NO

Initial ITS
Start location: l7
   0: l0 -> l1 : j^0'=j^post0, y^0'=y^post0, i^0'=i^post0, x^0'=x^post0, (1-x^0+x^post0 == 0 /\ j^0-j^post0 == 0 /\ 1-y^0+y^post0 == 0 /\ i^0-i^post0 == 0), cost: 1
   4: l1 -> l2 : j^0'=j^post4, y^0'=y^post4, i^0'=i^post4, x^0'=x^post4, (-i^post4+i^0 == 0 /\ -x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -j^post4+j^0 == 0), cost: 1
   1: l2 -> l3 : j^0'=j^post1, y^0'=y^post1, i^0'=i^post1, x^0'=x^post1, (i^0-i^post1 == 0 /\ -x^0 <= 0 /\ y^0-y^post1 == 0 /\ j^0-j^post1 == 0 /\ x^0 <= 0 /\ -x^post1+x^0 == 0), cost: 1
   2: l2 -> l0 : j^0'=j^post2, y^0'=y^post2, i^0'=i^post2, x^0'=x^post2, (-y^post2+y^0 == 0 /\ j^0-j^post2 == 0 /\ 1-x^0 <= 0 /\ -i^post2+i^0 == 0 /\ -x^post2+x^0 == 0), cost: 1
   3: l2 -> l0 : j^0'=j^post3, y^0'=y^post3, i^0'=i^post3, x^0'=x^post3, (-i^post3+i^0 == 0 /\ -x^post3+x^0 == 0 /\ -y^post3+y^0 == 0 /\ j^0-j^post3 == 0 /\ 1+x^0 <= 0), cost: 1
   6: l3 -> l4 : j^0'=j^post6, y^0'=y^post6, i^0'=i^post6, x^0'=x^post6, (j^0-j^post6 == 0 /\ 1+j^0-i^0 <= 0 /\ i^0-i^post6 == 0 /\ y^0-y^post6 == 0 /\ -x^post6+x^0 == 0), cost: 1
   7: l3 -> l4 : j^0'=j^post7, y^0'=y^post7, i^0'=i^post7, x^0'=x^post7, (-x^post7+x^0 == 0 /\ 1-j^0+i^0 <= 0 /\ -i^post7+i^0 == 0 /\ -y^post7+y^0 == 0 /\ j^0-j^post7 == 0), cost: 1
   8: l3 -> l4 : j^0'=j^post8, y^0'=y^post8, i^0'=i^post8, x^0'=x^post8, (j^0-i^0 <= 0 /\ x^0-x^post8 == 0 /\ -j^0+i^0 <= 0 /\ -i^post8+i^0 == 0 /\ -j^post8+j^0 == 0 /\ y^0-y^post8 == 0), cost: 1
   5: l4 -> l5 : j^0'=j^post5, y^0'=y^post5, i^0'=i^post5, x^0'=x^post5, (y^0-y^post5 == 0 /\ x^0-x^post5 == 0 /\ j^0-j^post5 == 0 /\ i^0-i^post5 == 0), cost: 1
   9: l6 -> l1 : j^0'=j^post9, y^0'=y^post9, i^0'=i^post9, x^0'=x^post9, (-j^0+y^post9 == 0 /\ j^0-j^post9 == 0 /\ x^post9-i^0 == 0 /\ i^0-i^post9 == 0), cost: 1
  10: l7 -> l6 : j^0'=j^post10, y^0'=y^post10, i^0'=i^post10, x^0'=x^post10, (j^0-j^post10 == 0 /\ i^0-i^post10 == 0 /\ -x^post10+x^0 == 0 /\ y^0-y^post10 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l7
   0: l0 -> l1 : j^0'=j^post0, y^0'=y^post0, i^0'=i^post0, x^0'=x^post0, (1-x^0+x^post0 == 0 /\ j^0-j^post0 == 0 /\ 1-y^0+y^post0 == 0 /\ i^0-i^post0 == 0), cost: 1
   4: l1 -> l2 : j^0'=j^post4, y^0'=y^post4, i^0'=i^post4, x^0'=x^post4, (-i^post4+i^0 == 0 /\ -x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -j^post4+j^0 == 0), cost: 1
   2: l2 -> l0 : j^0'=j^post2, y^0'=y^post2, i^0'=i^post2, x^0'=x^post2, (-y^post2+y^0 == 0 /\ j^0-j^post2 == 0 /\ 1-x^0 <= 0 /\ -i^post2+i^0 == 0 /\ -x^post2+x^0 == 0), cost: 1
   3: l2 -> l0 : j^0'=j^post3, y^0'=y^post3, i^0'=i^post3, x^0'=x^post3, (-i^post3+i^0 == 0 /\ -x^post3+x^0 == 0 /\ -y^post3+y^0 == 0 /\ j^0-j^post3 == 0 /\ 1+x^0 <= 0), cost: 1
   9: l6 -> l1 : j^0'=j^post9, y^0'=y^post9, i^0'=i^post9, x^0'=x^post9, (-j^0+y^post9 == 0 /\ j^0-j^post9 == 0 /\ x^post9-i^0 == 0 /\ i^0-i^post9 == 0), cost: 1
  10: l7 -> l6 : j^0'=j^post10, y^0'=y^post10, i^0'=i^post10, x^0'=x^post10, (j^0-j^post10 == 0 /\ i^0-i^post10 == 0 /\ -x^post10+x^0 == 0 /\ y^0-y^post10 == 0), cost: 1


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

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

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

Applied preprocessing
Original rule:
l1 -> l2 : j^0'=j^post4, y^0'=y^post4, i^0'=i^post4, x^0'=x^post4, (-i^post4+i^0 == 0 /\ -x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -j^post4+j^0 == 0), cost: 1
New rule:
l1 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l1 : j^0'=j^post9, y^0'=y^post9, i^0'=i^post9, x^0'=x^post9, (-j^0+y^post9 == 0 /\ j^0-j^post9 == 0 /\ x^post9-i^0 == 0 /\ i^0-i^post9 == 0), cost: 1
New rule:
l6 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : j^0'=j^post10, y^0'=y^post10, i^0'=i^post10, x^0'=x^post10, (j^0-j^post10 == 0 /\ i^0-i^post10 == 0 /\ -x^post10+x^0 == 0 /\ y^0-y^post10 == 0), cost: 1
New rule:
l7 -> l6 : TRUE, cost: 1

Simplified rules
Start location: l7
  11: l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  14: l1 -> l2 : TRUE, cost: 1
  12: l2 -> l0 : -1+x^0 >= 0, cost: 1
  13: l2 -> l0 : 1+x^0 <= 0, cost: 1
  15: l6 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 1
  16: l7 -> l6 : TRUE, cost: 1


Eliminating location l6 by chaining:

Applied chaining
First rule:
l7 -> l6 : TRUE, cost: 1
Second rule:
l6 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 1
New rule:
l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2

Applied deletion
Removed the following rules: 15 16

Eliminated locations on linear paths
Start location: l7
  11: l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  14: l1 -> l2 : TRUE, cost: 1
  12: l2 -> l0 : -1+x^0 >= 0, cost: 1
  13: l2 -> l0 : 1+x^0 <= 0, cost: 1
  17: l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : -1+x^0 >= 0, cost: 1
New rule:
l1 -> l0 : -1+x^0 >= 0, cost: 2

Applied chaining
First rule:
l1 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : 1+x^0 <= 0, cost: 1
New rule:
l1 -> l0 : 1+x^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 12 13 14

Eliminated locations on tree-shaped paths
Start location: l7
  11: l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
  18: l1 -> l0 : -1+x^0 >= 0, cost: 2
  19: l1 -> l0 : 1+x^0 <= 0, cost: 2
  17: l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : -1+x^0 >= 0, cost: 2
Second rule:
l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
New rule:
l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, -1+x^0 >= 0, cost: 3

Applied chaining
First rule:
l1 -> l0 : 1+x^0 <= 0, cost: 2
Second rule:
l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
New rule:
l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, 1+x^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 11 18 19

Eliminated locations on tree-shaped paths
Start location: l7
  20: l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, -1+x^0 >= 0, cost: 3
  21: l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, 1+x^0 <= 0, cost: 3
  17: l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, -1+x^0 >= 0, cost: 3
New rule:
l1 -> l1 : y^0'=-n+y^0, x^0'=-n+x^0, (n >= 0 /\ -n+x^0 >= 0), cost: 3*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_iadfNO.txt

Applied instantiation
Original rule:
l1 -> l1 : y^0'=-n+y^0, x^0'=-n+x^0, (n >= 0 /\ -n+x^0 >= 0), cost: 3*n
New rule:
l1 -> l1 : y^0'=y^0-x^0, x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 3*x^0

Applied nonterm
Original rule:
l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, 1+x^0 <= 0, cost: 3
New rule:
l1 -> [8] : (n0 >= 0 /\ -1-x^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_gFeoHj.txt

Applied simplification
Original rule:
l1 -> l1 : y^0'=y^0-x^0, x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 3*x^0
New rule:
l1 -> l1 : y^0'=y^0-x^0, x^0'=0, x^0 >= 0, cost: 3*x^0

Applied simplification
Original rule:
l1 -> [8] : (n0 >= 0 /\ -1-x^0 >= 0), cost: NONTERM
New rule:
l1 -> [8] : (n0 >= 0 /\ 1+x^0 <= 0), cost: NONTERM

Applied deletion
Removed the following rules: 20 21

Accelerated simple loops
Start location: l7
  24: l1 -> l1 : y^0'=y^0-x^0, x^0'=0, x^0 >= 0, cost: 3*x^0
  25: l1 -> [8] : (n0 >= 0 /\ 1+x^0 <= 0), cost: NONTERM
  17: l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2


Applied chaining
First rule:
l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2
Second rule:
l1 -> l1 : y^0'=y^0-x^0, x^0'=0, x^0 >= 0, cost: 3*x^0
New rule:
l7 -> l1 : y^0'=j^0-i^0, x^0'=0, i^0 >= 0, cost: 2+3*i^0

Applied chaining
First rule:
l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2
Second rule:
l1 -> [8] : (n0 >= 0 /\ 1+x^0 <= 0), cost: NONTERM
New rule:
l7 -> [8] : 1+i^0 <= 0, cost: NONTERM

Applied deletion
Removed the following rules: 24 25

Chained accelerated rules with incoming rules
Start location: l7
  17: l7 -> l1 : y^0'=j^0, x^0'=i^0, TRUE, cost: 2
  26: l7 -> l1 : y^0'=j^0-i^0, x^0'=0, i^0 >= 0, cost: 2+3*i^0
  27: l7 -> [8] : 1+i^0 <= 0, cost: NONTERM


Removed unreachable locations and irrelevant leafs
Start location: l7
  27: l7 -> [8] : 1+i^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+i^0 <= 0