NO

Initial ITS
Start location: l5
   0: l0 -> l1 : nd^0'=nd^post0, x^0'=x^post0, p^0'=p^post0, (nd^0 <= 0 /\ nd^0-nd^post0 == 0 /\ x^0-x^post0 == 0 /\ -2+p^post0 == 0), cost: 1
   1: l0 -> l1 : nd^0'=nd^post1, x^0'=x^post1, p^0'=p^post1, (1-nd^0 <= 0 /\ x^0-x^post1 == 0 /\ nd^0-nd^post1 == 0 /\ -1+p^post1 == 0), cost: 1
   2: l1 -> l0 : nd^0'=nd^post2, x^0'=x^post2, p^0'=p^post2, (0 == 0 /\ x^0-x^post2 == 0 /\ p^0-p^post2 == 0), cost: 1
   3: l2 -> l3 : nd^0'=nd^post3, x^0'=x^post3, p^0'=p^post3, (nd^0 <= 0 /\ p^0-p^post3 == 0 /\ 2-x^0+x^post3 == 0 /\ nd^0-nd^post3 == 0), cost: 1
   4: l2 -> l3 : nd^0'=nd^post4, x^0'=x^post4, p^0'=p^post4, (1-nd^0 <= 0 /\ 1-x^0+x^post4 == 0 /\ p^0-p^post4 == 0 /\ nd^0-nd^post4 == 0), cost: 1
   5: l3 -> l1 : nd^0'=nd^post5, x^0'=x^post5, p^0'=p^post5, (x^0 <= 0 /\ nd^0-nd^post5 == 0 /\ x^0-x^post5 == 0 /\ p^0-p^post5 == 0), cost: 1
   6: l3 -> l2 : nd^0'=nd^post6, x^0'=x^post6, p^0'=p^post6, (0 == 0 /\ p^0-p^post6 == 0 /\ 1-x^0 <= 0 /\ x^0-x^post6 == 0), cost: 1
   7: l4 -> l3 : nd^0'=nd^post7, x^0'=x^post7, p^0'=p^post7, (p^post7 == 0 /\ x^0-x^post7 == 0 /\ nd^0-nd^post7 == 0), cost: 1
   8: l5 -> l4 : nd^0'=nd^post8, x^0'=x^post8, p^0'=p^post8, (nd^0-nd^post8 == 0 /\ x^0-x^post8 == 0 /\ p^0-p^post8 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : nd^0'=nd^post0, x^0'=x^post0, p^0'=p^post0, (nd^0 <= 0 /\ nd^0-nd^post0 == 0 /\ x^0-x^post0 == 0 /\ -2+p^post0 == 0), cost: 1
New rule:
l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l0 -> l1 : nd^0'=nd^post1, x^0'=x^post1, p^0'=p^post1, (1-nd^0 <= 0 /\ x^0-x^post1 == 0 /\ nd^0-nd^post1 == 0 /\ -1+p^post1 == 0), cost: 1
New rule:
l0 -> l1 : p^0'=1, -1+nd^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : nd^0'=nd^post2, x^0'=x^post2, p^0'=p^post2, (0 == 0 /\ x^0-x^post2 == 0 /\ p^0-p^post2 == 0), cost: 1
New rule:
l1 -> l0 : nd^0'=nd^post2, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : nd^0'=nd^post3, x^0'=x^post3, p^0'=p^post3, (nd^0 <= 0 /\ p^0-p^post3 == 0 /\ 2-x^0+x^post3 == 0 /\ nd^0-nd^post3 == 0), cost: 1
New rule:
l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : nd^0'=nd^post4, x^0'=x^post4, p^0'=p^post4, (1-nd^0 <= 0 /\ 1-x^0+x^post4 == 0 /\ p^0-p^post4 == 0 /\ nd^0-nd^post4 == 0), cost: 1
New rule:
l2 -> l3 : x^0'=-1+x^0, -1+nd^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : nd^0'=nd^post5, x^0'=x^post5, p^0'=p^post5, (x^0 <= 0 /\ nd^0-nd^post5 == 0 /\ x^0-x^post5 == 0 /\ p^0-p^post5 == 0), cost: 1
New rule:
l3 -> l1 : x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : nd^0'=nd^post6, x^0'=x^post6, p^0'=p^post6, (0 == 0 /\ p^0-p^post6 == 0 /\ 1-x^0 <= 0 /\ x^0-x^post6 == 0), cost: 1
New rule:
l3 -> l2 : nd^0'=nd^post6, -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : nd^0'=nd^post7, x^0'=x^post7, p^0'=p^post7, (p^post7 == 0 /\ x^0-x^post7 == 0 /\ nd^0-nd^post7 == 0), cost: 1
New rule:
l4 -> l3 : p^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : nd^0'=nd^post8, x^0'=x^post8, p^0'=p^post8, (nd^0-nd^post8 == 0 /\ x^0-x^post8 == 0 /\ p^0-p^post8 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Simplified rules
Start location: l5
   9: l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1
  10: l0 -> l1 : p^0'=1, -1+nd^0 >= 0, cost: 1
  11: l1 -> l0 : nd^0'=nd^post2, 0 == 0, cost: 1
  12: l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1
  13: l2 -> l3 : x^0'=-1+x^0, -1+nd^0 >= 0, cost: 1
  14: l3 -> l1 : x^0 <= 0, cost: 1
  15: l3 -> l2 : nd^0'=nd^post6, -1+x^0 >= 0, cost: 1
  16: l4 -> l3 : p^0'=0, TRUE, cost: 1
  17: l5 -> l4 : TRUE, cost: 1


Eliminating location l4 by chaining:

Applied chaining
First rule:
l5 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l3 : p^0'=0, TRUE, cost: 1
New rule:
l5 -> l3 : p^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 16 17

Eliminated locations on linear paths
Start location: l5
   9: l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1
  10: l0 -> l1 : p^0'=1, -1+nd^0 >= 0, cost: 1
  11: l1 -> l0 : nd^0'=nd^post2, 0 == 0, cost: 1
  12: l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1
  13: l2 -> l3 : x^0'=-1+x^0, -1+nd^0 >= 0, cost: 1
  14: l3 -> l1 : x^0 <= 0, cost: 1
  15: l3 -> l2 : nd^0'=nd^post6, -1+x^0 >= 0, cost: 1
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : nd^0'=nd^post6, -1+x^0 >= 0, cost: 1
Second rule:
l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-2+x^0, (nd^post6 <= 0 /\ -1+x^0 >= 0), cost: 2

Applied chaining
First rule:
l3 -> l2 : nd^0'=nd^post6, -1+x^0 >= 0, cost: 1
Second rule:
l2 -> l3 : x^0'=-1+x^0, -1+nd^0 >= 0, cost: 1
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2

Applied deletion
Removed the following rules: 12 13 15

Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : nd^0'=nd^post2, 0 == 0, cost: 1
Second rule:
l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, (0 == 0 /\ nd^post2 <= 0), cost: 2

Applied simplification
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, (0 == 0 /\ nd^post2 <= 0), cost: 2
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2

Applied chaining
First rule:
l1 -> l0 : nd^0'=nd^post2, 0 == 0, cost: 1
Second rule:
l0 -> l1 : p^0'=1, -1+nd^0 >= 0, cost: 1
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, (0 == 0 /\ -1+nd^post2 >= 0), cost: 2

Applied simplification
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, (0 == 0 /\ -1+nd^post2 >= 0), cost: 2
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2

Applied deletion
Removed the following rules: 9 10 11

Eliminated locations on tree-shaped paths
Start location: l5
  21: l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2
  22: l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2
  14: l3 -> l1 : x^0 <= 0, cost: 1
  19: l3 -> l3 : nd^0'=nd^post6, x^0'=-2+x^0, (nd^post6 <= 0 /\ -1+x^0 >= 0), cost: 2
  20: l3 -> l3 : nd^0'=nd^post6, x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2


Applied nonterm
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2
New rule:
l1 -> [6] : -nd^post2 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, -nd^post2 >= 0, cost: 2*n1

Applied nonterm
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2
New rule:
l1 -> [6] : -1+nd^post2 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2*n3

Applied simplification
Original rule:
l1 -> [6] : -nd^post2 >= 0, cost: NONTERM
New rule:
l1 -> [6] : nd^post2 <= 0, cost: NONTERM

Applied simplification
Original rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, -nd^post2 >= 0, cost: 2*n1
New rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2*n1

Applied deletion
Removed the following rules: 21 22

Applied acceleration
Original rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-2+x^0, (nd^post6 <= 0 /\ -1+x^0 >= 0), cost: 2
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, (-nd^post6 >= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2*n7

Applied acceleration
Original rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-n9, (x^0-n9 >= 0 /\ -1+n9 >= 0 /\ -1+nd^post6 >= 0), cost: 2*n9

Applied instantiation
Original rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-n9, (x^0-n9 >= 0 /\ -1+n9 >= 0 /\ -1+nd^post6 >= 0), cost: 2*n9
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=0, (0 >= 0 /\ -1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2*x^0

Applied simplification
Original rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, (-nd^post6 >= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2*n7
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2*n7

Applied simplification
Original rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=0, (0 >= 0 /\ -1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2*x^0
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2*x^0

Applied deletion
Removed the following rules: 19 20

Accelerated simple loops
Start location: l5
  25: l1 -> [6] : -1+nd^post2 >= 0, cost: NONTERM
  26: l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2*n3
  27: l1 -> [6] : nd^post2 <= 0, cost: NONTERM
  28: l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2*n1
  14: l3 -> l1 : x^0 <= 0, cost: 1
  31: l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2*n7
  32: l3 -> l3 : nd^0'=nd^post6, x^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2*x^0
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l3 -> l1 : x^0 <= 0, cost: 1
Second rule:
l1 -> [6] : -1+nd^post2 >= 0, cost: NONTERM
New rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM

Applied chaining
First rule:
l3 -> l1 : x^0 <= 0, cost: 1
Second rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=1, -1+nd^post2 >= 0, cost: 2*n3
New rule:
l3 -> l1 : nd^0'=nd^post2, p^0'=1, (-1+nd^post2 >= 0 /\ x^0 <= 0), cost: 1+2*n3

Applied chaining
First rule:
l3 -> l1 : x^0 <= 0, cost: 1
Second rule:
l1 -> [6] : nd^post2 <= 0, cost: NONTERM
New rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM

Applied chaining
First rule:
l3 -> l1 : x^0 <= 0, cost: 1
Second rule:
l1 -> l1 : nd^0'=nd^post2, p^0'=2, nd^post2 <= 0, cost: 2*n1
New rule:
l3 -> l1 : nd^0'=nd^post2, p^0'=2, (nd^post2 <= 0 /\ x^0 <= 0), cost: 1+2*n1

Applied deletion
Removed the following rules: 25 26 27 28

Applied chaining
First rule:
l5 -> l3 : p^0'=0, TRUE, cost: 2
Second rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2*n7
New rule:
l5 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, p^0'=0, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2+2*n7

Applied chaining
First rule:
l5 -> l3 : p^0'=0, TRUE, cost: 2
Second rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2*x^0
New rule:
l5 -> l3 : nd^0'=nd^post6, x^0'=0, p^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0

Applied deletion
Removed the following rules: 31 32

Chained accelerated rules with incoming rules
Start location: l5
  14: l3 -> l1 : x^0 <= 0, cost: 1
  33: l3 -> [6] : x^0 <= 0, cost: NONTERM
  34: l3 -> l1 : nd^0'=nd^post2, p^0'=1, (-1+nd^post2 >= 0 /\ x^0 <= 0), cost: 1+2*n3
  35: l3 -> [6] : x^0 <= 0, cost: NONTERM
  36: l3 -> l1 : nd^0'=nd^post2, p^0'=2, (nd^post2 <= 0 /\ x^0 <= 0), cost: 1+2*n1
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2
  37: l5 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, p^0'=0, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2+2*n7
  38: l5 -> l3 : nd^0'=nd^post6, x^0'=0, p^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0


Removed unreachable locations and irrelevant leafs
Start location: l5
  33: l3 -> [6] : x^0 <= 0, cost: NONTERM
  35: l3 -> [6] : x^0 <= 0, cost: NONTERM
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2
  37: l5 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, p^0'=0, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2+2*n7
  38: l5 -> l3 : nd^0'=nd^post6, x^0'=0, p^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0


Eliminating location l3 by chaining:

Applied chaining
First rule:
l5 -> l3 : p^0'=0, TRUE, cost: 2
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : x^0 <= 0, cost: NONTERM

Applied chaining
First rule:
l5 -> l3 : p^0'=0, TRUE, cost: 2
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : x^0 <= 0, cost: NONTERM

Applied chaining
First rule:
l5 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, p^0'=0, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2+2*n7
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ x^0-2*n7 <= 0 /\ -1+n7 >= 0), cost: NONTERM

Applied chaining
First rule:
l5 -> l3 : nd^0'=nd^post6, x^0'=x^0-2*n7, p^0'=0, (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ -1+n7 >= 0), cost: 2+2*n7
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ x^0-2*n7 <= 0 /\ -1+n7 >= 0), cost: NONTERM

Applied chaining
First rule:
l5 -> l3 : nd^0'=nd^post6, x^0'=0, p^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : (0 <= 0 /\ -1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM

Applied simplification
Original rule:
l5 -> [6] : (0 <= 0 /\ -1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM
New rule:
l5 -> [6] : (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM

Applied chaining
First rule:
l5 -> l3 : nd^0'=nd^post6, x^0'=0, p^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : (0 <= 0 /\ -1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM

Applied simplification
Original rule:
l5 -> [6] : (0 <= 0 /\ -1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM
New rule:
l5 -> [6] : (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 18 33 35 37 38

Eliminated locations on tree-shaped paths
Start location: l5
  39: l5 -> [6] : x^0 <= 0, cost: NONTERM
  40: l5 -> [6] : x^0 <= 0, cost: NONTERM
  41: l5 -> [6] : (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ x^0-2*n7 <= 0 /\ -1+n7 >= 0), cost: NONTERM
  42: l5 -> [6] : (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ x^0-2*n7 <= 0 /\ -1+n7 >= 0), cost: NONTERM
  43: l5 -> [6] : (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM
  44: l5 -> [6] : (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM


Removed duplicate rules (ignoring updates)
Start location: l5
  40: l5 -> [6] : x^0 <= 0, cost: NONTERM
  42: l5 -> [6] : (nd^post6 <= 0 /\ 1+x^0-2*n7 >= 0 /\ x^0-2*n7 <= 0 /\ -1+n7 >= 0), cost: NONTERM
  44: l5 -> [6] : (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 40 via SMT.

Proved the following lower bound
Complexity:  Nonterm
Cpx degree: Nonterm

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  x^0 <= 0