WORST_CASE(Omega(0),?)

Initial ITS
Start location: l6
   0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post0, __disjvr_2^0'=__disjvr_2^post0, y^0'=y^post0, __disjvr_1^0'=__disjvr_1^post0, x^0'=x^post0, (1+2*y^0-x^0 <= 0 /\ y^0-y^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0 /\ -1-2*y^0+x^0 <= 0 /\ -__disjvr_1^post0+__disjvr_1^0 == 0 /\ __disjvr_2^0-__disjvr_2^post0 == 0 /\ -1+x^post0-3*x^0 == 0), cost: 1
   1: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post1, __disjvr_2^0'=__disjvr_2^post1, y^0'=y^post1, __disjvr_1^0'=__disjvr_1^post1, x^0'=x^post1, (-2*y^0+x^0 <= 0 /\ -y^post1+y^0 == 0 /\ 2*y^0-x^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ __disjvr_1^0-__disjvr_1^post1 == 0 /\ x^post1-y^0 == 0 /\ -__disjvr_2^post1+__disjvr_2^0 == 0), cost: 1
   2: l1 -> l2 : __disjvr_0^0'=__disjvr_0^post2, __disjvr_2^0'=__disjvr_2^post2, y^0'=y^post2, __disjvr_1^0'=__disjvr_1^post2, x^0'=x^post2, (__disjvr_0^0-__disjvr_0^post2 == 0 /\ -__disjvr_1^post2+__disjvr_1^0 == 0 /\ -y^post2+y^0 == 0 /\ -__disjvr_0^0+__disjvr_0^post2 == 0 /\ __disjvr_2^0-__disjvr_2^post2 == 0 /\ -x^post2+x^0 == 0), cost: 1
   3: l2 -> l3 : __disjvr_0^0'=__disjvr_0^post3, __disjvr_2^0'=__disjvr_2^post3, y^0'=y^post3, __disjvr_1^0'=__disjvr_1^post3, x^0'=x^post3, (-x^post3+x^0 == 0 /\ -__disjvr_1^0+__disjvr_1^post3 == 0 /\ y^0-y^post3 == 0 /\ __disjvr_1^0-__disjvr_1^post3 == 0 /\ __disjvr_2^0-__disjvr_2^post3 == 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0), cost: 1
   4: l3 -> l4 : __disjvr_0^0'=__disjvr_0^post4, __disjvr_2^0'=__disjvr_2^post4, y^0'=y^post4, __disjvr_1^0'=__disjvr_1^post4, x^0'=x^post4, (-x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -__disjvr_2^0+__disjvr_2^post4 == 0 /\ -__disjvr_1^post4+__disjvr_1^0 == 0 /\ __disjvr_0^0-__disjvr_0^post4 == 0 /\ __disjvr_2^0-__disjvr_2^post4 == 0), cost: 1
   5: l4 -> l0 : __disjvr_0^0'=__disjvr_0^post5, __disjvr_2^0'=__disjvr_2^post5, y^0'=y^post5, __disjvr_1^0'=__disjvr_1^post5, x^0'=x^post5, (0 == 0 /\ -x^post5+x^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ -__disjvr_1^post5+__disjvr_1^0 == 0 /\ __disjvr_2^0-__disjvr_2^post5 == 0), cost: 1
   6: l5 -> l1 : __disjvr_0^0'=__disjvr_0^post6, __disjvr_2^0'=__disjvr_2^post6, y^0'=y^post6, __disjvr_1^0'=__disjvr_1^post6, x^0'=x^post6, (0 == 0 /\ -y^post6+y^0 == 0 /\ 1-x^post6 <= 0 /\ __disjvr_0^0-__disjvr_0^post6 == 0 /\ __disjvr_2^0-__disjvr_2^post6 == 0 /\ -__disjvr_1^post6+__disjvr_1^0 == 0), cost: 1
   7: l6 -> l5 : __disjvr_0^0'=__disjvr_0^post7, __disjvr_2^0'=__disjvr_2^post7, y^0'=y^post7, __disjvr_1^0'=__disjvr_1^post7, x^0'=x^post7, (-__disjvr_1^post7+__disjvr_1^0 == 0 /\ __disjvr_2^0-__disjvr_2^post7 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ y^0-y^post7 == 0 /\ -x^post7+x^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : __disjvr_0^0'=__disjvr_0^post0, __disjvr_2^0'=__disjvr_2^post0, y^0'=y^post0, __disjvr_1^0'=__disjvr_1^post0, x^0'=x^post0, (1+2*y^0-x^0 <= 0 /\ y^0-y^post0 == 0 /\ __disjvr_0^0-__disjvr_0^post0 == 0 /\ -1-2*y^0+x^0 <= 0 /\ -__disjvr_1^post0+__disjvr_1^0 == 0 /\ __disjvr_2^0-__disjvr_2^post0 == 0 /\ -1+x^post0-3*x^0 == 0), cost: 1
New rule:
l0 -> l1 : x^0'=1+3*x^0, 1+2*y^0-x^0 == 0, cost: 1

Applied preprocessing
Original rule:
l0 -> l1 : __disjvr_0^0'=__disjvr_0^post1, __disjvr_2^0'=__disjvr_2^post1, y^0'=y^post1, __disjvr_1^0'=__disjvr_1^post1, x^0'=x^post1, (-2*y^0+x^0 <= 0 /\ -y^post1+y^0 == 0 /\ 2*y^0-x^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post1 == 0 /\ __disjvr_1^0-__disjvr_1^post1 == 0 /\ x^post1-y^0 == 0 /\ -__disjvr_2^post1+__disjvr_2^0 == 0), cost: 1
New rule:
l0 -> l1 : x^0'=y^0, -2*y^0+x^0 == 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : __disjvr_0^0'=__disjvr_0^post2, __disjvr_2^0'=__disjvr_2^post2, y^0'=y^post2, __disjvr_1^0'=__disjvr_1^post2, x^0'=x^post2, (__disjvr_0^0-__disjvr_0^post2 == 0 /\ -__disjvr_1^post2+__disjvr_1^0 == 0 /\ -y^post2+y^0 == 0 /\ -__disjvr_0^0+__disjvr_0^post2 == 0 /\ __disjvr_2^0-__disjvr_2^post2 == 0 /\ -x^post2+x^0 == 0), cost: 1
New rule:
l1 -> l2 : 0 == 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : __disjvr_0^0'=__disjvr_0^post3, __disjvr_2^0'=__disjvr_2^post3, y^0'=y^post3, __disjvr_1^0'=__disjvr_1^post3, x^0'=x^post3, (-x^post3+x^0 == 0 /\ -__disjvr_1^0+__disjvr_1^post3 == 0 /\ y^0-y^post3 == 0 /\ __disjvr_1^0-__disjvr_1^post3 == 0 /\ __disjvr_2^0-__disjvr_2^post3 == 0 /\ __disjvr_0^0-__disjvr_0^post3 == 0), cost: 1
New rule:
l2 -> l3 : 0 == 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l4 : __disjvr_0^0'=__disjvr_0^post4, __disjvr_2^0'=__disjvr_2^post4, y^0'=y^post4, __disjvr_1^0'=__disjvr_1^post4, x^0'=x^post4, (-x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -__disjvr_2^0+__disjvr_2^post4 == 0 /\ -__disjvr_1^post4+__disjvr_1^0 == 0 /\ __disjvr_0^0-__disjvr_0^post4 == 0 /\ __disjvr_2^0-__disjvr_2^post4 == 0), cost: 1
New rule:
l3 -> l4 : 0 == 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : __disjvr_0^0'=__disjvr_0^post5, __disjvr_2^0'=__disjvr_2^post5, y^0'=y^post5, __disjvr_1^0'=__disjvr_1^post5, x^0'=x^post5, (0 == 0 /\ -x^post5+x^0 == 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ -__disjvr_1^post5+__disjvr_1^0 == 0 /\ __disjvr_2^0-__disjvr_2^post5 == 0), cost: 1
New rule:
l4 -> l0 : y^0'=y^post5, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l1 : __disjvr_0^0'=__disjvr_0^post6, __disjvr_2^0'=__disjvr_2^post6, y^0'=y^post6, __disjvr_1^0'=__disjvr_1^post6, x^0'=x^post6, (0 == 0 /\ -y^post6+y^0 == 0 /\ 1-x^post6 <= 0 /\ __disjvr_0^0-__disjvr_0^post6 == 0 /\ __disjvr_2^0-__disjvr_2^post6 == 0 /\ -__disjvr_1^post6+__disjvr_1^0 == 0), cost: 1
New rule:
l5 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : __disjvr_0^0'=__disjvr_0^post7, __disjvr_2^0'=__disjvr_2^post7, y^0'=y^post7, __disjvr_1^0'=__disjvr_1^post7, x^0'=x^post7, (-__disjvr_1^post7+__disjvr_1^0 == 0 /\ __disjvr_2^0-__disjvr_2^post7 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ y^0-y^post7 == 0 /\ -x^post7+x^0 == 0), cost: 1
New rule:
l6 -> l5 : TRUE, cost: 1

Simplified rules
Start location: l6
   8: l0 -> l1 : x^0'=1+3*x^0, 1+2*y^0-x^0 == 0, cost: 1
   9: l0 -> l1 : x^0'=y^0, -2*y^0+x^0 == 0, cost: 1
  10: l1 -> l2 : 0 == 0, cost: 1
  11: l2 -> l3 : 0 == 0, cost: 1
  12: l3 -> l4 : 0 == 0, cost: 1
  13: l4 -> l0 : y^0'=y^post5, 0 == 0, cost: 1
  14: l5 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 1
  15: l6 -> l5 : TRUE, cost: 1


Eliminating location l5 by chaining:

Applied chaining
First rule:
l6 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 1
New rule:
l6 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 2

Applied deletion
Removed the following rules: 14 15

Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : 0 == 0, cost: 1
Second rule:
l2 -> l3 : 0 == 0, cost: 1
New rule:
l1 -> l3 : 0 == 0, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : 0 == 0, cost: 2
Second rule:
l3 -> l4 : 0 == 0, cost: 1
New rule:
l1 -> l4 : 0 == 0, cost: 3

Applied deletion
Removed the following rules: 12 17

Eliminating location l4 by chaining:

Applied chaining
First rule:
l1 -> l4 : 0 == 0, cost: 3
Second rule:
l4 -> l0 : y^0'=y^post5, 0 == 0, cost: 1
New rule:
l1 -> l0 : y^0'=y^post5, 0 == 0, cost: 4

Applied deletion
Removed the following rules: 13 18

Eliminated locations on linear paths
Start location: l6
   8: l0 -> l1 : x^0'=1+3*x^0, 1+2*y^0-x^0 == 0, cost: 1
   9: l0 -> l1 : x^0'=y^0, -2*y^0+x^0 == 0, cost: 1
  19: l1 -> l0 : y^0'=y^post5, 0 == 0, cost: 4
  16: l6 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : y^0'=y^post5, 0 == 0, cost: 4
Second rule:
l0 -> l1 : x^0'=1+3*x^0, 1+2*y^0-x^0 == 0, cost: 1
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, (0 == 0 /\ 1+2*y^post5-x^0 == 0), cost: 5

Applied simplification
Original rule:
l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, (0 == 0 /\ 1+2*y^post5-x^0 == 0), cost: 5
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, 1+2*y^post5-x^0 == 0, cost: 5

Applied chaining
First rule:
l1 -> l0 : y^0'=y^post5, 0 == 0, cost: 4
Second rule:
l0 -> l1 : x^0'=y^0, -2*y^0+x^0 == 0, cost: 1
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (0 == 0 /\ -2*y^post5+x^0 == 0), cost: 5

Applied simplification
Original rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (0 == 0 /\ -2*y^post5+x^0 == 0), cost: 5
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, -2*y^post5+x^0 == 0, cost: 5

Applied deletion
Removed the following rules: 8 9 19

Eliminated locations on tree-shaped paths
Start location: l6
  20: l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, 1+2*y^post5-x^0 == 0, cost: 5
  21: l1 -> l1 : y^0'=y^post5, x^0'=y^post5, -2*y^post5+x^0 == 0, cost: 5
  16: l6 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, -2*y^post5+x^0 == 0, cost: 5
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (-1+n2 >= 0 /\ 2*y^post5-x^0 >= 0 /\ y^post5 >= 0 /\ -y^post5 >= 0 /\ -2*y^post5+x^0 >= 0), cost: 5*n2

Applied unrolling
Original rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, -2*y^post5+x^0 == 0, cost: 5
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (-y^post5 == 0 /\ -2*y^post5+x^0 == 0), cost: 10

Applied non-termination processor
Original rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (-y^post5 == 0 /\ -2*y^post5+x^0 == 0), cost: 10
New rule:
l1 -> [7] : (-y^post5 == 0 /\ -2*y^post5+x^0 == 0), cost: NONTERM

Applied chaining
First rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, -2*y^post5+x^0 == 0, cost: 5
Second rule:
l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, 1+2*y^post5-x^0 == 0, cost: 5
New rule:
l1 -> l1 : y^0'=-1, x^0'=-2, 2+x^0 == 0, cost: 10

Applied nonterm
Original rule:
l1 -> l1 : y^0'=-1, x^0'=-2, 2+x^0 == 0, cost: 10
New rule:
l1 -> [7] : (2+x^0 >= 0 /\ -2-x^0 >= 0), cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1, x^0'=-2, 2+x^0 == 0, cost: 10
New rule:
l1 -> l1 : y^0'=-1, x^0'=-2, (2+x^0 >= 0 /\ -2-x^0 >= 0), cost: 10*n6

Applied chaining
First rule:
l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, 1+2*y^post5-x^0 == 0, cost: 5
Second rule:
l1 -> [7] : (2+x^0 >= 0 /\ -2-x^0 >= 0), cost: NONTERM
New rule:
l1 -> [7] : (-3-3*x^0 >= 0 /\ 3+3*x^0 >= 0 /\ 1+2*y^post5-x^0 == 0), cost: NONTERM

Heuristically decided not to add the following rule:
l1 -> l1 : y^0'=-1, x^0'=-2, (2+x^0 >= 0 /\ -2-x^0 >= 0), cost: 10*n6

Applied simplification
Original rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (-1+n2 >= 0 /\ 2*y^post5-x^0 >= 0 /\ y^post5 >= 0 /\ -y^post5 >= 0 /\ -2*y^post5+x^0 >= 0), cost: 5*n2
New rule:
l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (-1+n2 >= 0 /\ 2*y^post5-x^0 >= 0 /\ y^post5 <= 0 /\ y^post5 >= 0 /\ -2*y^post5+x^0 >= 0), cost: 5*n2

Applied simplification
Original rule:
l1 -> [7] : (-y^post5 == 0 /\ -2*y^post5+x^0 == 0), cost: NONTERM
New rule:
l1 -> [7] : (y^post5 == 0 /\ -2*y^post5+x^0 == 0), cost: NONTERM

Applied simplification
Original rule:
l1 -> [7] : (2+x^0 >= 0 /\ -2-x^0 >= 0), cost: NONTERM
New rule:
l1 -> [7] : (2+x^0 <= 0 /\ 2+x^0 >= 0), cost: NONTERM

Applied simplification
Original rule:
l1 -> [7] : (-3-3*x^0 >= 0 /\ 3+3*x^0 >= 0 /\ 1+2*y^post5-x^0 == 0), cost: NONTERM
New rule:
l1 -> [7] : (1+x^0 <= 0 /\ 1+x^0 >= 0 /\ 1+2*y^post5-x^0 == 0), cost: NONTERM

Applied deletion
Removed the following rules: 21

Accelerated simple loops
Start location: l6
  20: l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, 1+2*y^post5-x^0 == 0, cost: 5
  26: l1 -> l1 : y^0'=y^post5, x^0'=y^post5, (-1+n2 >= 0 /\ 2*y^post5-x^0 >= 0 /\ y^post5 <= 0 /\ y^post5 >= 0 /\ -2*y^post5+x^0 >= 0), cost: 5*n2
  27: l1 -> [7] : (y^post5 == 0 /\ -2*y^post5+x^0 == 0), cost: NONTERM
  28: l1 -> [7] : (2+x^0 <= 0 /\ 2+x^0 >= 0), cost: NONTERM
  29: l1 -> [7] : (1+x^0 <= 0 /\ 1+x^0 >= 0 /\ 1+2*y^post5-x^0 == 0), cost: NONTERM
  16: l6 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 2


Applied chaining
First rule:
l6 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 2
Second rule:
l1 -> l1 : y^0'=y^post5, x^0'=1+3*x^0, 1+2*y^post5-x^0 == 0, cost: 5
New rule:
l6 -> l1 : y^0'=y^post5, x^0'=4+6*y^post5, y^post5 >= 0, cost: 7

Applied deletion
Removed the following rules: 20 26 27 28 29

Chained accelerated rules with incoming rules
Start location: l6
  16: l6 -> l1 : x^0'=x^post6, -1+x^post6 >= 0, cost: 2
  30: l6 -> l1 : y^0'=y^post5, x^0'=4+6*y^post5, y^post5 >= 0, cost: 7


Removed unreachable locations and irrelevant leafs
Start location: l6
  <empty>


Computing asymptotic complexity

Proved the following lower bound
Complexity:  Unknown
Cpx degree: ?

Solved cost: 0
Rule cost:   0