NO

Initial ITS
Start location: l5
   0: l0 -> l1 : y^0'=y^post0, x^0'=x^post0, (-x^post0+x^0 == 0 /\ y^post0-x^0 == 0 /\ 1-x^0 <= 0), cost: 1
   1: l1 -> l2 : y^0'=y^post1, x^0'=x^post1, (y^0 <= 0 /\ x^0-x^post1 == 0 /\ y^0-y^post1 == 0), cost: 1
   2: l1 -> l3 : y^0'=y^post2, x^0'=x^post2, (1-y^0 <= 0 /\ 1-y^0+y^post2 == 0 /\ x^0-x^post2 == 0), cost: 1
   4: l2 -> l0 : y^0'=y^post4, x^0'=x^post4, (x^0-x^post4 == 0 /\ -1-y^0+y^post4 == 0), cost: 1
   5: l2 -> l0 : y^0'=y^post5, x^0'=x^post5, (1+x^post5-x^0 == 0 /\ -1-y^0+y^post5 == 0), cost: 1
   3: l3 -> l1 : y^0'=y^post3, x^0'=x^post3, (y^0-y^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
   6: l4 -> l0 : y^0'=y^post6, x^0'=x^post6, (-x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
   7: l5 -> l4 : y^0'=y^post7, x^0'=x^post7, (x^0-x^post7 == 0 /\ y^0-y^post7 == 0), cost: 1


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

Applied preprocessing
Original rule:
l1 -> l2 : y^0'=y^post1, x^0'=x^post1, (y^0 <= 0 /\ x^0-x^post1 == 0 /\ y^0-y^post1 == 0), cost: 1
New rule:
l1 -> l2 : y^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l3 : y^0'=y^post2, x^0'=x^post2, (1-y^0 <= 0 /\ 1-y^0+y^post2 == 0 /\ x^0-x^post2 == 0), cost: 1
New rule:
l1 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : y^0'=y^post3, x^0'=x^post3, (y^0-y^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
New rule:
l3 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : y^0'=y^post4, x^0'=x^post4, (x^0-x^post4 == 0 /\ -1-y^0+y^post4 == 0), cost: 1
New rule:
l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : y^0'=y^post5, x^0'=x^post5, (1+x^post5-x^0 == 0 /\ -1-y^0+y^post5 == 0), cost: 1
New rule:
l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : y^0'=y^post6, x^0'=x^post6, (-x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
New rule:
l4 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : y^0'=y^post7, x^0'=x^post7, (x^0-x^post7 == 0 /\ y^0-y^post7 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Simplified rules
Start location: l5
   8: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
   9: l1 -> l2 : y^0 <= 0, cost: 1
  10: l1 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
  12: l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  11: l3 -> l1 : TRUE, cost: 1
  14: l4 -> l0 : TRUE, cost: 1
  15: l5 -> l4 : TRUE, cost: 1


Eliminating location l4 by chaining:

Applied chaining
First rule:
l5 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l0 : TRUE, cost: 1
New rule:
l5 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 14 15

Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
Second rule:
l3 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminated locations on linear paths
Start location: l5
   8: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
   9: l1 -> l2 : y^0 <= 0, cost: 1
  17: l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
  12: l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  16: l5 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
New rule:
l1 -> l1 : y^0'=-n+y^0, (n >= 0 /\ -n+y^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_HjLFDa.txt

Applied instantiation
Original rule:
l1 -> l1 : y^0'=-n+y^0, (n >= 0 /\ -n+y^0 >= 0), cost: 2*n
New rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0), cost: 2*y^0

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

Applied deletion
Removed the following rules: 17

Accelerated simple loops
Start location: l5
   8: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
   9: l1 -> l2 : y^0 <= 0, cost: 1
  19: l1 -> l1 : y^0'=0, y^0 >= 0, cost: 2*y^0
  12: l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  16: l5 -> l0 : TRUE, cost: 2


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

Applied deletion
Removed the following rules: 19

Chained accelerated rules with incoming rules
Start location: l5
   8: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
  20: l0 -> l1 : y^0'=0, -1+x^0 >= 0, cost: 1+2*x^0
   9: l1 -> l2 : y^0 <= 0, cost: 1
  12: l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  16: l5 -> l0 : TRUE, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : y^0'=0, -1+x^0 >= 0, cost: 1+2*x^0
Second rule:
l1 -> l2 : y^0 <= 0, cost: 1
New rule:
l0 -> l2 : y^0'=0, (0 <= 0 /\ -1+x^0 >= 0), cost: 2+2*x^0

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

Applied deletion
Removed the following rules: 8 9 20

Eliminated locations on tree-shaped paths
Start location: l5
  21: l0 -> l2 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0
  12: l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  16: l5 -> l0 : TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0
Second rule:
l2 -> l0 : y^0'=1+y^0, TRUE, cost: 1
New rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0

Applied chaining
First rule:
l0 -> l2 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0
Second rule:
l2 -> l0 : y^0'=1+y^0, x^0'=-1+x^0, TRUE, cost: 1
New rule:
l0 -> l0 : y^0'=1, x^0'=-1+x^0, -1+x^0 >= 0, cost: 3+2*x^0

Applied deletion
Removed the following rules: 12 13 21

Eliminated locations on tree-shaped paths
Start location: l5
  22: l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
  23: l0 -> l0 : y^0'=1, x^0'=-1+x^0, -1+x^0 >= 0, cost: 3+2*x^0
  16: l5 -> l0 : TRUE, cost: 2


Applied nonterm
Original rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
New rule:
l0 -> [7] : (-1+n0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_cOKJlb.txt

Applied acceleration
Original rule:
l0 -> l0 : y^0'=1, x^0'=-1+x^0, -1+x^0 >= 0, cost: 3+2*x^0
New rule:
l0 -> l0 : y^0'=1, x^0'=-n1+x^0, (-n1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2*n1*x^0+4*n1-n1^2
Sub-proof via acceration calculus written to file:///tmp/tmpnam_gDBOCC.txt

Applied instantiation
Original rule:
l0 -> l0 : y^0'=1, x^0'=-n1+x^0, (-n1+x^0 >= 0 /\ -1+n1 >= 0), cost: 2*n1*x^0+4*n1-n1^2
New rule:
l0 -> l0 : y^0'=1, x^0'=0, (0 >= 0 /\ -1+x^0 >= 0), cost: 4*x^0+x^0^2

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

Applied deletion
Removed the following rules: 22 23

Accelerated simple loops
Start location: l5
  24: l0 -> [7] : (-1+n0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
  26: l0 -> l0 : y^0'=1, x^0'=0, -1+x^0 >= 0, cost: 4*x^0+x^0^2
  16: l5 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [7] : (-1+n0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l5 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : y^0'=1, x^0'=0, -1+x^0 >= 0, cost: 4*x^0+x^0^2
New rule:
l5 -> l0 : y^0'=1, x^0'=0, -1+x^0 >= 0, cost: 2+4*x^0+x^0^2

Applied deletion
Removed the following rules: 24 26

Chained accelerated rules with incoming rules
Start location: l5
  16: l5 -> l0 : TRUE, cost: 2
  27: l5 -> [7] : -1+x^0 >= 0, cost: NONTERM
  28: l5 -> l0 : y^0'=1, x^0'=0, -1+x^0 >= 0, cost: 2+4*x^0+x^0^2


Removed unreachable locations and irrelevant leafs
Start location: l5
  27: l5 -> [7] : -1+x^0 >= 0, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 27 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  -1+x^0 >= 0