NO

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


Applied preprocessing
Original rule:
l0 -> l1 : x^0'=x^post0, (0 == 0 /\ 1-x^0 <= 0), cost: 1
New rule:
l0 -> l1 : x^0'=x^post0, -1+x^0 >= 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:
l0 -> l2 : x^0'=x^post2, (1+x^post2-x^0 == 0 /\ 1-x^0 <= 0), cost: 1
New rule:
l0 -> l2 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post3, x^0-x^post3 == 0, cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

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

Applied preprocessing
Original rule:
l4 -> l3 : x^0'=x^post5, -x^post5+x^0 == 0, cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l1 : x^0'=x^post0, -1+x^0 >= 0, cost: 1
   8: l0 -> l2 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1
   7: l1 -> l0 : TRUE, cost: 1
   9: l2 -> l0 : TRUE, cost: 1
  10: l3 -> l0 : TRUE, cost: 1
  11: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l0 : TRUE, cost: 1
New rule:
l4 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 6 7

Eliminating location l2 by chaining:

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

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l4
  13: l0 -> l0 : x^0'=x^post0, -1+x^0 >= 0, cost: 2
  14: l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
  12: l4 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^post0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_OeoClg.txt

Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^post0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> [5] : (x^0-x^post0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_adaKcc.txt

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^0-n0, (x^0-n0 >= 0 /\ n0 >= 0), cost: 2*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_JNKbMM.txt

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n0, (x^0-n0 >= 0 /\ n0 >= 0), cost: 2*n0
New rule:
l0 -> l0 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0

Applied chaining
First rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=x^post0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^post0, -2+x^0 >= 0, cost: 4

Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^post0, -2+x^0 >= 0, cost: 4
New rule:
l0 -> l0 : x^0'=x^post0, (-2+x^0 >= 0 /\ -2+x^post0 >= 0 /\ -1+n1 >= 0), cost: 4*n1
Sub-proof via acceration calculus written to file:///tmp/tmpnam_JCIEoB.txt

Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^post0, -2+x^0 >= 0, cost: 4
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_fLllcC.txt

Applied chaining
First rule:
l0 -> l0 : x^0'=x^post0, -1+x^0 >= 0, cost: 2
Second rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0), cost: NONTERM
New rule:
l0 -> [5] : (0 <= 0 /\ -2+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied chaining
First rule:
l0 -> l0 : x^0'=x^post0, -1+x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: 4

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: 4
New rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+n2 >= 0 /\ -1+x^post0 >= 0 /\ -2+x^post0 >= 0 /\ -1+x^0 >= 0), cost: 4*n2
Sub-proof via acceration calculus written to file:///tmp/tmpnam_bBdCkd.txt

Applied nonterm
Original rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: 4
New rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_goFDeH.txt

Applied chaining
First rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
Second rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM

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

Applied acceleration
Original rule:
l0 -> l0 : x^0'=x^post0, (-2+x^0 >= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0), cost: 2+2*n
New rule:
l0 -> l0 : x^0'=x^post0, (-2+x^0 >= 0 /\ -1+x^post0 >= 0 /\ -1+n3 >= 0 /\ -2+x^post0 >= 0 /\ -1+n >= 0), cost: 2*n3+2*n3*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_DhPFBI.txt

Applied nonterm
Original rule:
l0 -> l0 : x^0'=x^post0, (-2+x^0 >= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0), cost: 2+2*n
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_MiJkDM.txt

Applied chaining
First rule:
l0 -> l0 : x^0'=x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2*n
Second rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0), cost: NONTERM
New rule:
l0 -> [5] : (0 <= 0 /\ -1+x^post0 >= 0 /\ -2+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM

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

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2+2*n
New rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+x^post0 >= 0 /\ -1+n4 >= 0 /\ -2+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2*n4+2*n*n4
Sub-proof via acceration calculus written to file:///tmp/tmpnam_bNgaLn.txt

Applied nonterm
Original rule:
l0 -> l0 : x^0'=-1+x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2+2*n
New rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
Sub-proof via acceration calculus written to file:///tmp/tmpnam_LEmlhJ.txt

Applied chaining
First rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
Second rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM

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

Applied simplification
Original rule:
l0 -> [5] : (0 <= 0 /\ -2+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied simplification
Original rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied simplification
Original rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0), cost: NONTERM

Applied simplification
Original rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+n >= 0), cost: NONTERM

Applied simplification
Original rule:
l0 -> [5] : (0 <= 0 /\ -1+x^post0 >= 0 /\ -2+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied simplification
Original rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM

Applied simplification
Original rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+n >= 0), cost: NONTERM

Applied deletion
Removed the following rules: 13 14

Accelerated simple loops
Start location: l4
  15: l0 -> l0 : x^0'=x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2*n
  16: l0 -> [5] : (x^0-x^post0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM
  18: l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0), cost: NONTERM
  26: l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
  27: l0 -> [5] : (-2+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
  28: l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM
  29: l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+n >= 0), cost: NONTERM
  30: l0 -> [5] : (-2+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
  31: l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
  12: l4 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2*n
New rule:
l4 -> l0 : x^0'=x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2+2*n

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (x^0-x^post0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [5] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0), cost: NONTERM
New rule:
l4 -> [5] : -2+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
New rule:
l4 -> l0 : x^0'=0, x^0 >= 0, cost: 2+2*x^0

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (-2+x^post0 >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [5] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [5] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (-2+x^0 >= 0 /\ x^0-x^post0 <= 0 /\ -1+n >= 0), cost: NONTERM
New rule:
l4 -> [5] : -2+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (-2+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [5] : -1+x^0 >= 0, cost: NONTERM

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> [5] : (1+x^0-x^post0 <= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: NONTERM
New rule:
l4 -> [5] : -1+x^0 >= 0, cost: NONTERM

Applied deletion
Removed the following rules: 15 16 18 26 27 28 29 30 31

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : TRUE, cost: 2
  32: l4 -> l0 : x^0'=x^post0, (-1+x^post0 >= 0 /\ -1+n >= 0 /\ -1+x^0 >= 0), cost: 2+2*n
  33: l4 -> [5] : -1+x^0 >= 0, cost: NONTERM
  34: l4 -> [5] : -2+x^0 >= 0, cost: NONTERM
  35: l4 -> l0 : x^0'=0, x^0 >= 0, cost: 2+2*x^0


Removed unreachable locations and irrelevant leafs
Start location: l4
  33: l4 -> [5] : -1+x^0 >= 0, cost: NONTERM
  34: l4 -> [5] : -2+x^0 >= 0, cost: NONTERM


Computing asymptotic complexity
Proved nontermination of rule 33 via SMT.

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

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