NO

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


Removed unreachable rules and leafs
Start location: l5
   0: l0 -> l1 : p^0'=p^post0, r^0'=r^post0, N^0'=N^post0, q^0'=q^post0, (p^0-p^post0 == 0 /\ -p^0+r^post0 == 0 /\ q^0-q^post0 == 0 /\ N^0-N^post0 == 0), cost: 1
   1: l0 -> l1 : p^0'=p^post1, r^0'=r^post1, N^0'=N^post1, q^0'=q^post1, (N^0-N^post1 == 0 /\ q^post1-p^0 == 0 /\ r^0-r^post1 == 0 /\ p^0-p^post1 == 0), cost: 1
   4: l1 -> l2 : p^0'=p^post4, r^0'=r^post4, N^0'=N^post4, q^0'=q^post4, (-N^post4+N^0 == 0 /\ -q^post4+q^0 == 0 /\ -r^post4+r^0 == 0 /\ -p^post4+p^0 == 0), cost: 1
   3: l2 -> l0 : p^0'=p^post3, r^0'=r^post3, N^0'=N^post3, q^0'=q^post3, (0 == 0 /\ -N^post3+N^0 == 0 /\ -q^post3+q^0 == 0 /\ -r^post3+r^0 == 0 /\ 2+r^0-q^0 <= 0), cost: 1
   5: l4 -> l1 : p^0'=p^post5, r^0'=r^post5, N^0'=N^post5, q^0'=q^post5, (-N^0+q^post5 == 0 /\ p^0-p^post5 == 0 /\ -1+r^post5 == 0 /\ N^0-N^post5 == 0), cost: 1
   6: l5 -> l4 : p^0'=p^post6, r^0'=r^post6, N^0'=N^post6, q^0'=q^post6, (p^0-p^post6 == 0 /\ N^0-N^post6 == 0 /\ r^0-r^post6 == 0 /\ -q^post6+q^0 == 0), cost: 1


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

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

Applied preprocessing
Original rule:
l2 -> l0 : p^0'=p^post3, r^0'=r^post3, N^0'=N^post3, q^0'=q^post3, (0 == 0 /\ -N^post3+N^0 == 0 /\ -q^post3+q^0 == 0 /\ -r^post3+r^0 == 0 /\ 2+r^0-q^0 <= 0), cost: 1
New rule:
l2 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : p^0'=p^post4, r^0'=r^post4, N^0'=N^post4, q^0'=q^post4, (-N^post4+N^0 == 0 /\ -q^post4+q^0 == 0 /\ -r^post4+r^0 == 0 /\ -p^post4+p^0 == 0), cost: 1
New rule:
l1 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l1 : p^0'=p^post5, r^0'=r^post5, N^0'=N^post5, q^0'=q^post5, (-N^0+q^post5 == 0 /\ p^0-p^post5 == 0 /\ -1+r^post5 == 0 /\ N^0-N^post5 == 0), cost: 1
New rule:
l4 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 1

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

Simplified rules
Start location: l5
   7: l0 -> l1 : r^0'=p^0, TRUE, cost: 1
   8: l0 -> l1 : q^0'=p^0, TRUE, cost: 1
  10: l1 -> l2 : TRUE, cost: 1
   9: l2 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 1
  11: l4 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 1
  12: l5 -> l4 : TRUE, cost: 1


Eliminating location l4 by chaining:

Applied chaining
First rule:
l5 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 1
New rule:
l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2

Applied deletion
Removed the following rules: 11 12

Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 1
New rule:
l1 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 9 10

Eliminated locations on linear paths
Start location: l5
   7: l0 -> l1 : r^0'=p^0, TRUE, cost: 1
   8: l0 -> l1 : q^0'=p^0, TRUE, cost: 1
  14: l1 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 2
  13: l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 2
Second rule:
l0 -> l1 : r^0'=p^0, TRUE, cost: 1
New rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3

Applied chaining
First rule:
l1 -> l0 : p^0'=p^post3, 2+r^0-q^0 <= 0, cost: 2
Second rule:
l0 -> l1 : q^0'=p^0, TRUE, cost: 1
New rule:
l1 -> l1 : p^0'=p^post3, q^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 7 8 14

Eliminated locations on tree-shaped paths
Start location: l5
  15: l1 -> l1 : p^0'=p^post3, r^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3
  16: l1 -> l1 : p^0'=p^post3, q^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3
  13: l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3
New rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (-2+q^0-p^post3 >= 0 /\ -1+n >= 0 /\ -2-r^0+q^0 >= 0), cost: 3*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_fIMhbN.txt

Applied nonterm
Original rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3
New rule:
l1 -> [6] : (-r^0+p^post3 <= 0 /\ -2-r^0+q^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_DhEHEm.txt

Applied acceleration
Original rule:
l1 -> l1 : p^0'=p^post3, q^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3
New rule:
l1 -> l1 : p^0'=p^post3, q^0'=p^post3, (-1+n0 >= 0 /\ -2-r^0+q^0 >= 0 /\ -2-r^0+p^post3 >= 0), cost: 3*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_jBcIBJ.txt

Applied nonterm
Original rule:
l1 -> l1 : p^0'=p^post3, q^0'=p^post3, 2+r^0-q^0 <= 0, cost: 3
New rule:
l1 -> [6] : (q^0-p^post3 <= 0 /\ -2-r^0+q^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_INLJgh.txt

Applied deletion
Removed the following rules: 15 16

Accelerated simple loops
Start location: l5
  17: l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (-2+q^0-p^post3 >= 0 /\ -1+n >= 0 /\ -2-r^0+q^0 >= 0), cost: 3*n
  18: l1 -> [6] : (-r^0+p^post3 <= 0 /\ -2-r^0+q^0 >= 0), cost: NONTERM
  19: l1 -> l1 : p^0'=p^post3, q^0'=p^post3, (-1+n0 >= 0 /\ -2-r^0+q^0 >= 0 /\ -2-r^0+p^post3 >= 0), cost: 3*n0
  20: l1 -> [6] : (q^0-p^post3 <= 0 /\ -2-r^0+q^0 >= 0), cost: NONTERM
  13: l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2


Applied chaining
First rule:
l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2
Second rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (-2+q^0-p^post3 >= 0 /\ -1+n >= 0 /\ -2-r^0+q^0 >= 0), cost: 3*n
New rule:
l5 -> l1 : p^0'=p^post3, r^0'=p^post3, q^0'=N^0, (-2+N^0-p^post3 >= 0 /\ -3+N^0 >= 0 /\ -1+n >= 0), cost: 2+3*n

Applied chaining
First rule:
l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2
Second rule:
l1 -> [6] : (-r^0+p^post3 <= 0 /\ -2-r^0+q^0 >= 0), cost: NONTERM
New rule:
l5 -> [6] : -3+N^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2
Second rule:
l1 -> l1 : p^0'=p^post3, q^0'=p^post3, (-1+n0 >= 0 /\ -2-r^0+q^0 >= 0 /\ -2-r^0+p^post3 >= 0), cost: 3*n0
New rule:
l5 -> l1 : p^0'=p^post3, r^0'=1, q^0'=p^post3, (-3+N^0 >= 0 /\ -3+p^post3 >= 0 /\ -1+n0 >= 0), cost: 2+3*n0

Applied chaining
First rule:
l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2
Second rule:
l1 -> [6] : (q^0-p^post3 <= 0 /\ -2-r^0+q^0 >= 0), cost: NONTERM
New rule:
l5 -> [6] : -3+N^0 >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 17 18 19 20

Chained accelerated rules with incoming rules
Start location: l5
  13: l5 -> l1 : r^0'=1, q^0'=N^0, TRUE, cost: 2
  21: l5 -> l1 : p^0'=p^post3, r^0'=p^post3, q^0'=N^0, (-2+N^0-p^post3 >= 0 /\ -3+N^0 >= 0 /\ -1+n >= 0), cost: 2+3*n
  22: l5 -> [6] : -3+N^0 >= 0, cost: NONTERM
  23: l5 -> l1 : p^0'=p^post3, r^0'=1, q^0'=p^post3, (-3+N^0 >= 0 /\ -3+p^post3 >= 0 /\ -1+n0 >= 0), cost: 2+3*n0


Removed unreachable locations and irrelevant leafs
Start location: l5
  22: l5 -> [6] : -3+N^0 >= 0, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 22 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  -3+N^0 >= 0