NO

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

Applied preprocessing
Original rule:
l1 -> l0 : x^0'=x^post1, z^0'=z^post1, y^0'=y^post1, (z^0-z^post1 == 0 /\ x^0-x^post1 == 0 /\ y^0-y^post1 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l0 -> l2 : x^0'=x^post2, z^0'=z^post2, y^0'=y^post2, (2-z^0+z^post2 == 0 /\ -x^0+x^post2-z^0 == 0 /\ -1-y^0+y^post2 == 0), cost: 1
New rule:
l0 -> l2 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post3, z^0'=z^post3, y^0'=y^post3, (y^0-y^post3 == 0 /\ x^0-x^post3 == 0 /\ z^0-z^post3 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : x^0'=x^post4, z^0'=z^post4, y^0'=y^post4, (-x^0 <= 0 /\ z^0-z^post4 == 0 /\ y^0-y^post4 == 0 /\ x^0-x^post4 == 0), cost: 1
New rule:
l3 -> l0 : x^0 >= 0, 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, y^0'=-2+y^0, TRUE, cost: 1
   8: l0 -> l2 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 1
   7: l1 -> l0 : TRUE, cost: 1
   9: l2 -> l0 : TRUE, cost: 1
  10: l3 -> l0 : x^0 >= 0, 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 -> l0 : x^0 >= 0, cost: 1
New rule:
l4 -> l0 : x^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 6 7

Eliminating location l2 by chaining:

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

Applied deletion
Removed the following rules: 8 9

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


Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^0+y^0, y^0'=-2+y^0, TRUE, cost: 2
New rule:
l0 -> [5] : TRUE, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^0+y^0, y^0'=-2+y^0, TRUE, cost: 2
New rule:
l0 -> l0 : x^0'=x^0+n1+n1*y^0-n1^2, y^0'=-2*n1+y^0, TRUE, cost: 2*n1

Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 2
New rule:
l0 -> [5] : TRUE, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 2
New rule:
l0 -> l0 : x^0'=x^0-n3^2+z^0*n3+n3, z^0'=z^0-2*n3, y^0'=y^0+n3, TRUE, cost: 2*n3

Applied chaining
First rule:
l0 -> l0 : x^0'=x^0+y^0, y^0'=-2+y^0, TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 2
New rule:
l0 -> l0 : x^0'=x^0+z^0+y^0, z^0'=-2+z^0, y^0'=-1+y^0, TRUE, cost: 4

Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^0+z^0+y^0, z^0'=-2+z^0, y^0'=-1+y^0, TRUE, cost: 4
New rule:
l0 -> [5] : TRUE, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^0+z^0+y^0, z^0'=-2+z^0, y^0'=-1+y^0, TRUE, cost: 4
New rule:
l0 -> l0 : x^0'=x^0+n5*y^0+3/2*n5-3/2*n5^2+z^0*n5, z^0'=z^0-2*n5, y^0'=-n5+y^0, TRUE, cost: 4*n5

Applied chaining
First rule:
l0 -> l0 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 2
Second rule:
l0 -> [5] : TRUE, cost: NONTERM
New rule:
l0 -> [5] : TRUE, cost: NONTERM

Applied chaining
First rule:
l0 -> l0 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+n5*y^0+3/2*n5-3/2*n5^2+z^0*n5, z^0'=z^0-2*n5, y^0'=-n5+y^0, TRUE, cost: 4*n5
New rule:
l0 -> l0 : x^0'=x^0+n5*(1+y^0)+z^0+3/2*n5-3/2*n5^2+n5*(-2+z^0), z^0'=-2+z^0-2*n5, y^0'=1-n5+y^0, TRUE, cost: 2+4*n5

Applied chaining
First rule:
l0 -> l0 : x^0'=x^0+z^0, z^0'=-2+z^0, y^0'=1+y^0, TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+y^0, y^0'=-2+y^0, TRUE, cost: 2
New rule:
l0 -> l0 : x^0'=1+x^0+z^0+y^0, z^0'=-2+z^0, y^0'=-1+y^0, TRUE, cost: 4

Applied nonterm
Original rule:
l0 -> l0 : x^0'=1+x^0+z^0+y^0, z^0'=-2+z^0, y^0'=-1+y^0, TRUE, cost: 4
New rule:
l0 -> [5] : TRUE, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : x^0'=1+x^0+z^0+y^0, z^0'=-2+z^0, y^0'=-1+y^0, TRUE, cost: 4
New rule:
l0 -> l0 : x^0'=x^0+5/2*n7+n7*y^0+n7*z^0-3/2*n7^2, z^0'=-2*n7+z^0, y^0'=-n7+y^0, TRUE, cost: 4*n7

Applied chaining
First rule:
l0 -> l0 : x^0'=x^0+y^0, y^0'=-2+y^0, TRUE, cost: 2
Second rule:
l0 -> [5] : TRUE, cost: NONTERM
New rule:
l0 -> [5] : TRUE, cost: NONTERM

Applied chaining
First rule:
l0 -> l0 : x^0'=x^0+y^0, y^0'=-2+y^0, TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+5/2*n7+n7*y^0+n7*z^0-3/2*n7^2, z^0'=-2*n7+z^0, y^0'=-n7+y^0, TRUE, cost: 4*n7
New rule:
l0 -> l0 : x^0'=x^0+n7*(-2+y^0)+5/2*n7+n7*z^0-3/2*n7^2+y^0, z^0'=-2*n7+z^0, y^0'=-2-n7+y^0, TRUE, cost: 2+4*n7

Applied deletion
Removed the following rules: 13 14

Applied deletion
Removed the following rules: 15 17 19 20 23

Accelerated simple loops
Start location: l4
  16: l0 -> l0 : x^0'=x^0+n1+n1*y^0-n1^2, y^0'=-2*n1+y^0, TRUE, cost: 2*n1
  18: l0 -> l0 : x^0'=x^0-n3^2+z^0*n3+n3, z^0'=z^0-2*n3, y^0'=y^0+n3, TRUE, cost: 2*n3
  21: l0 -> l0 : x^0'=x^0+n5*y^0+3/2*n5-3/2*n5^2+z^0*n5, z^0'=z^0-2*n5, y^0'=-n5+y^0, TRUE, cost: 4*n5
  22: l0 -> l0 : x^0'=x^0+n5*(1+y^0)+z^0+3/2*n5-3/2*n5^2+n5*(-2+z^0), z^0'=-2+z^0-2*n5, y^0'=1-n5+y^0, TRUE, cost: 2+4*n5
  24: l0 -> [5] : TRUE, cost: NONTERM
  25: l0 -> l0 : x^0'=x^0+5/2*n7+n7*y^0+n7*z^0-3/2*n7^2, z^0'=-2*n7+z^0, y^0'=-n7+y^0, TRUE, cost: 4*n7
  26: l0 -> l0 : x^0'=x^0+n7*(-2+y^0)+5/2*n7+n7*z^0-3/2*n7^2+y^0, z^0'=-2*n7+z^0, y^0'=-2-n7+y^0, TRUE, cost: 2+4*n7
  12: l4 -> l0 : x^0 >= 0, cost: 2


Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+n1+n1*y^0-n1^2, y^0'=-2*n1+y^0, TRUE, cost: 2*n1
New rule:
l4 -> l0 : x^0'=x^0+n1+n1*y^0-n1^2, y^0'=-2*n1+y^0, x^0 >= 0, cost: 2+2*n1

Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0-n3^2+z^0*n3+n3, z^0'=z^0-2*n3, y^0'=y^0+n3, TRUE, cost: 2*n3
New rule:
l4 -> l0 : x^0'=x^0-n3^2+z^0*n3+n3, z^0'=z^0-2*n3, y^0'=y^0+n3, x^0 >= 0, cost: 2+2*n3

Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+n5*y^0+3/2*n5-3/2*n5^2+z^0*n5, z^0'=z^0-2*n5, y^0'=-n5+y^0, TRUE, cost: 4*n5
New rule:
l4 -> l0 : x^0'=x^0+n5*y^0+3/2*n5-3/2*n5^2+z^0*n5, z^0'=z^0-2*n5, y^0'=-n5+y^0, x^0 >= 0, cost: 2+4*n5

Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+n5*(1+y^0)+z^0+3/2*n5-3/2*n5^2+n5*(-2+z^0), z^0'=-2+z^0-2*n5, y^0'=1-n5+y^0, TRUE, cost: 2+4*n5
New rule:
l4 -> l0 : x^0'=x^0+n5*(1+y^0)+z^0+3/2*n5-3/2*n5^2+n5*(-2+z^0), z^0'=-2+z^0-2*n5, y^0'=1-n5+y^0, x^0 >= 0, cost: 4+4*n5

Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> [5] : TRUE, cost: NONTERM
New rule:
l4 -> [5] : x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+5/2*n7+n7*y^0+n7*z^0-3/2*n7^2, z^0'=-2*n7+z^0, y^0'=-n7+y^0, TRUE, cost: 4*n7
New rule:
l4 -> l0 : x^0'=x^0+5/2*n7+n7*y^0+n7*z^0-3/2*n7^2, z^0'=-2*n7+z^0, y^0'=-n7+y^0, x^0 >= 0, cost: 2+4*n7

Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^0+n7*(-2+y^0)+5/2*n7+n7*z^0-3/2*n7^2+y^0, z^0'=-2*n7+z^0, y^0'=-2-n7+y^0, TRUE, cost: 2+4*n7
New rule:
l4 -> l0 : x^0'=x^0+n7*(-2+y^0)+5/2*n7+n7*z^0-3/2*n7^2+y^0, z^0'=-2*n7+z^0, y^0'=-2-n7+y^0, x^0 >= 0, cost: 4+4*n7

Applied deletion
Removed the following rules: 16 18 21 22 24 25 26

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : x^0 >= 0, cost: 2
  27: l4 -> l0 : x^0'=x^0+n1+n1*y^0-n1^2, y^0'=-2*n1+y^0, x^0 >= 0, cost: 2+2*n1
  28: l4 -> l0 : x^0'=x^0-n3^2+z^0*n3+n3, z^0'=z^0-2*n3, y^0'=y^0+n3, x^0 >= 0, cost: 2+2*n3
  29: l4 -> l0 : x^0'=x^0+n5*y^0+3/2*n5-3/2*n5^2+z^0*n5, z^0'=z^0-2*n5, y^0'=-n5+y^0, x^0 >= 0, cost: 2+4*n5
  30: l4 -> l0 : x^0'=x^0+n5*(1+y^0)+z^0+3/2*n5-3/2*n5^2+n5*(-2+z^0), z^0'=-2+z^0-2*n5, y^0'=1-n5+y^0, x^0 >= 0, cost: 4+4*n5
  31: l4 -> [5] : x^0 >= 0, cost: NONTERM
  32: l4 -> l0 : x^0'=x^0+5/2*n7+n7*y^0+n7*z^0-3/2*n7^2, z^0'=-2*n7+z^0, y^0'=-n7+y^0, x^0 >= 0, cost: 2+4*n7
  33: l4 -> l0 : x^0'=x^0+n7*(-2+y^0)+5/2*n7+n7*z^0-3/2*n7^2+y^0, z^0'=-2*n7+z^0, y^0'=-2-n7+y^0, x^0 >= 0, cost: 4+4*n7


Removed unreachable locations and irrelevant leafs
Start location: l4
  31: l4 -> [5] : x^0 >= 0, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 31 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  x^0 >= 0