NO

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


Applied preprocessing
Original rule:
l0 -> l1 : x^0'=x^post0, y^0'=y^post0, (x^0-x^post0 == 0 /\ -x^0+y^post0 == 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 : x^0'=x^post1, y^0'=y^post1, (1+y^post1-y^0 == 0 /\ 1-y^0 <= 0 /\ x^0-x^post1 == 0), cost: 1
New rule:
l1 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1

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

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

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

Applied preprocessing
Original rule:
l3 -> l0 : x^0'=x^post5, y^0'=y^post5, (1-x^0+x^post5 == 0 /\ -1-y^0+y^post5 == 0), cost: 1
New rule:
l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, TRUE, cost: 1

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

Applied preprocessing
Original rule:
l5 -> l4 : x^0'=x^post7, y^0'=y^post7, (x^0-x^post7 == 0 /\ -y^post7+y^0 == 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'=-1+y^0, -1+y^0 >= 0, cost: 1
  11: l1 -> l3 : TRUE, cost: 1
  10: l2 -> l1 : TRUE, cost: 1
  12: l3 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, 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 l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
Second rule:
l2 -> 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: 9 10

Eliminated locations on linear paths
Start location: l5
   8: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
  11: l1 -> l3 : TRUE, cost: 1
  17: l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
  12: l3 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^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'=-n0+y^0, (n0 >= 0 /\ -n0+y^0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l1 -> l1 : y^0'=-n0+y^0, (n0 >= 0 /\ -n0+y^0 >= 0), cost: 2*n0
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
  11: l1 -> l3 : TRUE, cost: 1
  19: l1 -> l1 : y^0'=0, y^0 >= 0, cost: 2*y^0
  12: l3 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^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
  11: l1 -> l3 : TRUE, cost: 1
  12: l3 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, TRUE, cost: 1
  16: l5 -> l0 : TRUE, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
Second rule:
l1 -> l3 : TRUE, cost: 1
New rule:
l0 -> l3 : y^0'=x^0, -1+x^0 >= 0, cost: 2

Applied chaining
First rule:
l0 -> l1 : y^0'=0, -1+x^0 >= 0, cost: 1+2*x^0
Second rule:
l1 -> l3 : TRUE, cost: 1
New rule:
l0 -> l3 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0

Applied deletion
Removed the following rules: 8 11 20

Eliminated locations on tree-shaped paths
Start location: l5
  21: l0 -> l3 : y^0'=x^0, -1+x^0 >= 0, cost: 2
  22: l0 -> l3 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0
  12: l3 -> l0 : y^0'=1+y^0, TRUE, cost: 1
  13: l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, TRUE, cost: 1
  16: l5 -> l0 : TRUE, cost: 2


Eliminating location l3 by chaining:

Applied chaining
First rule:
l0 -> l3 : y^0'=x^0, -1+x^0 >= 0, cost: 2
Second rule:
l3 -> l0 : y^0'=1+y^0, TRUE, cost: 1
New rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3

Applied chaining
First rule:
l0 -> l3 : y^0'=x^0, -1+x^0 >= 0, cost: 2
Second rule:
l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=-1+x^0, y^0'=1+x^0, -1+x^0 >= 0, cost: 3

Applied chaining
First rule:
l0 -> l3 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0
Second rule:
l3 -> 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 -> l3 : y^0'=0, -1+x^0 >= 0, cost: 2+2*x^0
Second rule:
l3 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=-1+x^0, y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0

Applied deletion
Removed the following rules: 12 13 21 22

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


Applied nonterm
Original rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3
New rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3
New rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3*n6

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, y^0'=1+x^0, -1+x^0 >= 0, cost: 3
New rule:
l0 -> l0 : x^0'=x^0-n8, y^0'=2+x^0-n8, (x^0-n8 >= 0 /\ -1+n8 >= 0), cost: 3*n8

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n8, y^0'=2+x^0-n8, (x^0-n8 >= 0 /\ -1+n8 >= 0), cost: 3*n8
New rule:
l0 -> l0 : x^0'=0, y^0'=2, (0 >= 0 /\ -1+x^0 >= 0), cost: 3*x^0

Applied nonterm
Original rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
New rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
New rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n10+3*n10

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
New rule:
l0 -> l0 : x^0'=x^0-n12, y^0'=1, (-1+n12 >= 0 /\ x^0-n12 >= 0), cost: 2*x^0*n12+4*n12-n12^2

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n12, y^0'=1, (-1+n12 >= 0 /\ x^0-n12 >= 0), cost: 2*x^0*n12+4*n12-n12^2
New rule:
l0 -> l0 : x^0'=0, y^0'=1, (0 >= 0 /\ -1+x^0 >= 0), cost: 4*x^0+x^0^2

Applied chaining
First rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3
Second rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
New rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 6+2*x^0

Applied nonterm
Original rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 6+2*x^0
New rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 6+2*x^0
New rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n16+6*n16

Applied chaining
First rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
Second rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM
New rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
Second rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n16+6*n16
New rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0+2*x^0*n16+6*n16

Applied chaining
First rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0
Second rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3
New rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 6+2*x^0

Applied nonterm
Original rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 6+2*x^0
New rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 6+2*x^0
New rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 6*n26+2*x^0*n26

Applied chaining
First rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3
Second rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM
New rule:
l0 -> [7] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3
Second rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 6*n26+2*x^0*n26
New rule:
l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3+6*n26+2*x^0*n26

Applied simplification
Original rule:
l0 -> l0 : x^0'=0, y^0'=2, (0 >= 0 /\ -1+x^0 >= 0), cost: 3*x^0
New rule:
l0 -> l0 : x^0'=0, y^0'=2, -1+x^0 >= 0, cost: 3*x^0

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

Applied deletion
Removed the following rules: 23 24 25 26

Applied deletion
Removed the following rules: 27 30 33 34 37 39

Accelerated simple loops
Start location: l5
  28: l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3*n6
  31: l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n10+3*n10
  35: l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n16+6*n16
  36: l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0+2*x^0*n16+6*n16
  38: l0 -> [7] : -1+x^0 >= 0, cost: NONTERM
  40: l0 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3+6*n26+2*x^0*n26
  41: l0 -> l0 : x^0'=0, y^0'=2, -1+x^0 >= 0, cost: 3*x^0
  42: l0 -> l0 : x^0'=0, y^0'=1, -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 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 3*n6
New rule:
l5 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 2+3*n6

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n10+3*n10
New rule:
l5 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2+2*x^0*n10+3*n10

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2*x^0*n16+6*n16
New rule:
l5 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2+2*x^0*n16+6*n16

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 3+2*x^0+2*x^0*n16+6*n16
New rule:
l5 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 5+2*x^0+2*x^0*n16+6*n16

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [7] : -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, -1+x^0 >= 0, cost: 3+6*n26+2*x^0*n26
New rule:
l5 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 5+6*n26+2*x^0*n26

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=0, y^0'=2, -1+x^0 >= 0, cost: 3*x^0
New rule:
l5 -> l0 : x^0'=0, y^0'=2, -1+x^0 >= 0, cost: 2+3*x^0

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

Applied deletion
Removed the following rules: 28 31 35 36 38 40 41 42

Chained accelerated rules with incoming rules
Start location: l5
  16: l5 -> l0 : TRUE, cost: 2
  43: l5 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 2+3*n6
  44: l5 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2+2*x^0*n10+3*n10
  45: l5 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 2+2*x^0*n16+6*n16
  46: l5 -> l0 : y^0'=1, -1+x^0 >= 0, cost: 5+2*x^0+2*x^0*n16+6*n16
  47: l5 -> [7] : -1+x^0 >= 0, cost: NONTERM
  48: l5 -> l0 : y^0'=1+x^0, -1+x^0 >= 0, cost: 5+6*n26+2*x^0*n26
  49: l5 -> l0 : x^0'=0, y^0'=2, -1+x^0 >= 0, cost: 2+3*x^0
  50: l5 -> l0 : x^0'=0, y^0'=1, -1+x^0 >= 0, cost: 2+4*x^0+x^0^2


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


Computing asymptotic complexity
Proved nontermination of rule 47 via SMT.

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

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