=x1^post1, (j^0-j^post1 == 0 /\ y2^0-y2^post1 == 0 /\ tmp3^0-tmp3^post1 == 0 /\ -x1^post1+x1^0 == 0), cost: 1
New rule:
l0 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : tmp3^0'=tmp3^post3, y2^0'=y2^post3, j^0'=j^post3, x1^0'=x1^post3, (-j^post3+j^0 == 0 /\ -3+j^0 <= 0 /\ -x1^post3+x1^0 == 0 /\ -y2^post3+y2^0 == 0 /\ tmp3^0-tmp3^post3 == 0), cost: 1
New rule:
l2 -> l0 : -3+j^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l2 : tmp3^0'=tmp3^post5, y2^0'=y2^post5, j^0'=j^post5, x1^0'=x1^post5, (y2^0-y2^post5 == 0 /\ x1^0-x1^post5 == 0 /\ tmp3^0-tmp3^post5 == 0 /\ j^0-j^post5 == 0), cost: 1
New rule:
l6 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l6 : tmp3^0'=tmp3^post8, y2^0'=y2^post8, j^0'=j^post8, x1^0'=x1^post8, (x1^0-x1^post8 == 0 /\ -1+j^post8-j^0 == 0 /\ -tmp3^post8+tmp3^0 == 0 /\ y2^0-y2^post8 == 0), cost: 1
New rule:
l1 -> l6 : j^0'=1+j^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : tmp3^0'=tmp3^post9, y2^0'=y2^post9, j^0'=j^post9, x1^0'=x1^post9, (-x1^post9+x1^0 == 0 /\ y2^0-y2^post9 == 0 /\ tmp3^0-tmp3^post9 == 0 /\ j^post9 == 0), cost: 1
New rule:
l7 -> l6 : j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l8 -> l7 : tmp3^0'=tmp3^post10, y2^0'=y2^post10, j^0'=j^post10, x1^0'=x1^post10, (tmp3^0-tmp3^post10 == 0 /\ j^0-j^post10 == 0 /\ -x1^post10+x1^0 == 0 /\ y2^0-y2^post10 == 0), cost: 1
New rule:
l8 -> l7 : TRUE, cost: 1

Simplified rules
Start location: l8
  11: l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, 0 == 0, cost: 1
  12: l0 -> l1 : TRUE, cost: 1
  15: l1 -> l6 : j^0'=1+j^0, TRUE, cost: 1
  13: l2 -> l0 : -3+j^0 <= 0, cost: 1
  14: l6 -> l2 : TRUE, cost: 1
  16: l7 -> l6 : j^0'=0, TRUE, cost: 1
  17: l8 -> l7 : TRUE, cost: 1


Eliminating location l7 by chaining:

Applied chaining
First rule:
l8 -> l7 : TRUE, cost: 1
Second rule:
l7 -> l6 : j^0'=0, TRUE, cost: 1
New rule:
l8 -> l6 : j^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 16 17

Eliminating location l2 by chaining:

Applied chaining
First rule:
l6 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : -3+j^0 <= 0, cost: 1
New rule:
l6 -> l0 : -3+j^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 13 14

Eliminated locations on linear paths
Start location: l8
  11: l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, 0 == 0, cost: 1
  12: l0 -> l1 : TRUE, cost: 1
  15: l1 -> l6 : j^0'=1+j^0, TRUE, cost: 1
  19: l6 -> l0 : -3+j^0 <= 0, cost: 2
  18: l8 -> l6 : j^0'=0, TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l6 -> l0 : -3+j^0 <= 0, cost: 2
Second rule:
l0 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, 0 == 0, cost: 1
New rule:
l6 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, (0 == 0 /\ -3+j^0 <= 0), cost: 3

Applied simplification
Original rule:
l6 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, (0 == 0 /\ -3+j^0 <= 0), cost: 3
New rule:
l6 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, -3+j^0 <= 0, cost: 3

Applied chaining
First rule:
l6 -> l0 : -3+j^0 <= 0, cost: 2
Second rule:
l0 -> l1 : TRUE, cost: 1
New rule:
l6 -> l1 : -3+j^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 11 12 19

Eliminated locations on tree-shaped paths
Start location: l8
  15: l1 -> l6 : j^0'=1+j^0, TRUE, cost: 1
  20: l6 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, -3+j^0 <= 0, cost: 3
  21: l6 -> l1 : -3+j^0 <= 0, cost: 3
  18: l8 -> l6 : j^0'=0, TRUE, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l6 -> l1 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, x1^0'=j^0, -3+j^0 <= 0, cost: 3
Second rule:
l1 -> l6 : j^0'=1+j^0, TRUE, cost: 1
New rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, j^0'=1+j^0, x1^0'=j^0, -3+j^0 <= 0, cost: 4

Applied chaining
First rule:
l6 -> l1 : -3+j^0 <= 0, cost: 3
Second rule:
l1 -> l6 : j^0'=1+j^0, TRUE, cost: 1
New rule:
l6 -> l6 : j^0'=1+j^0, -3+j^0 <= 0, cost: 4

Applied deletion
Removed the following rules: 15 20 21

Eliminated locations on tree-shaped paths
Start location: l8
  22: l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, j^0'=1+j^0, x1^0'=j^0, -3+j^0 <= 0, cost: 4
  23: l6 -> l6 : j^0'=1+j^0, -3+j^0 <= 0, cost: 4
  18: l8 -> l6 : j^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=1+j^0, j^0'=1+j^0, x1^0'=j^0, -3+j^0 <= 0, cost: 4
New rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=n+j^0, j^0'=n+j^0, x1^0'=-1+n+j^0, (4-n-j^0 >= 0 /\ -1+n >= 0), cost: 4*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_FfJIOj.txt

Applied instantiation
Original rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=n+j^0, j^0'=n+j^0, x1^0'=-1+n+j^0, (4-n-j^0 >= 0 /\ -1+n >= 0), cost: 4*n
New rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, (0 >= 0 /\ 3-j^0 >= 0), cost: 16-4*j^0

Applied acceleration
Original rule:
l6 -> l6 : j^0'=1+j^0, -3+j^0 <= 0, cost: 4
New rule:
l6 -> l6 : j^0'=n0+j^0, (4-n0-j^0 >= 0 /\ n0 >= 0), cost: 4*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_gODlEM.txt

Applied instantiation
Original rule:
l6 -> l6 : j^0'=n0+j^0, (4-n0-j^0 >= 0 /\ n0 >= 0), cost: 4*n0
New rule:
l6 -> l6 : j^0'=4, (0 >= 0 /\ 4-j^0 >= 0), cost: 16-4*j^0

Applied simplification
Original rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, (0 >= 0 /\ 3-j^0 >= 0), cost: 16-4*j^0
New rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, -3+j^0 <= 0, cost: 16-4*j^0

Applied simplification
Original rule:
l6 -> l6 : j^0'=4, (0 >= 0 /\ 4-j^0 >= 0), cost: 16-4*j^0
New rule:
l6 -> l6 : j^0'=4, -4+j^0 <= 0, cost: 16-4*j^0

Applied deletion
Removed the following rules: 22 23

Accelerated simple loops
Start location: l8
  26: l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, -3+j^0 <= 0, cost: 16-4*j^0
  27: l6 -> l6 : j^0'=4, -4+j^0 <= 0, cost: 16-4*j^0
  18: l8 -> l6 : j^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l8 -> l6 : j^0'=0, TRUE, cost: 2
Second rule:
l6 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, -3+j^0 <= 0, cost: 16-4*j^0
New rule:
l8 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, -3 <= 0, cost: 18

Applied chaining
First rule:
l8 -> l6 : j^0'=0, TRUE, cost: 2
Second rule:
l6 -> l6 : j^0'=4, -4+j^0 <= 0, cost: 16-4*j^0
New rule:
l8 -> l6 : j^0'=4, -4 <= 0, cost: 18

Applied deletion
Removed the following rules: 26 27

Chained accelerated rules with incoming rules
Start location: l8
  18: l8 -> l6 : j^0'=0, TRUE, cost: 2
  28: l8 -> l6 : tmp3^0'=tmp3^post0, y2^0'=4, j^0'=4, x1^0'=3, -3 <= 0, cost: 18
  29: l8 -> l6 : j^0'=4, -4 <= 0, cost: 18


Removed unreachable locations and irrelevant leafs
Start location: l8
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0