NO

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


Applied preprocessing
Original rule:
l0 -> l1 : x^0'=x^post0, (0 == 0 /\ -1+x^post0 <= 0 /\ 1-x^10 <= 0 /\ -1-x^post0 <= 0 /\ 2-x^10 <= 0), cost: 1
New rule:
l0 -> l1 : x^0'=x^post0, (-1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : x^0'=x^post1, -x^post1+x^0 == 0, cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post2, (0 == 0 /\ 2-x^post2 <= 0), cost: 1
New rule:
l2 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : x^0'=x^post3, x^0-x^post3 == 0, cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   4: l0 -> l1 : x^0'=x^post0, (-1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, 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 : x^0'=x^post2, -2+x^post2 >= 0, cost: 1
New rule:
l3 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : x^0'=x^post0, (-1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=x^post0, (-1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: 2

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   9: l0 -> l0 : x^0'=x^post0, (-1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: 2
   8: l3 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, cost: 2


Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^post0, (-1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: 2
New rule:
l0 -> [4] : (-1+n >= 0 /\ 1-x^post0 >= 0 /\ 1+x^post0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_HGbNDI.txt

Applied simplification
Original rule:
l0 -> [4] : (-1+n >= 0 /\ 1-x^post0 >= 0 /\ 1+x^post0 >= 0), cost: NONTERM
New rule:
l0 -> [4] : (-1+n >= 0 /\ -1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 9

Accelerated simple loops
Start location: l3
  11: l0 -> [4] : (-1+n >= 0 /\ -1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: NONTERM
   8: l3 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, cost: 2


Applied chaining
First rule:
l3 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, cost: 2
Second rule:
l0 -> [4] : (-1+n >= 0 /\ -1+x^post0 <= 0 /\ 1+x^post0 >= 0), cost: NONTERM
New rule:
l3 -> [4] : -2 <= 0, cost: NONTERM

Applied deletion
Removed the following rules: 11

Chained accelerated rules with incoming rules
Start location: l3
   8: l3 -> l0 : x^0'=x^post2, -2+x^post2 >= 0, cost: 2
  12: l3 -> [4] : -2 <= 0, cost: NONTERM


Removed unreachable locations and irrelevant leafs
Start location: l3
  12: l3 -> [4] : -2 <= 0, 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:  -2 <= 0