NO

Initial ITS
Start location: l4
   0: l0 -> l1 : x_1^0'=x_1^post0, y_1^0'=y_1^post0, (y_1^0-y_1^post0 == 0 /\ -2+x_1^post0 == 0), cost: 1
   3: l1 -> l2 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (0 == 0 /\ x_1^0-x_1^post3 == 0), cost: 1
   4: l1 -> l3 : x_1^0'=x_1^post4, y_1^0'=y_1^post4, (x_1^0-x_1^post4 == 0 /\ 2 <= 0 /\ -y_1^post4+y_1^0 == 0), cost: 1
   1: l2 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-y_1^post1+y_1^0 == 0 /\ 1-x_1^0+x_1^post1 == 0 /\ y_1^0 <= 0), cost: 1
   2: l2 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-1-x_1^0+x_1^post2 == 0 /\ 1-y_1^0 <= 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
   5: l4 -> l0 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (y_1^0-y_1^post5 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   0: l0 -> l1 : x_1^0'=x_1^post0, y_1^0'=y_1^post0, (y_1^0-y_1^post0 == 0 /\ -2+x_1^post0 == 0), cost: 1
   3: l1 -> l2 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (0 == 0 /\ x_1^0-x_1^post3 == 0), cost: 1
   1: l2 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-y_1^post1+y_1^0 == 0 /\ 1-x_1^0+x_1^post1 == 0 /\ y_1^0 <= 0), cost: 1
   2: l2 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-1-x_1^0+x_1^post2 == 0 /\ 1-y_1^0 <= 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
   5: l4 -> l0 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (y_1^0-y_1^post5 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : x_1^0'=x_1^post0, y_1^0'=y_1^post0, (y_1^0-y_1^post0 == 0 /\ -2+x_1^post0 == 0), cost: 1
New rule:
l0 -> l1 : x_1^0'=2, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-y_1^post1+y_1^0 == 0 /\ 1-x_1^0+x_1^post1 == 0 /\ y_1^0 <= 0), cost: 1
New rule:
l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-1-x_1^0+x_1^post2 == 0 /\ 1-y_1^0 <= 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
New rule:
l2 -> l1 : x_1^0'=1+x_1^0, -1+y_1^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (0 == 0 /\ x_1^0-x_1^post3 == 0), cost: 1
New rule:
l1 -> l2 : y_1^0'=y_1^post3, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (y_1^0-y_1^post5 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1
New rule:
l4 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l1 : x_1^0'=2, TRUE, cost: 1
   9: l1 -> l2 : y_1^0'=y_1^post3, 0 == 0, cost: 1
   7: l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1
   8: l2 -> l1 : x_1^0'=1+x_1^0, -1+y_1^0 >= 0, cost: 1
  10: l4 -> l0 : TRUE, cost: 1


Eliminating location l0 by chaining:

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : x_1^0'=2, TRUE, cost: 1
New rule:
l4 -> l1 : x_1^0'=2, TRUE, cost: 2

Applied deletion
Removed the following rules: 6 10

Eliminated locations on linear paths
Start location: l4
   9: l1 -> l2 : y_1^0'=y_1^post3, 0 == 0, cost: 1
   7: l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1
   8: l2 -> l1 : x_1^0'=1+x_1^0, -1+y_1^0 >= 0, cost: 1
  11: l4 -> l1 : x_1^0'=2, TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : y_1^0'=y_1^post3, 0 == 0, cost: 1
Second rule:
l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1
New rule:
l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post3, (0 == 0 /\ y_1^post3 <= 0), cost: 2

Applied simplification
Original rule:
l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post3, (0 == 0 /\ y_1^post3 <= 0), cost: 2
New rule:
l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2

Applied chaining
First rule:
l1 -> l2 : y_1^0'=y_1^post3, 0 == 0, cost: 1
Second rule:
l2 -> l1 : x_1^0'=1+x_1^0, -1+y_1^0 >= 0, cost: 1
New rule:
l1 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^post3, (0 == 0 /\ -1+y_1^post3 >= 0), cost: 2

Applied simplification
Original rule:
l1 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^post3, (0 == 0 /\ -1+y_1^post3 >= 0), cost: 2
New rule:
l1 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2

Applied deletion
Removed the following rules: 7 8 9

Eliminated locations on tree-shaped paths
Start location: l4
  12: l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2
  13: l1 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2
  11: l4 -> l1 : x_1^0'=2, TRUE, cost: 2


Applied nonterm
Original rule:
l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2
New rule:
l1 -> [5] : -y_1^post3 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2
New rule:
l1 -> l1 : x_1^0'=x_1^0-n1, y_1^0'=y_1^post3, -y_1^post3 >= 0, cost: 2*n1

Applied nonterm
Original rule:
l1 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2
New rule:
l1 -> [5] : -1+y_1^post3 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2
New rule:
l1 -> l1 : x_1^0'=x_1^0+n3, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2*n3

Applied simplification
Original rule:
l1 -> [5] : -y_1^post3 >= 0, cost: NONTERM
New rule:
l1 -> [5] : y_1^post3 <= 0, cost: NONTERM

Applied simplification
Original rule:
l1 -> l1 : x_1^0'=x_1^0-n1, y_1^0'=y_1^post3, -y_1^post3 >= 0, cost: 2*n1
New rule:
l1 -> l1 : x_1^0'=x_1^0-n1, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2*n1

Applied deletion
Removed the following rules: 12 13

Accelerated simple loops
Start location: l4
  16: l1 -> [5] : -1+y_1^post3 >= 0, cost: NONTERM
  17: l1 -> l1 : x_1^0'=x_1^0+n3, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2*n3
  18: l1 -> [5] : y_1^post3 <= 0, cost: NONTERM
  19: l1 -> l1 : x_1^0'=x_1^0-n1, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2*n1
  11: l4 -> l1 : x_1^0'=2, TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : x_1^0'=2, TRUE, cost: 2
Second rule:
l1 -> [5] : -1+y_1^post3 >= 0, cost: NONTERM
New rule:
l4 -> [5] : TRUE, cost: NONTERM

Applied chaining
First rule:
l4 -> l1 : x_1^0'=2, TRUE, cost: 2
Second rule:
l1 -> l1 : x_1^0'=x_1^0+n3, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2*n3
New rule:
l4 -> l1 : x_1^0'=2+n3, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2+2*n3

Applied chaining
First rule:
l4 -> l1 : x_1^0'=2, TRUE, cost: 2
Second rule:
l1 -> [5] : y_1^post3 <= 0, cost: NONTERM
New rule:
l4 -> [5] : TRUE, cost: NONTERM

Applied chaining
First rule:
l4 -> l1 : x_1^0'=2, TRUE, cost: 2
Second rule:
l1 -> l1 : x_1^0'=x_1^0-n1, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2*n1
New rule:
l4 -> l1 : x_1^0'=2-n1, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2+2*n1

Applied deletion
Removed the following rules: 16 17 18 19

Chained accelerated rules with incoming rules
Start location: l4
  11: l4 -> l1 : x_1^0'=2, TRUE, cost: 2
  20: l4 -> [5] : TRUE, cost: NONTERM
  21: l4 -> l1 : x_1^0'=2+n3, y_1^0'=y_1^post3, -1+y_1^post3 >= 0, cost: 2+2*n3
  22: l4 -> [5] : TRUE, cost: NONTERM
  23: l4 -> l1 : x_1^0'=2-n1, y_1^0'=y_1^post3, y_1^post3 <= 0, cost: 2+2*n1


Removed unreachable locations and irrelevant leafs
Start location: l4
  20: l4 -> [5] : TRUE, cost: NONTERM
  22: l4 -> [5] : TRUE, cost: NONTERM


Removed duplicate rules (ignoring updates)
Start location: l4
  22: l4 -> [5] : TRUE, 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:  TRUE