NO

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


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

Applied preprocessing
Original rule:
l0 -> l2 : x^0'=x^post1, z^0'=z^post1, y^0'=y^post1, (1-z^0+z^post1 == 0 /\ 2-z^0 <= 0 /\ x^0-x^post1 == 0 /\ -1-y^0+y^post1 == 0), cost: 1
New rule:
l0 -> l2 : z^0'=-1+z^0, y^0'=1+y^0, -2+z^0 >= 0, cost: 1

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

Applied preprocessing
Original rule:
l1 -> l0 : x^0'=x^post3, z^0'=z^post3, y^0'=y^post3, (y^0-y^post3 == 0 /\ 2-x^0 <= 0 /\ x^0-x^post3 == 0 /\ z^0-z^post3 == 0), cost: 1
New rule:
l1 -> l0 : -2+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : x^0'=x^post4, z^0'=z^post4, y^0'=y^post4, (z^0-z^post4 == 0 /\ y^0-y^post4 == 0 /\ x^0-x^post4 == 0), cost: 1
New rule:
l3 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : x^0'=x^post5, z^0'=z^post5, y^0'=y^post5, (x^0-x^post5 == 0 /\ z^0-z^post5 == 0 /\ y^0-y^post5 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, 0 == 0, cost: 1
   7: l0 -> l2 : z^0'=-1+z^0, y^0'=1+y^0, -2+z^0 >= 0, cost: 1
   9: l1 -> l0 : -2+x^0 >= 0, cost: 1
   8: l2 -> l0 : TRUE, cost: 1
  10: l3 -> l1 : TRUE, cost: 1
  11: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l1 : TRUE, cost: 1
New rule:
l4 -> l1 : TRUE, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l2 by chaining:

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

Applied deletion
Removed the following rules: 7 8

Eliminated locations on linear paths
Start location: l4
   6: l0 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, 0 == 0, cost: 1
  13: l0 -> l0 : z^0'=-1+z^0, y^0'=1+y^0, -2+z^0 >= 0, cost: 2
   9: l1 -> l0 : -2+x^0 >= 0, cost: 1
  12: l4 -> l1 : TRUE, cost: 2


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

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

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

Applied deletion
Removed the following rules: 13

Accelerated simple loops
Start location: l4
   6: l0 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, 0 == 0, cost: 1
  15: l0 -> l0 : z^0'=1, y^0'=-1+z^0+y^0, -1+z^0 >= 0, cost: -2+2*z^0
   9: l1 -> l0 : -2+x^0 >= 0, cost: 1
  12: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l1 -> l0 : -2+x^0 >= 0, cost: 1
Second rule:
l0 -> l0 : z^0'=1, y^0'=-1+z^0+y^0, -1+z^0 >= 0, cost: -2+2*z^0
New rule:
l1 -> l0 : z^0'=1, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: -1+2*z^0

Applied deletion
Removed the following rules: 15

Chained accelerated rules with incoming rules
Start location: l4
   6: l0 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, 0 == 0, cost: 1
   9: l1 -> l0 : -2+x^0 >= 0, cost: 1
  16: l1 -> l0 : z^0'=1, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: -1+2*z^0
  12: l4 -> l1 : TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : -2+x^0 >= 0, cost: 1
Second rule:
l0 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, 0 == 0, cost: 1
New rule:
l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, (0 == 0 /\ -2+x^0 >= 0), cost: 2

Applied simplification
Original rule:
l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, (0 == 0 /\ -2+x^0 >= 0), cost: 2
New rule:
l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, -2+x^0 >= 0, cost: 2

Applied chaining
First rule:
l1 -> l0 : z^0'=1, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: -1+2*z^0
Second rule:
l0 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, 0 == 0, cost: 1
New rule:
l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (0 == 0 /\ -1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (0 == 0 /\ -1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0
New rule:
l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0

Applied deletion
Removed the following rules: 6 9 16

Eliminated locations on tree-shaped paths
Start location: l4
  17: l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, -2+x^0 >= 0, cost: 2
  18: l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0
  12: l4 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, -2+x^0 >= 0, cost: 2
New rule:
l1 -> l1 : x^0'=x^0-n4*y^0, z^0'=z^post0, (-2+x^0-y^0*(-1+n4) >= 0 /\ -2+x^0 >= 0 /\ -1+n4 >= 0), cost: 2*n4

Applied recurrent set
Original rule:
l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, -2+x^0 >= 0, cost: 2
New rule:
l1 -> [6] : (y^0 <= 0 /\ -2+x^0 >= 0), cost: NONTERM

Applied fixed-point processor
Original rule:
l1 -> l1 : x^0'=x^0-y^0, z^0'=z^post0, -2+x^0 >= 0, cost: 2
New rule:
l1 -> [6] : (y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM

Applied fixed-point processor
Original rule:
l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0
New rule:
l1 -> [6] : (-1+z^0 >= 0 /\ -1+z^0+y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 17

Accelerated simple loops
Start location: l4
  18: l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0
  19: l1 -> l1 : x^0'=x^0-n4*y^0, z^0'=z^post0, (-2+x^0-y^0*(-1+n4) >= 0 /\ -2+x^0 >= 0 /\ -1+n4 >= 0), cost: 2*n4
  20: l1 -> [6] : (y^0 <= 0 /\ -2+x^0 >= 0), cost: NONTERM
  21: l1 -> [6] : (y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM
  22: l1 -> [6] : (-1+z^0 >= 0 /\ -1+z^0+y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM
  12: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2*z^0
New rule:
l4 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2+2*z^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=x^0-n4*y^0, z^0'=z^post0, (-2+x^0-y^0*(-1+n4) >= 0 /\ -2+x^0 >= 0 /\ -1+n4 >= 0), cost: 2*n4
New rule:
l4 -> l1 : x^0'=x^0-n4*y^0, z^0'=z^post0, (-2+x^0-y^0*(-1+n4) >= 0 /\ -2+x^0 >= 0 /\ -1+n4 >= 0), cost: 2+2*n4

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> [6] : (y^0 <= 0 /\ -2+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [6] : (y^0 <= 0 /\ -2+x^0 >= 0), cost: NONTERM

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> [6] : (y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [6] : (y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> [6] : (-1+z^0 >= 0 /\ -1+z^0+y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [6] : (-1+z^0 >= 0 /\ -1+z^0+y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 18 19 20 21 22

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l1 : TRUE, cost: 2
  23: l4 -> l1 : x^0'=1+x^0-z^0-y^0, z^0'=z^post0, y^0'=-1+z^0+y^0, (-1+z^0 >= 0 /\ -2+x^0 >= 0), cost: 2+2*z^0
  24: l4 -> l1 : x^0'=x^0-n4*y^0, z^0'=z^post0, (-2+x^0-y^0*(-1+n4) >= 0 /\ -2+x^0 >= 0 /\ -1+n4 >= 0), cost: 2+2*n4
  25: l4 -> [6] : (y^0 <= 0 /\ -2+x^0 >= 0), cost: NONTERM
  26: l4 -> [6] : (y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM
  27: l4 -> [6] : (-1+z^0 >= 0 /\ -1+z^0+y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM


Removed unreachable locations and irrelevant leafs
Start location: l4
  25: l4 -> [6] : (y^0 <= 0 /\ -2+x^0 >= 0), cost: NONTERM
  26: l4 -> [6] : (y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM
  27: l4 -> [6] : (-1+z^0 >= 0 /\ -1+z^0+y^0 == 0 /\ -2+x^0 >= 0), cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 25 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  (y^0 <= 0 /\ -2+x^0 >= 0)