NO

Initial ITS
Start location: l3
   0: l0 -> l1 : x_next^0'=x_next^post0, x^0'=x^post0, (0 == 0 /\ -1+x_next^post0-x^10 <= 0 /\ -x_next^10+x^10 == 0 /\ x^post0-x_next^post0 == 0 /\ 1-x_next^post0+x^10 <= 0), cost: 1
   1: l1 -> l0 : x_next^0'=x_next^post1, x^0'=x^post1, (x_next^0-x_next^post1 == 0 /\ x^0-x^post1 == 0), cost: 1
   2: l2 -> l0 : x_next^0'=x_next^post2, x^0'=x^post2, (x_next^0-x_next^post2 == 0 /\ -x^post2+x^0 == 0), cost: 1
   3: l3 -> l2 : x_next^0'=x_next^post3, x^0'=x^post3, (-x^post3+x^0 == 0 /\ x_next^0-x_next^post3 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : x_next^0'=x_next^post0, x^0'=x^post0, (0 == 0 /\ -1+x_next^post0-x^10 <= 0 /\ -x_next^10+x^10 == 0 /\ x^post0-x_next^post0 == 0 /\ 1-x_next^post0+x^10 <= 0), cost: 1
New rule:
l0 -> l1 : x_next^0'=1+x^10, x^0'=1+x^10, 0 == 0, cost: 1

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

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

Applied preprocessing
Original rule:
l3 -> l2 : x_next^0'=x_next^post3, x^0'=x^post3, (-x^post3+x^0 == 0 /\ x_next^0-x_next^post3 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   4: l0 -> l1 : x_next^0'=1+x^10, x^0'=1+x^10, 0 == 0, cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : TRUE, cost: 1
   7: 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: 6 7

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : x_next^0'=1+x^10, x^0'=1+x^10, 0 == 0, cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x_next^0'=1+x^10, x^0'=1+x^10, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   9: l0 -> l0 : x_next^0'=1+x^10, x^0'=1+x^10, 0 == 0, cost: 2
   8: l3 -> l0 : TRUE, cost: 2


Applied nonterm
Original rule:
l0 -> l0 : x_next^0'=1+x^10, x^0'=1+x^10, 0 == 0, cost: 2
New rule:
l0 -> [4] : (0 >= 0 /\ -1+n >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_ogAgij.txt

Applied simplification
Original rule:
l0 -> [4] : (0 >= 0 /\ -1+n >= 0), cost: NONTERM
New rule:
l0 -> [4] : -1+n >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 9

Accelerated simple loops
Start location: l3
  11: l0 -> [4] : -1+n >= 0, cost: NONTERM
   8: l3 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [4] : -1+n >= 0, cost: NONTERM
New rule:
l3 -> [4] : TRUE, cost: NONTERM

Applied deletion
Removed the following rules: 11

Chained accelerated rules with incoming rules
Start location: l3
   8: l3 -> l0 : TRUE, cost: 2
  12: l3 -> [4] : TRUE, cost: NONTERM


Removed unreachable locations and irrelevant leafs
Start location: l3
  12: l3 -> [4] : TRUE, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 12 via SMT.

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

Solved cost: NONTERM
Rule cost:   NONTERM
Rule guard:  TRUE