WORST_CASE(Omega(0),?)

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


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

Applied preprocessing
Original rule:
l0 -> l1 : id^0'=id^post1, x^0'=x^post1, m^0'=m^post1, (-x^post1 <= 0 /\ 1-x^0 <= 0 /\ -1-m^0+x^post1 <= 0 /\ id^0-id^post1 == 0 /\ 1-x^0+m^0 <= 0 /\ m^0-m^post1 == 0 /\ x^post1 == 0), cost: 1
New rule:
l0 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0), cost: 1

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

Applied preprocessing
Original rule:
l1 -> l0 : id^0'=id^post3, x^0'=x^post3, m^0'=m^post3, (m^0-m^post3 == 0 /\ 1-id^0+x^0 <= 0 /\ id^0-id^post3 == 0 /\ x^0-x^post3 == 0), cost: 1
New rule:
l1 -> l0 : 1-id^0+x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : id^0'=id^post4, x^0'=x^post4, m^0'=m^post4, (1-id^0 <= 0 /\ 1-m^0 <= 0 /\ -x^post4 <= 0 /\ -1+x^post4-m^0 <= 0 /\ -1-id^0+x^post4 == 0 /\ id^0-m^0 <= 0 /\ m^0-m^post4 == 0 /\ id^0-id^post4 == 0), cost: 1
New rule:
l2 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : id^0'=id^post5, x^0'=x^post5, m^0'=m^post5, (id^0-id^post5 == 0 /\ x^0-x^post5 == 0 /\ m^0-m^post5 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   6: l0 -> l1 : x^0'=1+x^0, (x^0-m^0 <= 0 /\ 1+x^0 >= 0), cost: 1
   7: l0 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0), cost: 1
   8: l1 -> l0 : 1+id^0-x^0 <= 0, cost: 1
   9: l1 -> l0 : 1-id^0+x^0 <= 0, cost: 1
  10: l2 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 1
  11: l3 -> l2 : TRUE, cost: 1


Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 1
New rule:
l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminated locations on linear paths
Start location: l3
   6: l0 -> l1 : x^0'=1+x^0, (x^0-m^0 <= 0 /\ 1+x^0 >= 0), cost: 1
   7: l0 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0), cost: 1
   8: l1 -> l0 : 1+id^0-x^0 <= 0, cost: 1
   9: l1 -> l0 : 1-id^0+x^0 <= 0, cost: 1
  12: l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2


Eliminating location l0 by chaining:

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

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

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

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

Applied deletion
Removed the following rules: 6 7 8 9

Eliminated locations on tree-shaped paths
Start location: l3
  13: l1 -> l1 : x^0'=1+x^0, (x^0-m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+x^0 >= 0), cost: 2
  14: l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+m^0 >= 0), cost: 2
  15: l1 -> l1 : x^0'=1+x^0, (x^0-m^0 <= 0 /\ 1-id^0+x^0 <= 0 /\ 1+x^0 >= 0), cost: 2
  16: l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 2
  12: l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2


Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+x^0, (x^0-m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+x^0 >= 0), cost: 2
New rule:
l1 -> l1 : x^0'=n3+x^0, (-1-id^0+x^0 >= 0 /\ n3 >= 0 /\ 1-n3-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2*n3

Applied instantiation
Original rule:
l1 -> l1 : x^0'=n3+x^0, (-1-id^0+x^0 >= 0 /\ n3 >= 0 /\ 1-n3-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2*n3
New rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0

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

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

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

Applied chaining
First rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+m^0 >= 0), cost: 2
Second rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0 <= 0 /\ 1+m^0 >= 0), cost: 4+2*m^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+m^0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0 <= 0 /\ 1+m^0 >= 0), cost: 4+2*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (-1-id^0 >= 0 /\ 1+m^0 >= 0 /\ -1+n19 >= 0 /\ -1+x^0-m^0 >= 0 /\ ((m^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+x^0 >= 0 /\ m^0 >= 0))), cost: 2*n19*m^0+4*n19

Applied chaining
First rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
Second rule:
l1 -> l1 : x^0'=1+m^0, (-1-id^0 >= 0 /\ 1+m^0 >= 0 /\ -1+n19 >= 0 /\ -1+x^0-m^0 >= 0 /\ ((m^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+x^0 >= 0 /\ m^0 >= 0))), cost: 2*n19*m^0+4*n19
New rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1-id^0 >= 0 /\ 1+m^0 >= 0 /\ -1+n19 >= 0 /\ 1+x^0 >= 0 /\ (m^0 >= 0 \/ (0 >= 0 /\ m^0 >= 0))), cost: 2+2*n19*m^0-2*x^0+4*n19+2*m^0

Applied chaining
First rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
Second rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+m^0 >= 0), cost: 2
New rule:
l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0), cost: 4-2*x^0+2*m^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0), cost: 4-2*x^0+2*m^0
New rule:
l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ -1+n21 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0 /\ ((1-x^0+m^0 >= 0 /\ 1+m^0 >= 0) \/ (1-x^0+m^0 >= 0 /\ m^0 >= 0))), cost: 2*m^0*n21+4*n21

Applied chaining
First rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+m^0 >= 0), cost: 2
Second rule:
l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ -1+n21 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0 /\ ((1-x^0+m^0 >= 0 /\ 1+m^0 >= 0) \/ (1-x^0+m^0 >= 0 /\ m^0 >= 0))), cost: 2*m^0*n21+4*n21
New rule:
l1 -> l1 : x^0'=0, (1 >= 0 /\ -1+n21 >= 0 /\ -1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+m^0 >= 0 /\ ((m^0 >= 0 /\ 1+m^0 >= 0) \/ 1+m^0 >= 0)), cost: 2+2*m^0*n21+4*n21

Applied chaining
First rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 2
Second rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1+id^0-m^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 4+2*m^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+m^0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 4+2*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (-1+n25 >= 0 /\ 1+m^0 >= 0 /\ -1+x^0-m^0 >= 0 /\ ((-1+id^0-x^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+id^0-x^0 >= 0 /\ -2+id^0-m^0 >= 0)) /\ ((m^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+x^0 >= 0 /\ m^0 >= 0))), cost: 4*n25+2*n25*m^0

Applied chaining
First rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1+id^0-m^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
Second rule:
l1 -> l1 : x^0'=1+m^0, (-1+n25 >= 0 /\ 1+m^0 >= 0 /\ -1+x^0-m^0 >= 0 /\ ((-1+id^0-x^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+id^0-x^0 >= 0 /\ -2+id^0-m^0 >= 0)) /\ ((m^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+x^0 >= 0 /\ m^0 >= 0))), cost: 4*n25+2*n25*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1+id^0-m^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1+n25 >= 0 /\ 1+m^0 >= 0 /\ 1+x^0 >= 0 /\ (m^0 >= 0 \/ (0 >= 0 /\ m^0 >= 0)) /\ (-2+id^0-m^0 >= 0 \/ (0 >= 0 /\ -2+id^0-m^0 >= 0))), cost: 2-2*x^0+4*n25+2*m^0+2*n25*m^0

Applied chaining
First rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1+id^0-m^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
Second rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 2
New rule:
l1 -> l1 : x^0'=0, (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ 2-id^0+m^0 <= 0 /\ 1+x^0 >= 0), cost: 4-2*x^0+2*m^0

Applied nonterm
Original rule:
l1 -> l1 : x^0'=0, (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ 2-id^0+m^0 <= 0 /\ 1+x^0 >= 0), cost: 4-2*x^0+2*m^0
New rule:
l1 -> [4] : (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0), cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : x^0'=0, (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ 2-id^0+m^0 <= 0 /\ 1+x^0 >= 0), cost: 4-2*x^0+2*m^0
New rule:
l1 -> l1 : x^0'=0, (m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0 /\ -1+n27 >= 0 /\ ((1-x^0+m^0 >= 0 /\ m^0 >= 0) \/ (1-x^0+m^0 >= 0 /\ 1+m^0 >= 0))), cost: 2*m^0*n27+4*n27

Applied chaining
First rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 2
Second rule:
l1 -> [4] : (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0), cost: NONTERM
New rule:
l1 -> [4] : (1 >= 0 /\ -1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0 /\ -2+id^0-m^0 >= 0), cost: NONTERM

Applied chaining
First rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 2
Second rule:
l1 -> l1 : x^0'=0, (m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0 /\ -1+n27 >= 0 /\ ((1-x^0+m^0 >= 0 /\ m^0 >= 0) \/ (1-x^0+m^0 >= 0 /\ 1+m^0 >= 0))), cost: 2*m^0*n27+4*n27
New rule:
l1 -> l1 : x^0'=0, (1 >= 0 /\ -1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0 /\ -2+id^0-m^0 >= 0 /\ -1+n27 >= 0 /\ (1+m^0 >= 0 \/ (m^0 >= 0 /\ 1+m^0 >= 0))), cost: 2+2*m^0*n27+4*n27

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

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

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

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+m^0, (-1-id^0 >= 0 /\ 1+m^0 >= 0 /\ -1+n19 >= 0 /\ -1+x^0-m^0 >= 0 /\ ((m^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+x^0 >= 0 /\ m^0 >= 0))), cost: 2*n19*m^0+4*n19
New rule:
l1 -> l1 : x^0'=1+m^0, (1+id^0 <= 0 /\ m^0 >= 0 /\ -1+n19 >= 0 /\ -1+x^0-m^0 >= 0), cost: 2*n19*m^0+4*n19

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1-id^0 >= 0 /\ 1+m^0 >= 0 /\ -1+n19 >= 0 /\ 1+x^0 >= 0 /\ (m^0 >= 0 \/ (0 >= 0 /\ m^0 >= 0))), cost: 2+2*n19*m^0-2*x^0+4*n19+2*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ -1+n19 >= 0 /\ 1+x^0 >= 0), cost: 2+2*n19*m^0-2*x^0+4*n19+2*m^0

Applied simplification
Original rule:
l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ -1+n21 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0 /\ ((1-x^0+m^0 >= 0 /\ 1+m^0 >= 0) \/ (1-x^0+m^0 >= 0 /\ m^0 >= 0))), cost: 2*m^0*n21+4*n21
New rule:
l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ -1+n21 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0), cost: 2*m^0*n21+4*n21

Applied simplification
Original rule:
l1 -> l1 : x^0'=0, (1 >= 0 /\ -1+n21 >= 0 /\ -1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+m^0 >= 0 /\ ((m^0 >= 0 /\ 1+m^0 >= 0) \/ 1+m^0 >= 0)), cost: 2+2*m^0*n21+4*n21
New rule:
l1 -> l1 : x^0'=0, (-1+n21 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0 <= 0 /\ m^0 >= 0), cost: 2+2*m^0*n21+4*n21

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+m^0, (-1+n25 >= 0 /\ 1+m^0 >= 0 /\ -1+x^0-m^0 >= 0 /\ ((-1+id^0-x^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+id^0-x^0 >= 0 /\ -2+id^0-m^0 >= 0)) /\ ((m^0 >= 0 /\ -1+x^0-m^0 >= 0) \/ (-1+x^0 >= 0 /\ m^0 >= 0))), cost: 4*n25+2*n25*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (-1+id^0-x^0 >= 0 /\ m^0 >= 0 /\ -1+n25 >= 0 /\ -1+x^0-m^0 >= 0), cost: 4*n25+2*n25*m^0

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1+id^0-m^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1+n25 >= 0 /\ 1+m^0 >= 0 /\ 1+x^0 >= 0 /\ (m^0 >= 0 \/ (0 >= 0 /\ m^0 >= 0)) /\ (-2+id^0-m^0 >= 0 \/ (0 >= 0 /\ -2+id^0-m^0 >= 0))), cost: 2-2*x^0+4*n25+2*m^0+2*n25*m^0
New rule:
l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ 1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -1+n25 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+4*n25+2*m^0+2*n25*m^0

Applied simplification
Original rule:
l1 -> [4] : (1 >= 0 /\ -1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0 /\ -2+id^0-m^0 >= 0), cost: NONTERM
New rule:
l1 -> [4] : (1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: NONTERM

Applied simplification
Original rule:
l1 -> l1 : x^0'=0, (m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0 /\ -1+n27 >= 0 /\ ((1-x^0+m^0 >= 0 /\ m^0 >= 0) \/ (1-x^0+m^0 >= 0 /\ 1+m^0 >= 0))), cost: 2*m^0*n27+4*n27
New rule:
l1 -> l1 : x^0'=0, (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0 /\ -1+n27 >= 0), cost: 2*m^0*n27+4*n27

Applied simplification
Original rule:
l1 -> l1 : x^0'=0, (1 >= 0 /\ -1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0 /\ -2+id^0-m^0 >= 0 /\ -1+n27 >= 0 /\ (1+m^0 >= 0 \/ (m^0 >= 0 /\ 1+m^0 >= 0))), cost: 2+2*m^0*n27+4*n27
New rule:
l1 -> l1 : x^0'=0, (1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1-id^0+x^0 <= 0 /\ -1+n27 >= 0), cost: 2+2*m^0*n27+4*n27

Applied deletion
Removed the following rules: 13 15

Accelerated simple loops
Start location: l3
  14: l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+m^0 >= 0), cost: 2
  16: l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: 2
  26: l1 -> [4] : (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0), cost: NONTERM
  30: l1 -> l1 : x^0'=1+m^0, (-1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
  31: l1 -> l1 : x^0'=1+m^0, (-1+id^0-m^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
  32: l1 -> l1 : x^0'=id^0, (1-id^0+m^0 >= 0 /\ id^0-x^0 >= 0 /\ 1+x^0 >= 0), cost: 2*id^0-2*x^0
  33: l1 -> l1 : x^0'=1+m^0, (1+id^0 <= 0 /\ m^0 >= 0 /\ -1+n19 >= 0 /\ -1+x^0-m^0 >= 0), cost: 2*n19*m^0+4*n19
  34: l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ -1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ -1+n19 >= 0 /\ 1+x^0 >= 0), cost: 2+2*n19*m^0-2*x^0+4*n19+2*m^0
  35: l1 -> l1 : x^0'=0, (-1-id^0+x^0 >= 0 /\ -1+n21 >= 0 /\ 1-x^0+m^0 >= 0 /\ -1-id^0 >= 0 /\ m^0 >= 0 /\ 1+x^0 >= 0), cost: 2*m^0*n21+4*n21
  36: l1 -> l1 : x^0'=0, (-1+n21 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0 <= 0 /\ m^0 >= 0), cost: 2+2*m^0*n21+4*n21
  37: l1 -> l1 : x^0'=1+m^0, (-1+id^0-x^0 >= 0 /\ m^0 >= 0 /\ -1+n25 >= 0 /\ -1+x^0-m^0 >= 0), cost: 4*n25+2*n25*m^0
  38: l1 -> l1 : x^0'=1+m^0, (0 >= 0 /\ 1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -1+n25 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+4*n25+2*m^0+2*n25*m^0
  39: l1 -> [4] : (1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1-id^0+x^0 <= 0), cost: NONTERM
  40: l1 -> l1 : x^0'=0, (1-x^0+m^0 >= 0 /\ m^0 >= 0 /\ -2+id^0-m^0 >= 0 /\ 1+x^0 >= 0 /\ -1+n27 >= 0), cost: 2*m^0*n27+4*n27
  41: l1 -> l1 : x^0'=0, (1-x^0+m^0 <= 0 /\ m^0 >= 0 /\ 1-id^0+x^0 <= 0 /\ -1+n27 >= 0), cost: 2+2*m^0*n27+4*n27
  12: l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2


Applied chaining
First rule:
l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2
Second rule:
l1 -> l1 : x^0'=0, (-1+x^0 >= 0 /\ 1-x^0+m^0 <= 0 /\ 1+id^0-x^0 <= 0 /\ 1+m^0 >= 0), cost: 2
New rule:
l3 -> l1 : x^0'=0, (-1+id^0 >= 0 /\ -id^0+m^0 == 0), cost: 4

Applied chaining
First rule:
l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2
Second rule:
l1 -> l1 : x^0'=1+m^0, (-1-id^0+x^0 >= 0 /\ 1-x^0+m^0 >= 0 /\ 1+x^0 >= 0), cost: 2-2*x^0+2*m^0
New rule:
l3 -> l1 : x^0'=1+m^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2-2*id^0+2*m^0

Applied deletion
Removed the following rules: 14 16 26 30 31 32 33 34 35 36 37 38 39 40 41

Chained accelerated rules with incoming rules
Start location: l3
  12: l3 -> l1 : x^0'=1+id^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2
  42: l3 -> l1 : x^0'=0, (-1+id^0 >= 0 /\ -id^0+m^0 == 0), cost: 4
  43: l3 -> l1 : x^0'=1+m^0, (-1+id^0 >= 0 /\ id^0-m^0 <= 0), cost: 2-2*id^0+2*m^0


Removed unreachable locations and irrelevant leafs
Start location: l3
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0