NO

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


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


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

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

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

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

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

Applied preprocessing
Original rule:
l5 -> l4 : N^0'=N^post6, q^0'=q^post6, p^0'=p^post6, r^0'=r^post6, (q^0-q^post6 == 0 /\ r^0-r^post6 == 0 /\ N^0-N^post6 == 0 /\ -p^post6+p^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-q^0+r^0 <= 0, cost: 1
  11: l4 -> l1 : q^0'=N^0, r^0'=1, 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 : q^0'=N^0, r^0'=1, TRUE, cost: 1
New rule:
l5 -> l1 : q^0'=N^0, r^0'=1, 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-q^0+r^0 <= 0, cost: 1
New rule:
l1 -> l0 : p^0'=p^post3, 2-q^0+r^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-q^0+r^0 <= 0, cost: 2
  13: l5 -> l1 : q^0'=N^0, r^0'=1, TRUE, cost: 2


Eliminating location l0 by chaining:

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

Applied chaining
First rule:
l1 -> l0 : p^0'=p^post3, 2-q^0+r^0 <= 0, cost: 2
Second rule:
l0 -> l1 : q^0'=p^0, TRUE, cost: 1
New rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, 2-q^0+r^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-q^0+r^0 <= 0, cost: 3
  16: l1 -> l1 : q^0'=p^post3, p^0'=p^post3, 2-q^0+r^0 <= 0, cost: 3
  13: l5 -> l1 : q^0'=N^0, r^0'=1, TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, 2-q^0+r^0 <= 0, cost: 3
New rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (-2+q^0-p^post3 >= 0 /\ -2+q^0-r^0 >= 0 /\ -1+n1 >= 0), cost: 3*n1

Applied unrolling
Original rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, 2-q^0+r^0 <= 0, cost: 3
New rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (2-q^0+p^post3 <= 0 /\ 2-q^0+r^0 <= 0), cost: 6

Applied non-termination processor
Original rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (2-q^0+p^post3 <= 0 /\ 2-q^0+r^0 <= 0), cost: 6
New rule:
l1 -> [6] : (2-q^0+p^post3 <= 0 /\ 2-q^0+r^0 <= 0), cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, 2-q^0+r^0 <= 0, cost: 3
New rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, (-2+q^0-r^0 >= 0 /\ -2+p^post3-r^0 >= 0 /\ -1+n3 >= 0), cost: 3*n3

Applied unrolling
Original rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, 2-q^0+r^0 <= 0, cost: 3
New rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, (2-q^0+r^0 <= 0 /\ 2-p^post3+r^0 <= 0), cost: 6

Applied non-termination processor
Original rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, (2-q^0+r^0 <= 0 /\ 2-p^post3+r^0 <= 0), cost: 6
New rule:
l1 -> [6] : (2-q^0+r^0 <= 0 /\ 2-p^post3+r^0 <= 0), cost: NONTERM

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 /\ -2+q^0-r^0 >= 0 /\ -1+n1 >= 0), cost: 3*n1
  18: l1 -> [6] : (2-q^0+p^post3 <= 0 /\ 2-q^0+r^0 <= 0), cost: NONTERM
  19: l1 -> l1 : q^0'=p^post3, p^0'=p^post3, (-2+q^0-r^0 >= 0 /\ -2+p^post3-r^0 >= 0 /\ -1+n3 >= 0), cost: 3*n3
  20: l1 -> [6] : (2-q^0+r^0 <= 0 /\ 2-p^post3+r^0 <= 0), cost: NONTERM
  13: l5 -> l1 : q^0'=N^0, r^0'=1, TRUE, cost: 2


Applied chaining
First rule:
l5 -> l1 : q^0'=N^0, r^0'=1, TRUE, cost: 2
Second rule:
l1 -> l1 : p^0'=p^post3, r^0'=p^post3, (-2+q^0-p^post3 >= 0 /\ -2+q^0-r^0 >= 0 /\ -1+n1 >= 0), cost: 3*n1
New rule:
l5 -> l1 : q^0'=N^0, p^0'=p^post3, r^0'=p^post3, (-3+N^0 >= 0 /\ -1+n1 >= 0 /\ -2+N^0-p^post3 >= 0), cost: 2+3*n1

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

Applied chaining
First rule:
l5 -> l1 : q^0'=N^0, r^0'=1, TRUE, cost: 2
Second rule:
l1 -> l1 : q^0'=p^post3, p^0'=p^post3, (-2+q^0-r^0 >= 0 /\ -2+p^post3-r^0 >= 0 /\ -1+n3 >= 0), cost: 3*n3
New rule:
l5 -> l1 : q^0'=p^post3, p^0'=p^post3, r^0'=1, (-3+N^0 >= 0 /\ -3+p^post3 >= 0 /\ -1+n3 >= 0), cost: 2+3*n3

Applied chaining
First rule:
l5 -> l1 : q^0'=N^0, r^0'=1, TRUE, cost: 2
Second rule:
l1 -> [6] : (2-q^0+r^0 <= 0 /\ 2-p^post3+r^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 : q^0'=N^0, r^0'=1, TRUE, cost: 2
  21: l5 -> l1 : q^0'=N^0, p^0'=p^post3, r^0'=p^post3, (-3+N^0 >= 0 /\ -1+n1 >= 0 /\ -2+N^0-p^post3 >= 0), cost: 2+3*n1
  22: l5 -> [6] : -3+N^0 >= 0, cost: NONTERM
  23: l5 -> l1 : q^0'=p^post3, p^0'=p^post3, r^0'=1, (-3+N^0 >= 0 /\ -3+p^post3 >= 0 /\ -1+n3 >= 0), cost: 2+3*n3
  24: l5 -> [6] : -3+N^0 >= 0, cost: NONTERM


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


Removed duplicate rules (ignoring updates)
Start location: l5
  24: l5 -> [6] : -3+N^0 >= 0, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 24 via SMT.

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

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