WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l2 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, b_7^0'=b_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-1-x_5^0+y_6^0 && Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && b_7^0==b_7^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1
      3: l0 -> l4 : Result_4^0'=Result_4^post_4, __disjvr_0^0'=__disjvr_0^post_4, b_7^0'=b_7^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ -x_5^0+y_6^0<=0 && Result_4^post_4==Result_4^post_4 && __disjvr_0^0==__disjvr_0^post_4 && b_7^0==b_7^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1
      1: l2 -> l3 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, b_7^0'=b_7^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 && b_7^0==b_7^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      2: l3 -> l1 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, b_7^0'=b_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ b_7^post_3==0 && y_6^post_3==-1+y_6^0 && Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && x_5^0==x_5^post_3 ], cost: 1
      5: l1 -> l0 : Result_4^0'=Result_4^post_6, __disjvr_0^0'=__disjvr_0^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ 0<=-1-x_5^0+y_6^0 && b_7^0<=0 && 0<=b_7^0 && b_7^post_6==1 && x_5^post_6==1+x_5^0 && Result_4^0==Result_4^post_6 && __disjvr_0^0==__disjvr_0^post_6 && y_6^0==y_6^post_6 ], cost: 1
      6: l1 -> l4 : Result_4^0'=Result_4^post_7, __disjvr_0^0'=__disjvr_0^post_7, b_7^0'=b_7^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ -x_5^0+y_6^0<=0 && Result_4^post_7==Result_4^post_7 && __disjvr_0^0==__disjvr_0^post_7 && b_7^0==b_7^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1
      4: l5 -> l1 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, b_7^0'=b_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ b_7^post_5==0 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      7: l6 -> l5 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, b_7^0'=b_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && b_7^0==b_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, b_7^0'=b_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && b_7^0==b_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      0: l0 -> l2 : Result_4^0'=Result_4^post_1, __disjvr_0^0'=__disjvr_0^post_1, b_7^0'=b_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ 0<=-1-x_5^0+y_6^0 && Result_4^0==Result_4^post_1 && __disjvr_0^0==__disjvr_0^post_1 && b_7^0==b_7^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1
      1: l2 -> l3 : Result_4^0'=Result_4^post_2, __disjvr_0^0'=__disjvr_0^post_2, b_7^0'=b_7^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 && b_7^0==b_7^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      2: l3 -> l1 : Result_4^0'=Result_4^post_3, __disjvr_0^0'=__disjvr_0^post_3, b_7^0'=b_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ b_7^post_3==0 && y_6^post_3==-1+y_6^0 && Result_4^0==Result_4^post_3 && __disjvr_0^0==__disjvr_0^post_3 && x_5^0==x_5^post_3 ], cost: 1
      5: l1 -> l0 : Result_4^0'=Result_4^post_6, __disjvr_0^0'=__disjvr_0^post_6, b_7^0'=b_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ 0<=-1-x_5^0+y_6^0 && b_7^0<=0 && 0<=b_7^0 && b_7^post_6==1 && x_5^post_6==1+x_5^0 && Result_4^0==Result_4^post_6 && __disjvr_0^0==__disjvr_0^post_6 && y_6^0==y_6^post_6 ], cost: 1
      4: l5 -> l1 : Result_4^0'=Result_4^post_5, __disjvr_0^0'=__disjvr_0^post_5, b_7^0'=b_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ b_7^post_5==0 && Result_4^0==Result_4^post_5 && __disjvr_0^0==__disjvr_0^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      7: l6 -> l5 : Result_4^0'=Result_4^post_8, __disjvr_0^0'=__disjvr_0^post_8, b_7^0'=b_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && __disjvr_0^0==__disjvr_0^post_8 && b_7^0==b_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l2 : [ 0<=-1-x_5^0+y_6^0 ], cost: 1
      1: l2 -> l3 : [], cost: 1
      2: l3 -> l1 : b_7^0'=0, y_6^0'=-1+y_6^0, [], cost: 1
      5: l1 -> l0 : b_7^0'=1, x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && b_7^0==0 ], cost: 1
      4: l5 -> l1 : b_7^0'=0, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
     11: l1 -> l1 : b_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=-1+y_6^0, [ b_7^0==0 && 0<=-2-x_5^0+y_6^0 ], cost: 4
      8: l6 -> l1 : b_7^0'=0, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     11: l1 -> l1 : b_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=-1+y_6^0, [ b_7^0==0 && 0<=-2-x_5^0+y_6^0 ], cost: 4

   Accelerated rule 11 with metering function meter (where 2*meter==-1-x_5^0+y_6^0), yielding the new rule 12.
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     12: l1 -> l1 : b_7^0'=0, x_5^0'=x_5^0+meter, y_6^0'=-meter+y_6^0, [ b_7^0==0 && 0<=-2-x_5^0+y_6^0 && 2*meter==-1-x_5^0+y_6^0 && meter>=1 ], cost: 4*meter
      8: l6 -> l1 : b_7^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      8: l6 -> l1 : b_7^0'=0, [], cost: 2
     13: l6 -> l1 : b_7^0'=0, x_5^0'=x_5^0+meter, y_6^0'=-meter+y_6^0, [ 0<=-2-x_5^0+y_6^0 && 2*meter==-1-x_5^0+y_6^0 && meter>=1 ], cost: 2+4*meter

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     13: l6 -> l1 : b_7^0'=0, x_5^0'=x_5^0+meter, y_6^0'=-meter+y_6^0, [ 0<=-2-x_5^0+y_6^0 && 2*meter==-1-x_5^0+y_6^0 && meter>=1 ], cost: 2+4*meter

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     13: l6 -> l1 : b_7^0'=0, x_5^0'=x_5^0+meter, y_6^0'=-meter+y_6^0, [ 0<=-2-x_5^0+y_6^0 && 2*meter==-1-x_5^0+y_6^0 && meter>=1 ], cost: 2+4*meter

Computing asymptotic complexity for rule 13
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -1-x_5^0+y_6^0 (+/+!), 2+x_5^0+2*meter-y_6^0 (+/+!), -x_5^0-2*meter+y_6^0 (+/+!), 2+4*meter (+) [not solved]

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

      applying transformation rule (C) using substitution {x_5^0==-2*n,meter==n,y_6^0==1}
      resulting limit problem:
      [solved]

   Solution:
      x_5^0 / -2*n
      meter / n
      y_6^0 / 1
   Resulting cost 2+4*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: 2+4*n
   Rule cost:   2+4*meter
   Rule guard:  [ 0<=-2-x_5^0+y_6^0 && 2*meter==-1-x_5^0+y_6^0 ]

WORST_CASE(Omega(n^1),?)