WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, tmp_7^0'=tmp_7^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ -x_5^0+y_6^0<=0 && Result_4^post_1==Result_4^post_1 && tmp_7^0==tmp_7^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1
      1: l0 -> l2 : Result_4^0'=Result_4^post_2, tmp_7^0'=tmp_7^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ 0<=-1-x_5^0+y_6^0 && tmp_7^post_2==tmp_7^post_2 && tmp_7^post_2<=0 && 0<=tmp_7^post_2 && y_6^post_2==-1+y_6^0 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 ], cost: 1
      3: l0 -> l4 : Result_4^0'=Result_4^post_4, tmp_7^0'=tmp_7^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 0<=-1-x_5^0+y_6^0 && tmp_7^post_4==tmp_7^post_4 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1
      2: l2 -> l0 : Result_4^0'=Result_4^post_3, tmp_7^0'=tmp_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && tmp_7^0==tmp_7^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      4: l4 -> l5 : Result_4^0'=Result_4^post_5, tmp_7^0'=tmp_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 1+tmp_7^0<=0 && Result_4^0==Result_4^post_5 && tmp_7^0==tmp_7^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      5: l4 -> l5 : Result_4^0'=Result_4^post_6, tmp_7^0'=tmp_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ 1<=tmp_7^0 && Result_4^0==Result_4^post_6 && tmp_7^0==tmp_7^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1
      6: l5 -> l3 : Result_4^0'=Result_4^post_7, tmp_7^0'=tmp_7^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ x_5^post_7==1+x_5^0 && Result_4^0==Result_4^post_7 && tmp_7^0==tmp_7^post_7 && y_6^0==y_6^post_7 ], cost: 1
      7: l3 -> l0 : Result_4^0'=Result_4^post_8, tmp_7^0'=tmp_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && tmp_7^0==tmp_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1
      8: l6 -> l0 : Result_4^0'=Result_4^post_9, tmp_7^0'=tmp_7^post_9, x_5^0'=x_5^post_9, y_6^0'=y_6^post_9, [ Result_4^0==Result_4^post_9 && tmp_7^0==tmp_7^post_9 && x_5^0==x_5^post_9 && y_6^0==y_6^post_9 ], cost: 1
      9: l7 -> l6 : Result_4^0'=Result_4^post_10, tmp_7^0'=tmp_7^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, [ Result_4^0==Result_4^post_10 && tmp_7^0==tmp_7^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: l7 -> l6 : Result_4^0'=Result_4^post_10, tmp_7^0'=tmp_7^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, [ Result_4^0==Result_4^post_10 && tmp_7^0==tmp_7^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      1: l0 -> l2 : Result_4^0'=Result_4^post_2, tmp_7^0'=tmp_7^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ 0<=-1-x_5^0+y_6^0 && tmp_7^post_2==tmp_7^post_2 && tmp_7^post_2<=0 && 0<=tmp_7^post_2 && y_6^post_2==-1+y_6^0 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 ], cost: 1
      3: l0 -> l4 : Result_4^0'=Result_4^post_4, tmp_7^0'=tmp_7^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 0<=-1-x_5^0+y_6^0 && tmp_7^post_4==tmp_7^post_4 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1
      2: l2 -> l0 : Result_4^0'=Result_4^post_3, tmp_7^0'=tmp_7^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && tmp_7^0==tmp_7^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      4: l4 -> l5 : Result_4^0'=Result_4^post_5, tmp_7^0'=tmp_7^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 1+tmp_7^0<=0 && Result_4^0==Result_4^post_5 && tmp_7^0==tmp_7^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      5: l4 -> l5 : Result_4^0'=Result_4^post_6, tmp_7^0'=tmp_7^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ 1<=tmp_7^0 && Result_4^0==Result_4^post_6 && tmp_7^0==tmp_7^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1
      6: l5 -> l3 : Result_4^0'=Result_4^post_7, tmp_7^0'=tmp_7^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ x_5^post_7==1+x_5^0 && Result_4^0==Result_4^post_7 && tmp_7^0==tmp_7^post_7 && y_6^0==y_6^post_7 ], cost: 1
      7: l3 -> l0 : Result_4^0'=Result_4^post_8, tmp_7^0'=tmp_7^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ Result_4^0==Result_4^post_8 && tmp_7^0==tmp_7^post_8 && x_5^0==x_5^post_8 && y_6^0==y_6^post_8 ], cost: 1
      8: l6 -> l0 : Result_4^0'=Result_4^post_9, tmp_7^0'=tmp_7^post_9, x_5^0'=x_5^post_9, y_6^0'=y_6^post_9, [ Result_4^0==Result_4^post_9 && tmp_7^0==tmp_7^post_9 && x_5^0==x_5^post_9 && y_6^0==y_6^post_9 ], cost: 1
      9: l7 -> l6 : Result_4^0'=Result_4^post_10, tmp_7^0'=tmp_7^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, [ Result_4^0==Result_4^post_10 && tmp_7^0==tmp_7^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      1: l0 -> l2 : tmp_7^0'=0, y_6^0'=-1+y_6^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 1
      3: l0 -> l4 : tmp_7^0'=tmp_7^post_4, [ 0<=-1-x_5^0+y_6^0 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      4: l4 -> l5 : [ 1+tmp_7^0<=0 ], cost: 1
      5: l4 -> l5 : [ 1<=tmp_7^0 ], cost: 1
      6: l5 -> l3 : x_5^0'=1+x_5^0, [], cost: 1
      7: l3 -> l0 : [], cost: 1
      8: l6 -> l0 : [], cost: 1
      9: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
      3: l0 -> l4 : tmp_7^0'=tmp_7^post_4, [ 0<=-1-x_5^0+y_6^0 ], cost: 1
     11: l0 -> l0 : tmp_7^0'=0, y_6^0'=-1+y_6^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2
      4: l4 -> l5 : [ 1+tmp_7^0<=0 ], cost: 1
      5: l4 -> l5 : [ 1<=tmp_7^0 ], cost: 1
     12: l5 -> l0 : x_5^0'=1+x_5^0, [], cost: 2
     10: l7 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     11: l0 -> l0 : tmp_7^0'=0, y_6^0'=-1+y_6^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2

   Accelerated rule 11 with metering function -x_5^0+y_6^0, yielding the new rule 13.
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
      3: l0 -> l4 : tmp_7^0'=tmp_7^post_4, [ 0<=-1-x_5^0+y_6^0 ], cost: 1
     13: l0 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: -2*x_5^0+2*y_6^0
      4: l4 -> l5 : [ 1+tmp_7^0<=0 ], cost: 1
      5: l4 -> l5 : [ 1<=tmp_7^0 ], cost: 1
     12: l5 -> l0 : x_5^0'=1+x_5^0, [], cost: 2
     10: l7 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
      3: l0 -> l4 : tmp_7^0'=tmp_7^post_4, [ 0<=-1-x_5^0+y_6^0 ], cost: 1
      4: l4 -> l5 : [ 1+tmp_7^0<=0 ], cost: 1
      5: l4 -> l5 : [ 1<=tmp_7^0 ], cost: 1
     12: l5 -> l0 : x_5^0'=1+x_5^0, [], cost: 2
     15: l5 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: -2*x_5^0+2*y_6^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0

Eliminated locations (on tree-shaped paths):
   Start location: l7
     16: l0 -> l5 : tmp_7^0'=tmp_7^post_4, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: 2
     17: l0 -> l5 : tmp_7^0'=tmp_7^post_4, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: 2
     12: l5 -> l0 : x_5^0'=1+x_5^0, [], cost: 2
     15: l5 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: -2*x_5^0+2*y_6^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0

Eliminated locations (on tree-shaped paths):
   Start location: l7
     18: l0 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: 4
     19: l0 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 1+tmp_7^post_4<=0 && 0<=-2-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0
     20: l0 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: 4
     21: l0 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 1<=tmp_7^post_4 && 0<=-2-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0

Accelerating simple loops of location 0.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     18: l0 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: 4
     20: l0 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=1+x_5^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: 4
     21: l0 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0

   Accelerated rule 18 with metering function -x_5^0+y_6^0, yielding the new rule 22.
   Accelerated rule 20 with metering function -x_5^0+y_6^0, yielding the new rule 23.
   Found no metering function for rule 21.
   Removing the simple loops: 18 20.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     21: l0 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0
     22: l0 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: -4*x_5^0+4*y_6^0
     23: l0 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: -4*x_5^0+4*y_6^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0

Chained accelerated rules (with incoming rules):
   Start location: l7
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0
     24: l7 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: 4-2*x_5^0+2*y_6^0
     25: l7 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: 2-4*x_5^0+4*y_6^0
     26: l7 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: 2-4*x_5^0+4*y_6^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0
     24: l7 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: 4-2*x_5^0+2*y_6^0
     25: l7 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: 2-4*x_5^0+4*y_6^0
     26: l7 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: 2-4*x_5^0+4*y_6^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     14: l7 -> l0 : tmp_7^0'=0, y_6^0'=x_5^0, [ 0<=-1-x_5^0+y_6^0 ], cost: 2-2*x_5^0+2*y_6^0
     24: l7 -> l0 : tmp_7^0'=0, x_5^0'=1+x_5^0, y_6^0'=1+x_5^0, [ 0<=-2-x_5^0+y_6^0 ], cost: 4-2*x_5^0+2*y_6^0
     25: l7 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1+tmp_7^post_4<=0 ], cost: 2-4*x_5^0+4*y_6^0
     26: l7 -> l0 : tmp_7^0'=tmp_7^post_4, x_5^0'=y_6^0, [ 0<=-1-x_5^0+y_6^0 && 1<=tmp_7^post_4 ], cost: 2-4*x_5^0+4*y_6^0

Computing asymptotic complexity for rule 14
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -x_5^0+y_6^0 (+/+!), 2-2*x_5^0+2*y_6^0 (+) [not solved]

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

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

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

WORST_CASE(Omega(n^1),?)