WORST_CASE(Omega(0),?)

Initial ITS
Start location: l3
   0: l0 -> l1 : c1^0'=c1^post0, pi^0'=pi^post0, m^0'=m^post0, seq^0'=seq^post0, n^0'=n^post0, z^0'=z^post0, c2^0'=c2^post0, pos^0'=pos^post0, max^0'=max^post0, wpos^0'=wpos^post0, (0 == 0 /\ 1-c1^10 <= 0 /\ -1+c1^10 <= 0 /\ -c2^post0 <= 0 /\ 1+m^10-max^0 <= 0 /\ -1+c2^post0 <= 0 /\ -c1^10 <= 0 /\ wpos^post0 == 0 /\ 1-pos^0 <= 0 /\ -1+pos^0 <= 0 /\ 1+m^20-max^0 <= 0 /\ 1-m^30 <= 0 /\ 1-c1^30 <= 0 /\ -1+c1^30 <= 0 /\ 1-m^0 <= 0 /\ -c1^30 <= 0 /\ 1-wpos^30 <= 0 /\ -1+wpos^30 <= 0 /\ -max^post0+max^0 == 0 /\ 1-z^20+z^post0 == 0 /\ pi^10 <= 0 /\ c2^10 <= 0 /\ 1-pi^20+pi^post0 == 0 /\ 1-wpos^50 <= 0 /\ -1+wpos^50 <= 0 /\ 1-c1^20 <= 0 /\ -1+c1^20 <= 0 /\ 1-pi^0+pi^10 == 0 /\ -1-seq^0+seq^post0 == 0 /\ 1-pi^20 <= 0 /\ -c1^20 <= 0 /\ 1-z^20 <= 0 /\ wpos^20 <= 0 /\ wpos^20 == 0 /\ 1-m^20 <= 0 /\ 1-pi^0 <= 0 /\ 1-c1^post0 <= 0 /\ -1+c1^post0 <= 0 /\ z^0 <= 0 /\ pos^10 <= 0 /\ pos^10 == 0 /\ 1-m^30+m^post0 == 0 /\ -c1^post0 <= 0 /\ -1+wpos^50-wpos^40 == 0 /\ 1-pos^post0 <= 0 /\ -1+pos^post0 <= 0 /\ pi^20-seq^post0 == 0 /\ -1+wpos^10-wpos^0 == 0 /\ -c1^40 <= 0 /\ 1-c2^30 <= 0 /\ -1+c2^30 <= 0 /\ c2^post0 <= 0 /\ -1-wpos^20+wpos^30 == 0 /\ 1-z^10+z^20 == 0 /\ -c2^30 <= 0 /\ -1+c1^40 <= 0 /\ -1-pos^10+pos^post0 == 0 /\ -1+m^30-m^20 == 0 /\ -1+c2^10 <= 0 /\ -z^10 <= 0 /\ wpos^40 <= 0 /\ wpos^40 == 0 /\ -c2^10 <= 0 /\ -n^post0+n^0 == 0 /\ 1-z^10 <= 0 /\ 1-c2^20 <= 0 /\ -1+c2^20 <= 0 /\ z^post0 <= 0 /\ 1-m^10 <= 0 /\ 1-m^0+m^10 == 0 /\ 1-wpos^10 <= 0 /\ -1+wpos^10 <= 0 /\ -c2^20 <= 0 /\ wpos^0 <= 0 /\ c1^40 <= 0 /\ -1+m^20-m^10 == 0), cost: 1
   1: l1 -> l0 : c1^0'=c1^post1, pi^0'=pi^post1, m^0'=m^post1, seq^0'=seq^post1, n^0'=n^post1, z^0'=z^post1, c2^0'=c2^post1, pos^0'=pos^post1, max^0'=max^post1, wpos^0'=wpos^post1, (pi^0-pi^post1 == 0 /\ -n^post1+n^0 == 0 /\ c1^0-c1^post1 == 0 /\ seq^0-seq^post1 == 0 /\ -z^post1+z^0 == 0 /\ -wpos^post1+wpos^0 == 0 /\ -pos^post1+pos^0 == 0 /\ m^0-m^post1 == 0 /\ c2^0-c2^post1 == 0 /\ -max^post1+max^0 == 0), cost: 1
   2: l2 -> l0 : c1^0'=c1^post2, pi^0'=pi^post2, m^0'=m^post2, seq^0'=seq^post2, n^0'=n^post2, z^0'=z^post2, c2^0'=c2^post2, pos^0'=pos^post2, max^0'=max^post2, wpos^0'=wpos^post2, (0 == 0 /\ -z^post2 <= 0 /\ 1-m^post2 <= 0 /\ -m^post2 <= 0 /\ -n^post2 <= 0 /\ -c1^post2 <= 0 /\ z^post2 <= 0 /\ c2^0-c2^post2 == 0 /\ -1+c1^post2 <= 0 /\ c1^post2 <= 0 /\ -1+seq^post2 == 0 /\ -seq^post2+pi^post2 == 0 /\ wpos^post2 == 0 /\ -1+pos^post2-pos^11 == 0 /\ -max^post2 <= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0 /\ pos^11 <= 0 /\ pos^11 == 0), cost: 1
   3: l3 -> l2 : c1^0'=c1^post3, pi^0'=pi^post3, m^0'=m^post3, seq^0'=seq^post3, n^0'=n^post3, z^0'=z^post3, c2^0'=c2^post3, pos^0'=pos^post3, max^0'=max^post3, wpos^0'=wpos^post3, (-n^post3+n^0 == 0 /\ m^0-m^post3 == 0 /\ c2^0-c2^post3 == 0 /\ -pi^post3+pi^0 == 0 /\ -z^post3+z^0 == 0 /\ pos^0-pos^post3 == 0 /\ c1^0-c1^post3 == 0 /\ -max^post3+max^0 == 0 /\ -wpos^post3+wpos^0 == 0 /\ seq^0-seq^post3 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : c1^0'=c1^post0, pi^0'=pi^post0, m^0'=m^post0, seq^0'=seq^post0, n^0'=n^post0, z^0'=z^post0, c2^0'=c2^post0, pos^0'=pos^post0, max^0'=max^post0, wpos^0'=wpos^post0, (0 == 0 /\ 1-c1^10 <= 0 /\ -1+c1^10 <= 0 /\ -c2^post0 <= 0 /\ 1+m^10-max^0 <= 0 /\ -1+c2^post0 <= 0 /\ -c1^10 <= 0 /\ wpos^post0 == 0 /\ 1-pos^0 <= 0 /\ -1+pos^0 <= 0 /\ 1+m^20-max^0 <= 0 /\ 1-m^30 <= 0 /\ 1-c1^30 <= 0 /\ -1+c1^30 <= 0 /\ 1-m^0 <= 0 /\ -c1^30 <= 0 /\ 1-wpos^30 <= 0 /\ -1+wpos^30 <= 0 /\ -max^post0+max^0 == 0 /\ 1-z^20+z^post0 == 0 /\ pi^10 <= 0 /\ c2^10 <= 0 /\ 1-pi^20+pi^post0 == 0 /\ 1-wpos^50 <= 0 /\ -1+wpos^50 <= 0 /\ 1-c1^20 <= 0 /\ -1+c1^20 <= 0 /\ 1-pi^0+pi^10 == 0 /\ -1-seq^0+seq^post0 == 0 /\ 1-pi^20 <= 0 /\ -c1^20 <= 0 /\ 1-z^20 <= 0 /\ wpos^20 <= 0 /\ wpos^20 == 0 /\ 1-m^20 <= 0 /\ 1-pi^0 <= 0 /\ 1-c1^post0 <= 0 /\ -1+c1^post0 <= 0 /\ z^0 <= 0 /\ pos^10 <= 0 /\ pos^10 == 0 /\ 1-m^30+m^post0 == 0 /\ -c1^post0 <= 0 /\ -1+wpos^50-wpos^40 == 0 /\ 1-pos^post0 <= 0 /\ -1+pos^post0 <= 0 /\ pi^20-seq^post0 == 0 /\ -1+wpos^10-wpos^0 == 0 /\ -c1^40 <= 0 /\ 1-c2^30 <= 0 /\ -1+c2^30 <= 0 /\ c2^post0 <= 0 /\ -1-wpos^20+wpos^30 == 0 /\ 1-z^10+z^20 == 0 /\ -c2^30 <= 0 /\ -1+c1^40 <= 0 /\ -1-pos^10+pos^post0 == 0 /\ -1+m^30-m^20 == 0 /\ -1+c2^10 <= 0 /\ -z^10 <= 0 /\ wpos^40 <= 0 /\ wpos^40 == 0 /\ -c2^10 <= 0 /\ -n^post0+n^0 == 0 /\ 1-z^10 <= 0 /\ 1-c2^20 <= 0 /\ -1+c2^20 <= 0 /\ z^post0 <= 0 /\ 1-m^10 <= 0 /\ 1-m^0+m^10 == 0 /\ 1-wpos^10 <= 0 /\ -1+wpos^10 <= 0 /\ -c2^20 <= 0 /\ wpos^0 <= 0 /\ c1^40 <= 0 /\ -1+m^20-m^10 == 0), cost: 1
New rule:
l0 -> l1 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : c1^0'=c1^post1, pi^0'=pi^post1, m^0'=m^post1, seq^0'=seq^post1, n^0'=n^post1, z^0'=z^post1, c2^0'=c2^post1, pos^0'=pos^post1, max^0'=max^post1, wpos^0'=wpos^post1, (pi^0-pi^post1 == 0 /\ -n^post1+n^0 == 0 /\ c1^0-c1^post1 == 0 /\ seq^0-seq^post1 == 0 /\ -z^post1+z^0 == 0 /\ -wpos^post1+wpos^0 == 0 /\ -pos^post1+pos^0 == 0 /\ m^0-m^post1 == 0 /\ c2^0-c2^post1 == 0 /\ -max^post1+max^0 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : c1^0'=c1^post2, pi^0'=pi^post2, m^0'=m^post2, seq^0'=seq^post2, n^0'=n^post2, z^0'=z^post2, c2^0'=c2^post2, pos^0'=pos^post2, max^0'=max^post2, wpos^0'=wpos^post2, (0 == 0 /\ -z^post2 <= 0 /\ 1-m^post2 <= 0 /\ -m^post2 <= 0 /\ -n^post2 <= 0 /\ -c1^post2 <= 0 /\ z^post2 <= 0 /\ c2^0-c2^post2 == 0 /\ -1+c1^post2 <= 0 /\ c1^post2 <= 0 /\ -1+seq^post2 == 0 /\ -seq^post2+pi^post2 == 0 /\ wpos^post2 == 0 /\ -1+pos^post2-pos^11 == 0 /\ -max^post2 <= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0 /\ pos^11 <= 0 /\ pos^11 == 0), cost: 1
New rule:
l2 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : c1^0'=c1^post3, pi^0'=pi^post3, m^0'=m^post3, seq^0'=seq^post3, n^0'=n^post3, z^0'=z^post3, c2^0'=c2^post3, pos^0'=pos^post3, max^0'=max^post3, wpos^0'=wpos^post3, (-n^post3+n^0 == 0 /\ m^0-m^post3 == 0 /\ c2^0-c2^post3 == 0 /\ -pi^post3+pi^0 == 0 /\ -z^post3+z^0 == 0 /\ pos^0-pos^post3 == 0 /\ c1^0-c1^post3 == 0 /\ -max^post3+max^0 == 0 /\ -wpos^post3+wpos^0 == 0 /\ seq^0-seq^post3 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   4: l0 -> l1 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^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 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 1
New rule:
l3 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 2

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   9: l0 -> l0 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 2
   8: l3 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 2


Accelerated simple loops
Start location: l3
   9: l0 -> l0 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 2
   8: l3 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 2


Applied chaining
First rule:
l3 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 2
Second rule:
l0 -> l0 : c1^0'=1, pi^0'=seq^0, seq^0'=1+seq^0, z^0'=0, c2^0'=0, pos^0'=1, wpos^0'=0, (-1+pos^0 == 0 /\ seq^0 >= 0 /\ -1+pi^0 == 0 /\ z^0 <= 0 /\ 1+m^0-max^0 <= 0 /\ -2+m^0 >= 0 /\ wpos^0 == 0), cost: 2
New rule:
l3 -> l0 : c1^0'=1, pi^0'=1, m^0'=m^post2, seq^0'=2, n^0'=n^post2, z^0'=0, c2^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (1-max^post2+m^post2 <= 0 /\ -n^post2+max^post2 <= 0 /\ -2+m^post2 >= 0), cost: 4

Applied deletion
Removed the following rules: 9

Chained accelerated rules with incoming rules
Start location: l3
   8: l3 -> l0 : c1^0'=0, pi^0'=1, m^0'=m^post2, seq^0'=1, n^0'=n^post2, z^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (-1+m^post2 >= 0 /\ -n^post2+max^post2 <= 0 /\ -max^post2+m^post2 <= 0), cost: 2
  10: l3 -> l0 : c1^0'=1, pi^0'=1, m^0'=m^post2, seq^0'=2, n^0'=n^post2, z^0'=0, c2^0'=0, pos^0'=1, max^0'=max^post2, wpos^0'=0, (1-max^post2+m^post2 <= 0 /\ -n^post2+max^post2 <= 0 /\ -2+m^post2 >= 0), cost: 4


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