NO

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


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

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

Applied preprocessing
Original rule:
l1 -> l0 : p^0'=p^post2, nd^0'=nd^post2, x^0'=x^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 : p^0'=p^post3, nd^0'=nd^post3, x^0'=x^post3, (-nd^post3+nd^0 == 0 /\ -p^post3+p^0 == 0 /\ 2+x^post3-x^0 == 0 /\ nd^0 <= 0), cost: 1
New rule:
l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1

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

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

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

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

Applied preprocessing
Original rule:
l5 -> l4 : p^0'=p^post8, nd^0'=nd^post8, x^0'=x^post8, (nd^0-nd^post8 == 0 /\ -x^post8+x^0 == 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 : p^0'=2, nd^0'=nd^post2, (0 == 0 /\ nd^post2 <= 0), cost: 2

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

Applied simplification
Original rule:
l1 -> l1 : p^0'=1, nd^0'=nd^post2, (0 == 0 /\ -1+nd^post2 >= 0), cost: 2
New rule:
l1 -> l1 : p^0'=1, nd^0'=nd^post2, -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 : p^0'=2, nd^0'=nd^post2, nd^post2 <= 0, cost: 2
  22: l1 -> l1 : p^0'=1, nd^0'=nd^post2, -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 : p^0'=2, nd^0'=nd^post2, nd^post2 <= 0, cost: 2
New rule:
l1 -> [6] : (-1+n >= 0 /\ -nd^post2 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_JfhPPo.txt

Applied nonterm
Original rule:
l1 -> l1 : p^0'=1, nd^0'=nd^post2, -1+nd^post2 >= 0, cost: 2
New rule:
l1 -> [6] : (-1+n0 >= 0 /\ -1+nd^post2 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_oGOoaD.txt

Applied simplification
Original rule:
l1 -> [6] : (-1+n >= 0 /\ -nd^post2 >= 0), cost: NONTERM
New rule:
l1 -> [6] : (nd^post2 <= 0 /\ -1+n >= 0), cost: NONTERM

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'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ -nd^post6 >= 0), cost: 2*n1
Sub-proof via acceration calculus written to file:///tmp/tmpnam_LGkbil.txt

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'=-n2+x^0, (-n2+x^0 >= 0 /\ -1+n2 >= 0 /\ -1+nd^post6 >= 0), cost: 2*n2
Sub-proof via acceration calculus written to file:///tmp/tmpnam_eCOFAA.txt

Applied instantiation
Original rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-n2+x^0, (-n2+x^0 >= 0 /\ -1+n2 >= 0 /\ -1+nd^post6 >= 0), cost: 2*n2
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'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ -nd^post6 >= 0), cost: 2*n1
New rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2*n1

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
  24: l1 -> [6] : (-1+n0 >= 0 /\ -1+nd^post2 >= 0), cost: NONTERM
  25: l1 -> [6] : (nd^post2 <= 0 /\ -1+n >= 0), cost: NONTERM
  14: l3 -> l1 : x^0 <= 0, cost: 1
  28: l3 -> l3 : nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2*n1
  29: 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+n0 >= 0 /\ -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 -> [6] : (nd^post2 <= 0 /\ -1+n >= 0), cost: NONTERM
New rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM

Applied deletion
Removed the following rules: 24 25

Applied chaining
First rule:
l5 -> l3 : p^0'=0, TRUE, cost: 2
Second rule:
l3 -> l3 : nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2*n1
New rule:
l5 -> l3 : p^0'=0, nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2+2*n1

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 : p^0'=0, nd^0'=nd^post6, x^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0

Applied deletion
Removed the following rules: 28 29

Chained accelerated rules with incoming rules
Start location: l5
  14: l3 -> l1 : x^0 <= 0, cost: 1
  30: l3 -> [6] : x^0 <= 0, cost: NONTERM
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2
  31: l5 -> l3 : p^0'=0, nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2+2*n1
  32: l5 -> l3 : p^0'=0, nd^0'=nd^post6, x^0'=0, (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: 2+2*x^0


Removed unreachable locations and irrelevant leafs
Start location: l5
  30: l3 -> [6] : x^0 <= 0, cost: NONTERM
  18: l5 -> l3 : p^0'=0, TRUE, cost: 2
  31: l5 -> l3 : p^0'=0, nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2+2*n1
  32: l5 -> l3 : p^0'=0, nd^0'=nd^post6, x^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, nd^0'=nd^post6, x^0'=-2*n1+x^0, (1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: 2+2*n1
Second rule:
l3 -> [6] : x^0 <= 0, cost: NONTERM
New rule:
l5 -> [6] : (-2*n1+x^0 <= 0 /\ 1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: NONTERM

Applied chaining
First rule:
l5 -> l3 : p^0'=0, nd^0'=nd^post6, x^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 30 31 32

Eliminated locations on tree-shaped paths
Start location: l5
  33: l5 -> [6] : x^0 <= 0, cost: NONTERM
  34: l5 -> [6] : (-2*n1+x^0 <= 0 /\ 1-2*n1+x^0 >= 0 /\ -1+n1 >= 0 /\ nd^post6 <= 0), cost: NONTERM
  35: l5 -> [6] : (-1+x^0 >= 0 /\ -1+nd^post6 >= 0), cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 33 via SMT.

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

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