NO

Initial ITS
Start location: l8
   0: l0 -> l1 : x^0'=x^post0, p^0'=p^post0, y^0'=y^post0, (-1+x^post0 == 0 /\ y^0-y^post0 == 0 /\ p^0-p^post0 == 0), cost: 1
   1: l1 -> l0 : x^0'=x^post1, p^0'=p^post1, y^0'=y^post1, (y^0-y^post1 == 0 /\ p^0-p^post1 == 0 /\ x^0-x^post1 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, p^0'=p^post2, y^0'=y^post2, (y^0-y^post2 == 0 /\ x^0-x^post2 == 0 /\ p^post2 == 0 /\ y^0 <= 0), cost: 1
   3: l2 -> l3 : x^0'=x^post3, p^0'=p^post3, y^0'=y^post3, (1+y^post3-y^0 == 0 /\ -p^post3+p^0 == 0 /\ -x^post3+x^0 == 0 /\ 1-y^0 <= 0), cost: 1
   4: l3 -> l2 : x^0'=x^post4, p^0'=p^post4, y^0'=y^post4, (-p^post4+p^0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
   5: l4 -> l0 : x^0'=x^post5, p^0'=p^post5, y^0'=y^post5, (-p^post5+p^0 == 0 /\ -y^post5+y^0 == 0 /\ 2 <= 0 /\ -x^post5+x^0 == 0), cost: 1
   6: l4 -> l5 : x^0'=x^post6, p^0'=p^post6, y^0'=y^post6, (x^0-x^post6 == 0 /\ -y^post6+y^0 == 0 /\ -1+p^post6-p^0 == 0), cost: 1
   7: l5 -> l4 : x^0'=x^post7, p^0'=p^post7, y^0'=y^post7, (-y^post7+y^0 == 0 /\ -p^post7+p^0 == 0 /\ x^0-x^post7 == 0), cost: 1
   8: l6 -> l2 : x^0'=x^post8, p^0'=p^post8, y^0'=y^post8, (x^0 <= 0 /\ p^0-p^post8 == 0 /\ -y^post8+y^0 == 0 /\ x^0-x^post8 == 0), cost: 1
   9: l6 -> l4 : x^0'=x^post9, p^0'=p^post9, y^0'=y^post9, (x^0-x^post9 == 0 /\ p^0-p^post9 == 0 /\ 1-x^0 <= 0 /\ -y^post9+y^0 == 0), cost: 1
  10: l7 -> l6 : x^0'=x^post10, p^0'=p^post10, y^0'=y^post10, (x^0-x^post10 == 0 /\ -y^post10+y^0 == 0 /\ p^post10 == 0), cost: 1
  11: l8 -> l7 : x^0'=x^post11, p^0'=p^post11, y^0'=y^post11, (x^0-x^post11 == 0 /\ p^0-p^post11 == 0 /\ -y^post11+y^0 == 0), cost: 1


Removed rules with unsatisfiable guard
Start location: l8
   0: l0 -> l1 : x^0'=x^post0, p^0'=p^post0, y^0'=y^post0, (-1+x^post0 == 0 /\ y^0-y^post0 == 0 /\ p^0-p^post0 == 0), cost: 1
   1: l1 -> l0 : x^0'=x^post1, p^0'=p^post1, y^0'=y^post1, (y^0-y^post1 == 0 /\ p^0-p^post1 == 0 /\ x^0-x^post1 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, p^0'=p^post2, y^0'=y^post2, (y^0-y^post2 == 0 /\ x^0-x^post2 == 0 /\ p^post2 == 0 /\ y^0 <= 0), cost: 1
   3: l2 -> l3 : x^0'=x^post3, p^0'=p^post3, y^0'=y^post3, (1+y^post3-y^0 == 0 /\ -p^post3+p^0 == 0 /\ -x^post3+x^0 == 0 /\ 1-y^0 <= 0), cost: 1
   4: l3 -> l2 : x^0'=x^post4, p^0'=p^post4, y^0'=y^post4, (-p^post4+p^0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
   6: l4 -> l5 : x^0'=x^post6, p^0'=p^post6, y^0'=y^post6, (x^0-x^post6 == 0 /\ -y^post6+y^0 == 0 /\ -1+p^post6-p^0 == 0), cost: 1
   7: l5 -> l4 : x^0'=x^post7, p^0'=p^post7, y^0'=y^post7, (-y^post7+y^0 == 0 /\ -p^post7+p^0 == 0 /\ x^0-x^post7 == 0), cost: 1
   8: l6 -> l2 : x^0'=x^post8, p^0'=p^post8, y^0'=y^post8, (x^0 <= 0 /\ p^0-p^post8 == 0 /\ -y^post8+y^0 == 0 /\ x^0-x^post8 == 0), cost: 1
   9: l6 -> l4 : x^0'=x^post9, p^0'=p^post9, y^0'=y^post9, (x^0-x^post9 == 0 /\ p^0-p^post9 == 0 /\ 1-x^0 <= 0 /\ -y^post9+y^0 == 0), cost: 1
  10: l7 -> l6 : x^0'=x^post10, p^0'=p^post10, y^0'=y^post10, (x^0-x^post10 == 0 /\ -y^post10+y^0 == 0 /\ p^post10 == 0), cost: 1
  11: l8 -> l7 : x^0'=x^post11, p^0'=p^post11, y^0'=y^post11, (x^0-x^post11 == 0 /\ p^0-p^post11 == 0 /\ -y^post11+y^0 == 0), cost: 1


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

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

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post2, p^0'=p^post2, y^0'=y^post2, (y^0-y^post2 == 0 /\ x^0-x^post2 == 0 /\ p^post2 == 0 /\ y^0 <= 0), cost: 1
New rule:
l2 -> l0 : p^0'=0, y^0 <= 0, cost: 1

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

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

Applied preprocessing
Original rule:
l4 -> l5 : x^0'=x^post6, p^0'=p^post6, y^0'=y^post6, (x^0-x^post6 == 0 /\ -y^post6+y^0 == 0 /\ -1+p^post6-p^0 == 0), cost: 1
New rule:
l4 -> l5 : p^0'=1+p^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : x^0'=x^post7, p^0'=p^post7, y^0'=y^post7, (-y^post7+y^0 == 0 /\ -p^post7+p^0 == 0 /\ x^0-x^post7 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l2 : x^0'=x^post8, p^0'=p^post8, y^0'=y^post8, (x^0 <= 0 /\ p^0-p^post8 == 0 /\ -y^post8+y^0 == 0 /\ x^0-x^post8 == 0), cost: 1
New rule:
l6 -> l2 : x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l4 : x^0'=x^post9, p^0'=p^post9, y^0'=y^post9, (x^0-x^post9 == 0 /\ p^0-p^post9 == 0 /\ 1-x^0 <= 0 /\ -y^post9+y^0 == 0), cost: 1
New rule:
l6 -> l4 : -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : x^0'=x^post10, p^0'=p^post10, y^0'=y^post10, (x^0-x^post10 == 0 /\ -y^post10+y^0 == 0 /\ p^post10 == 0), cost: 1
New rule:
l7 -> l6 : p^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l8 -> l7 : x^0'=x^post11, p^0'=p^post11, y^0'=y^post11, (x^0-x^post11 == 0 /\ p^0-p^post11 == 0 /\ -y^post11+y^0 == 0), cost: 1
New rule:
l8 -> l7 : TRUE, cost: 1

Simplified rules
Start location: l8
  12: l0 -> l1 : x^0'=1, TRUE, cost: 1
  13: l1 -> l0 : TRUE, cost: 1
  14: l2 -> l0 : p^0'=0, y^0 <= 0, cost: 1
  15: l2 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
  16: l3 -> l2 : TRUE, cost: 1
  17: l4 -> l5 : p^0'=1+p^0, TRUE, cost: 1
  18: l5 -> l4 : TRUE, cost: 1
  19: l6 -> l2 : x^0 <= 0, cost: 1
  20: l6 -> l4 : -1+x^0 >= 0, cost: 1
  21: l7 -> l6 : p^0'=0, TRUE, cost: 1
  22: l8 -> l7 : TRUE, cost: 1


Eliminating location l7 by chaining:

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

Applied deletion
Removed the following rules: 21 22

Eliminating location l3 by chaining:

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

Applied deletion
Removed the following rules: 15 16

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : x^0'=1, TRUE, cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=1, TRUE, cost: 2

Applied deletion
Removed the following rules: 12 13

Eliminating location l5 by chaining:

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

Applied deletion
Removed the following rules: 17 18

Eliminated locations on linear paths
Start location: l8
  25: l0 -> l0 : x^0'=1, TRUE, cost: 2
  14: l2 -> l0 : p^0'=0, y^0 <= 0, cost: 1
  24: l2 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
  26: l4 -> l4 : p^0'=1+p^0, TRUE, cost: 2
  19: l6 -> l2 : x^0 <= 0, cost: 1
  20: l6 -> l4 : -1+x^0 >= 0, cost: 1
  23: l8 -> l6 : p^0'=0, TRUE, cost: 2


Applied nonterm
Original rule:
l0 -> l0 : x^0'=1, TRUE, cost: 2
New rule:
l0 -> [9] : -1+n >= 0, cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_mABLJp.txt

Applied deletion
Removed the following rules: 25

Applied acceleration
Original rule:
l2 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
New rule:
l2 -> l2 : y^0'=-n0+y^0, (-n0+y^0 >= 0 /\ n0 >= 0), cost: 2*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_peoDFM.txt

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

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

Applied deletion
Removed the following rules: 24

Applied nonterm
Original rule:
l4 -> l4 : p^0'=1+p^0, TRUE, cost: 2
New rule:
l4 -> [11] : n1 >= 0, cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_Pnalll.txt

Applied deletion
Removed the following rules: 26

Accelerated simple loops
Start location: l8
  27: l0 -> [9] : -1+n >= 0, cost: NONTERM
  14: l2 -> l0 : p^0'=0, y^0 <= 0, cost: 1
  29: l2 -> l2 : y^0'=0, y^0 >= 0, cost: 2*y^0
  30: l4 -> [11] : n1 >= 0, cost: NONTERM
  19: l6 -> l2 : x^0 <= 0, cost: 1
  20: l6 -> l4 : -1+x^0 >= 0, cost: 1
  23: l8 -> l6 : p^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l2 -> l0 : p^0'=0, y^0 <= 0, cost: 1
Second rule:
l0 -> [9] : -1+n >= 0, cost: NONTERM
New rule:
l2 -> [9] : y^0 <= 0, cost: NONTERM

Applied deletion
Removed the following rules: 27

Applied chaining
First rule:
l6 -> l2 : x^0 <= 0, cost: 1
Second rule:
l2 -> l2 : y^0'=0, y^0 >= 0, cost: 2*y^0
New rule:
l6 -> l2 : y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 1+2*y^0

Applied deletion
Removed the following rules: 29

Applied chaining
First rule:
l6 -> l4 : -1+x^0 >= 0, cost: 1
Second rule:
l4 -> [11] : n1 >= 0, cost: NONTERM
New rule:
l6 -> [11] : -1+x^0 >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 30

Chained accelerated rules with incoming rules
Start location: l8
  14: l2 -> l0 : p^0'=0, y^0 <= 0, cost: 1
  31: l2 -> [9] : y^0 <= 0, cost: NONTERM
  19: l6 -> l2 : x^0 <= 0, cost: 1
  20: l6 -> l4 : -1+x^0 >= 0, cost: 1
  32: l6 -> l2 : y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 1+2*y^0
  33: l6 -> [11] : -1+x^0 >= 0, cost: NONTERM
  23: l8 -> l6 : p^0'=0, TRUE, cost: 2


Removed unreachable locations and irrelevant leafs
Start location: l8
  31: l2 -> [9] : y^0 <= 0, cost: NONTERM
  19: l6 -> l2 : x^0 <= 0, cost: 1
  32: l6 -> l2 : y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 1+2*y^0
  33: l6 -> [11] : -1+x^0 >= 0, cost: NONTERM
  23: l8 -> l6 : p^0'=0, TRUE, cost: 2


Eliminating location l6 by chaining:

Applied chaining
First rule:
l8 -> l6 : p^0'=0, TRUE, cost: 2
Second rule:
l6 -> l2 : x^0 <= 0, cost: 1
New rule:
l8 -> l2 : p^0'=0, x^0 <= 0, cost: 3

Applied chaining
First rule:
l8 -> l6 : p^0'=0, TRUE, cost: 2
Second rule:
l6 -> l2 : y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 1+2*y^0
New rule:
l8 -> l2 : p^0'=0, y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 3+2*y^0

Applied chaining
First rule:
l8 -> l6 : p^0'=0, TRUE, cost: 2
Second rule:
l6 -> [11] : -1+x^0 >= 0, cost: NONTERM
New rule:
l8 -> [11] : -1+x^0 >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 19 23 32 33

Eliminated locations on tree-shaped paths
Start location: l8
  31: l2 -> [9] : y^0 <= 0, cost: NONTERM
  34: l8 -> l2 : p^0'=0, x^0 <= 0, cost: 3
  35: l8 -> l2 : p^0'=0, y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 3+2*y^0
  36: l8 -> [11] : -1+x^0 >= 0, cost: NONTERM


Eliminating location l2 by chaining:

Applied chaining
First rule:
l8 -> l2 : p^0'=0, x^0 <= 0, cost: 3
Second rule:
l2 -> [9] : y^0 <= 0, cost: NONTERM
New rule:
l8 -> [9] : (x^0 <= 0 /\ y^0 <= 0), cost: NONTERM

Applied chaining
First rule:
l8 -> l2 : p^0'=0, y^0'=0, (x^0 <= 0 /\ y^0 >= 0), cost: 3+2*y^0
Second rule:
l2 -> [9] : y^0 <= 0, cost: NONTERM
New rule:
l8 -> [9] : (0 <= 0 /\ x^0 <= 0 /\ y^0 >= 0), cost: NONTERM

Applied simplification
Original rule:
l8 -> [9] : (0 <= 0 /\ x^0 <= 0 /\ y^0 >= 0), cost: NONTERM
New rule:
l8 -> [9] : (x^0 <= 0 /\ y^0 >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 31 34 35

Eliminated locations on tree-shaped paths
Start location: l8
  36: l8 -> [11] : -1+x^0 >= 0, cost: NONTERM
  37: l8 -> [9] : (x^0 <= 0 /\ y^0 <= 0), cost: NONTERM
  38: l8 -> [9] : (x^0 <= 0 /\ y^0 >= 0), cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 36 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  -1+x^0 >= 0