NO

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


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

Applied preprocessing
Original rule:
l1 -> l0 : y^0'=y^post1, x^0'=x^post1, z^0'=z^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 : y^0'=y^post2, x^0'=x^post2, z^0'=z^post2, (x^post2-x^0-z^0 == 0 /\ 2-z^0+z^post2 == 0 /\ -1-y^0+y^post2 == 0), cost: 1
New rule:
l0 -> l2 : y^0'=1+y^0, x^0'=x^0+z^0, z^0'=-2+z^0, TRUE, cost: 1

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

Applied preprocessing
Original rule:
l3 -> l0 : y^0'=y^post4, x^0'=x^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -z^post4+z^0 == 0 /\ -x^0 <= 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l3 -> l0 : x^0 >= 0, cost: 1

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

Simplified rules
Start location: l4
   6: l0 -> l1 : y^0'=-2+y^0, x^0'=y^0+x^0, TRUE, cost: 1
   8: l0 -> l2 : y^0'=1+y^0, x^0'=x^0+z^0, z^0'=-2+z^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 : y^0'=-2+y^0, x^0'=y^0+x^0, TRUE, cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : y^0'=-2+y^0, x^0'=y^0+x^0, TRUE, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l2 by chaining:

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

Applied deletion
Removed the following rules: 8 9

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


Applied nonterm
Original rule:
l0 -> l0 : y^0'=-2+y^0, x^0'=y^0+x^0, TRUE, cost: 2
New rule:
l0 -> [5] : n >= 0, cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_hPfcaB.txt

Applied nonterm
Original rule:
l0 -> l0 : y^0'=1+y^0, x^0'=x^0+z^0, z^0'=-2+z^0, TRUE, cost: 2
New rule:
l0 -> [5] : n0 >= 0, cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_BElaNf.txt

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

Applied nonterm
Original rule:
l0 -> l0 : y^0'=-1+y^0, x^0'=1+y^0+x^0+z^0, z^0'=-2+z^0, TRUE, cost: 4
New rule:
l0 -> [5] : n1 >= 0, cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_dNcBeG.txt

Applied chaining
First rule:
l0 -> l0 : y^0'=-2+y^0, x^0'=y^0+x^0, TRUE, cost: 2
Second rule:
l0 -> [5] : n1 >= 0, cost: NONTERM
New rule:
l0 -> [5] : n1 >= 0, cost: NONTERM

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

Applied nonterm
Original rule:
l0 -> l0 : y^0'=-1+y^0, x^0'=y^0+x^0+z^0, z^0'=-2+z^0, TRUE, cost: 4
New rule:
l0 -> [5] : n2 >= 0, cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_oPnNca.txt

Applied chaining
First rule:
l0 -> l0 : y^0'=1+y^0, x^0'=x^0+z^0, z^0'=-2+z^0, TRUE, cost: 2
Second rule:
l0 -> [5] : n2 >= 0, cost: NONTERM
New rule:
l0 -> [5] : n2 >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 13 14

Accelerated simple loops
Start location: l4
  15: l0 -> [5] : n >= 0, cost: NONTERM
  16: l0 -> [5] : n0 >= 0, cost: NONTERM
  17: l0 -> [5] : n1 >= 0, cost: NONTERM
  18: l0 -> [5] : n2 >= 0, cost: NONTERM
  12: l4 -> l0 : x^0 >= 0, cost: 2


Applied chaining
First rule:
l4 -> l0 : x^0 >= 0, cost: 2
Second rule:
l0 -> [5] : n >= 0, 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 -> [5] : n0 >= 0, 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 -> [5] : n1 >= 0, 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 -> [5] : n2 >= 0, cost: NONTERM
New rule:
l4 -> [5] : x^0 >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 15 16 17 18

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : x^0 >= 0, cost: 2
  19: l4 -> [5] : x^0 >= 0, cost: NONTERM


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


Computing asymptotic complexity
Proved nontermination of rule 19 via SMT.

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

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