NO

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


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

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

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

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


Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l3 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l3
   5: l0 -> l1 : -1+x^0 >= 0, cost: 1
   6: l1 -> l0 : x^0'=z^0, y^0'=-1+y^0, TRUE, cost: 1
   7: l1 -> l0 : x^0'=-1+x^0, TRUE, cost: 1
  10: l3 -> l0 : TRUE, cost: 2


Eliminating location l1 by chaining:

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

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

Applied deletion
Removed the following rules: 5 6 7

Eliminated locations on tree-shaped paths
Start location: l3
  11: l0 -> l0 : x^0'=z^0, y^0'=-1+y^0, -1+x^0 >= 0, cost: 2
  12: l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
  10: l3 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x^0'=z^0, y^0'=-1+y^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=z^0, y^0'=-n1+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2*n1

Applied unrolling
Original rule:
l0 -> l0 : x^0'=z^0, y^0'=-1+y^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=z^0, y^0'=-2+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: 4

Applied non-termination processor
Original rule:
l0 -> l0 : x^0'=z^0, y^0'=-2+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: 4
New rule:
l0 -> [4] : (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^0-n3, (n3 >= 0 /\ x^0-n3 >= 0), cost: 2*n3

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n3, (n3 >= 0 /\ x^0-n3 >= 0), cost: 2*n3
New rule:
l0 -> l0 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0

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

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

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

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

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

Applied chaining
First rule:
l0 -> l0 : x^0'=z^0, y^0'=-1+y^0, -1+x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=z^0, y^0'=y^0-n7, (-2+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 4*n7
New rule:
l0 -> l0 : x^0'=z^0, y^0'=-1+y^0-n7, (-1+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7

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

Applied simplification
Original rule:
l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+z^0 >= 0), cost: 4*n5
New rule:
l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+z^0 >= 0), cost: 4*n5

Applied simplification
Original rule:
l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+x^0 >= 0 /\ -2+z^0 >= 0), cost: 2+4*n5
New rule:
l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+n5 >= 0 /\ -2+x^0 >= 0 /\ -2+z^0 >= 0), cost: 2+4*n5

Applied deletion
Removed the following rules: 11 12

Accelerated simple loops
Start location: l3
  13: l0 -> l0 : x^0'=z^0, y^0'=-n1+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2*n1
  14: l0 -> [4] : (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
  18: l0 -> l0 : x^0'=z^0, y^0'=y^0-n7, (-2+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 4*n7
  19: l0 -> l0 : x^0'=z^0, y^0'=-1+y^0-n7, (-1+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7
  20: l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
  21: l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+z^0 >= 0), cost: 4*n5
  22: l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+n5 >= 0 /\ -2+x^0 >= 0 /\ -2+z^0 >= 0), cost: 2+4*n5
  10: l3 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=z^0, y^0'=-n1+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2*n1
New rule:
l3 -> l0 : x^0'=z^0, y^0'=-n1+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2+2*n1

Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [4] : (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l3 -> [4] : (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=z^0, y^0'=y^0-n7, (-2+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 4*n7
New rule:
l3 -> l0 : x^0'=z^0, y^0'=y^0-n7, (-2+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7

Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=z^0, y^0'=-1+y^0-n7, (-1+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7
New rule:
l3 -> l0 : x^0'=z^0, y^0'=-1+y^0-n7, (-1+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 4+4*n7

Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
New rule:
l3 -> l0 : x^0'=0, x^0 >= 0, cost: 2+2*x^0

Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+z^0 >= 0), cost: 4*n5
New rule:
l3 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+z^0 >= 0), cost: 2+4*n5

Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+n5 >= 0 /\ -2+x^0 >= 0 /\ -2+z^0 >= 0), cost: 2+4*n5
New rule:
l3 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+n5 >= 0 /\ -2+x^0 >= 0 /\ -2+z^0 >= 0), cost: 4+4*n5

Applied deletion
Removed the following rules: 13 14 18 19 20 21 22

Chained accelerated rules with incoming rules
Start location: l3
  10: l3 -> l0 : TRUE, cost: 2
  23: l3 -> l0 : x^0'=z^0, y^0'=-n1+y^0, (-1+z^0 >= 0 /\ -1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2+2*n1
  24: l3 -> [4] : (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
  25: l3 -> l0 : x^0'=z^0, y^0'=y^0-n7, (-2+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 2+4*n7
  26: l3 -> l0 : x^0'=z^0, y^0'=-1+y^0-n7, (-1+x^0 >= 0 /\ -2+z^0 >= 0 /\ -1+n7 >= 0), cost: 4+4*n7
  27: l3 -> l0 : x^0'=0, x^0 >= 0, cost: 2+2*x^0
  28: l3 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+x^0 >= 0 /\ -1+n5 >= 0 /\ -2+z^0 >= 0), cost: 2+4*n5
  29: l3 -> l0 : x^0'=-1+z^0, y^0'=-n5+y^0, (-1+n5 >= 0 /\ -2+x^0 >= 0 /\ -2+z^0 >= 0), cost: 4+4*n5


Removed unreachable locations and irrelevant leafs
Start location: l3
  24: l3 -> [4] : (-1+z^0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 24 via SMT.

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

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