NO

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


Removed unreachable rules and leafs
Start location: l4
   1: l0 -> l2 : x^0'=x^post1, y^0'=y^post1, (-y^post1+y^0 == 0 /\ -x^0+x^post1+y^0 == 0 /\ -x^0 <= 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, y^0'=y^post2, (-y^post2+y^0 == 0 /\ x^0-x^post2 == 0), cost: 1
   3: l3 -> l0 : x^0'=x^post3, y^0'=y^post3, (1+x^0+y^0 <= 0 /\ x^0-x^post3 == 0 /\ 1-x^0 <= 0 /\ y^0-y^post3 == 0), cost: 1
   4: l4 -> l3 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post4 == 0 /\ -y^post4+y^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : x^0'=x^post1, y^0'=y^post1, (-y^post1+y^0 == 0 /\ -x^0+x^post1+y^0 == 0 /\ -x^0 <= 0), cost: 1
New rule:
l0 -> l2 : x^0'=x^0-y^0, x^0 >= 0, cost: 1

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

Applied preprocessing
Original rule:
l3 -> l0 : x^0'=x^post3, y^0'=y^post3, (1+x^0+y^0 <= 0 /\ x^0-x^post3 == 0 /\ 1-x^0 <= 0 /\ y^0-y^post3 == 0), cost: 1
New rule:
l3 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post4 == 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   5: l0 -> l2 : x^0'=x^0-y^0, x^0 >= 0, cost: 1
   6: l2 -> l0 : TRUE, cost: 1
   7: l3 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 1
   8: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 1
New rule:
l4 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : x^0'=x^0-y^0, x^0 >= 0, cost: 1
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=x^0-y^0, x^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 5 6

Eliminated locations on linear paths
Start location: l4
  10: l0 -> l0 : x^0'=x^0-y^0, x^0 >= 0, cost: 2
   9: l4 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^0-y^0, x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^0-n0*y^0, (x^0 >= 0 /\ n0 >= 0 /\ x^0-y^0*(-1+n0) >= 0), cost: 2*n0

Applied recurrent set
Original rule:
l0 -> l0 : x^0'=x^0-y^0, x^0 >= 0, cost: 2
New rule:
l0 -> [5] : (x^0 >= 0 /\ 1+y^0 <= 0), cost: NONTERM

Applied fixed-point processor
Original rule:
l0 -> l0 : x^0'=x^0-y^0, x^0 >= 0, cost: 2
New rule:
l0 -> [5] : (x^0 >= 0 /\ y^0 == 0), cost: NONTERM

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  11: l0 -> l0 : x^0'=x^0-n0*y^0, (x^0 >= 0 /\ n0 >= 0 /\ x^0-y^0*(-1+n0) >= 0), cost: 2*n0
  12: l0 -> [5] : (x^0 >= 0 /\ 1+y^0 <= 0), cost: NONTERM
  13: l0 -> [5] : (x^0 >= 0 /\ y^0 == 0), cost: NONTERM
   9: l4 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2


Applied chaining
First rule:
l4 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2
Second rule:
l0 -> l0 : x^0'=x^0-n0*y^0, (x^0 >= 0 /\ n0 >= 0 /\ x^0-y^0*(-1+n0) >= 0), cost: 2*n0
New rule:
l4 -> l0 : x^0'=x^0-n0*y^0, (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0 /\ x^0-y^0*(-1+n0) >= 0), cost: 2+2*n0

Applied chaining
First rule:
l4 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2
Second rule:
l0 -> [5] : (x^0 >= 0 /\ 1+y^0 <= 0), cost: NONTERM
New rule:
l4 -> [5] : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 11 12 13

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l0 : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2
  14: l4 -> l0 : x^0'=x^0-n0*y^0, (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0 /\ x^0-y^0*(-1+n0) >= 0), cost: 2+2*n0
  15: l4 -> [5] : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM


Removed unreachable locations and irrelevant leafs
Start location: l4
  15: l4 -> [5] : (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 15 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  (1+x^0+y^0 <= 0 /\ -1+x^0 >= 0)