WORST_CASE(Omega(n^1),?)

### Pre-processing the ITS problem ###

Initial linear ITS problem
   Start location: l5
      0: l0 -> l2 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, k_7^0'=k_7^post_1, w_8^0'=w_8^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-2-x_5^0 && x_5^post_1==1+x_5^0 && y_6^post_1==1+y_6^0 && Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && k_7^0==k_7^post_1 && w_8^0==w_8^post_1 ], cost: 1
      3: l0 -> l3 : Result_4^0'=Result_4^post_4, __disjvr_0^0'=__disjvr_0^post_4, k_7^0'=k_7^post_4, w_8^0'=w_8^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ -1-x_5^0<=0 && Result_4^post_4==Result_4^post_4 && __disjvr_0^0==__disjvr_0^post_4 && k_7^0==k_7^post_4 && w_8^0==w_8^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1
      1: l2 -> l1 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, k_7^0'=k_7^post_2, w_8^0'=w_8^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ __disjvr_0^post_2==__disjvr_0^0 && Result_4^0==Result_4^post_2 && __disjvr_0^0==__disjvr_0^post_2 && k_7^0==k_7^post_2 && w_8^0==w_8^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      2: l1 -> l0 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, k_7^0'=k_7^post_3, w_8^0'=w_8^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && k_7^0==k_7^post_3 && w_8^0==w_8^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      4: l4 -> l0 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, k_7^0'=k_7^post_5, w_8^0'=w_8^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 0<=-2+k_7^0 && 0<=-2+w_8^0 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && k_7^0==k_7^post_5 && w_8^0==w_8^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, __disjvr_0^0'=__disjvr_0^post_6, k_7^0'=k_7^post_6, w_8^0'=w_8^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ -1+k_7^0<=0 && Result_4^post_6==Result_4^post_6 && __disjvr_0^0==__disjvr_0^post_6 && k_7^0==k_7^post_6 && w_8^0==w_8^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1
      6: l5 -> l4 : Result_4^0'=Result_4^post_7, __disjvr_0^0'=__disjvr_0^post_7, k_7^0'=k_7^post_7, w_8^0'=w_8^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && __disjvr_0^0==__disjvr_0^post_7 && k_7^0==k_7^post_7 && w_8^0==w_8^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l4 : Result_4^0'=Result_4^post_7, __disjvr_0^0'=__disjvr_0^post_7, k_7^0'=k_7^post_7, w_8^0'=w_8^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && __disjvr_0^0==__disjvr_0^post_7 && k_7^0==k_7^post_7 && w_8^0==w_8^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      0: l0 -> l2 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, k_7^0'=k_7^post_1, w_8^0'=w_8^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-2-x_5^0 && x_5^post_1==1+x_5^0 && y_6^post_1==1+y_6^0 && Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && k_7^0==k_7^post_1 && w_8^0==w_8^post_1 ], cost: 1
      1: l2 -> l1 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, k_7^0'=k_7^post_2, w_8^0'=w_8^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ __disjvr_0^post_2==__disjvr_0^0 && Result_4^0==Result_4^post_2 && __disjvr_0^0==__disjvr_0^post_2 && k_7^0==k_7^post_2 && w_8^0==w_8^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      2: l1 -> l0 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, k_7^0'=k_7^post_3, w_8^0'=w_8^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && k_7^0==k_7^post_3 && w_8^0==w_8^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      4: l4 -> l0 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, k_7^0'=k_7^post_5, w_8^0'=w_8^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 0<=-2+k_7^0 && 0<=-2+w_8^0 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && k_7^0==k_7^post_5 && w_8^0==w_8^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      6: l5 -> l4 : Result_4^0'=Result_4^post_7, __disjvr_0^0'=__disjvr_0^post_7, k_7^0'=k_7^post_7, w_8^0'=w_8^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && __disjvr_0^0==__disjvr_0^post_7 && k_7^0==k_7^post_7 && w_8^0==w_8^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      0: l0 -> l2 : x_5^0'=1+x_5^0, y_6^0'=1+y_6^0, [ 0<=-2-x_5^0 ], cost: 1
      1: l2 -> l1 : [], cost: 1
      2: l1 -> l0 : [], cost: 1
      4: l4 -> l0 : [ 0<=-2+k_7^0 && 0<=-2+w_8^0 ], cost: 1
      6: l5 -> l4 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      9: l0 -> l0 : x_5^0'=1+x_5^0, y_6^0'=1+y_6^0, [ 0<=-2-x_5^0 ], cost: 3
      7: l5 -> l0 : [ 0<=-2+k_7^0 && 0<=-2+w_8^0 ], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      9: l0 -> l0 : x_5^0'=1+x_5^0, y_6^0'=1+y_6^0, [ 0<=-2-x_5^0 ], cost: 3

   Accelerated rule 9 with metering function -1-x_5^0, yielding the new rule 10.
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
     10: l0 -> l0 : x_5^0'=-1, y_6^0'=-1+y_6^0-x_5^0, [ 0<=-2-x_5^0 ], cost: -3-3*x_5^0
      7: l5 -> l0 : [ 0<=-2+k_7^0 && 0<=-2+w_8^0 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      7: l5 -> l0 : [ 0<=-2+k_7^0 && 0<=-2+w_8^0 ], cost: 2
     11: l5 -> l0 : x_5^0'=-1, y_6^0'=-1+y_6^0-x_5^0, [ 0<=-2+k_7^0 && 0<=-2+w_8^0 && 0<=-2-x_5^0 ], cost: -1-3*x_5^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     11: l5 -> l0 : x_5^0'=-1, y_6^0'=-1+y_6^0-x_5^0, [ 0<=-2+k_7^0 && 0<=-2+w_8^0 && 0<=-2-x_5^0 ], cost: -1-3*x_5^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     11: l5 -> l0 : x_5^0'=-1, y_6^0'=-1+y_6^0-x_5^0, [ 0<=-2+k_7^0 && 0<=-2+w_8^0 && 0<=-2-x_5^0 ], cost: -1-3*x_5^0

Computing asymptotic complexity for rule 11
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -1-x_5^0 (+/+!), -1+w_8^0 (+/+!), -1+k_7^0 (+/+!), -1-3*x_5^0 (+) [not solved]

      removing all constraints (solved by SMT)
      resulting limit problem: [solved]

      applying transformation rule (C) using substitution {k_7^0==n,w_8^0==n,x_5^0==-n}
      resulting limit problem:
      [solved]

   Solution:
      k_7^0 / n
      w_8^0 / n
      x_5^0 / -n
   Resulting cost -1+3*n has complexity: Poly(n^1)

Found new complexity Poly(n^1).

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Poly(n^1)
   Cpx degree:  1
   Solved cost: -1+3*n
   Rule cost:   -1-3*x_5^0
   Rule guard:  [ 0<=-2+k_7^0 && 0<=-2+w_8^0 && 0<=-2-x_5^0 ]

WORST_CASE(Omega(n^1),?)