WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : Result^0'=Result^post_1, __const_99^0'=__const_99^post_1, __disjvr_0^0'=__disjvr_0^post_1, x^0'=x^post_1, y^0'=y^post_1, [ -x^0<=0 && Result^post_1==Result^post_1 && __const_99^0==__const_99^post_1 && __disjvr_0^0==__disjvr_0^post_1 && x^0==x^post_1 && y^0==y^post_1 ], cost: 1
      1: l0 -> l3 : Result^0'=Result^post_2, __const_99^0'=__const_99^post_2, __disjvr_0^0'=__disjvr_0^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 0<=-1-x^0 && Result^0==Result^post_2 && __const_99^0==__const_99^post_2 && __disjvr_0^0==__disjvr_0^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      5: l0 -> l5 : Result^0'=Result^post_6, __const_99^0'=__const_99^post_6, __disjvr_0^0'=__disjvr_0^post_6, x^0'=x^post_6, y^0'=y^post_6, [ 0<=-1-x^0 && y^0<=-1 && -1<=y^0 && y^post_6==1+y^0 && x^post_6==x^0-__const_99^0 && Result^0==Result^post_6 && __const_99^0==__const_99^post_6 && __disjvr_0^0==__disjvr_0^post_6 ], cost: 1
      2: l3 -> l4 : Result^0'=Result^post_3, __const_99^0'=__const_99^post_3, __disjvr_0^0'=__disjvr_0^post_3, x^0'=x^post_3, y^0'=y^post_3, [ __disjvr_0^post_3==__disjvr_0^0 && Result^0==Result^post_3 && __const_99^0==__const_99^post_3 && __disjvr_0^0==__disjvr_0^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l4 -> l2 : Result^0'=Result^post_4, __const_99^0'=__const_99^post_4, __disjvr_0^0'=__disjvr_0^post_4, x^0'=x^post_4, y^0'=y^post_4, [ x^post_4==1+x^0 && y^post_4==1+y^0 && Result^0==Result^post_4 && __const_99^0==__const_99^post_4 && __disjvr_0^0==__disjvr_0^post_4 ], cost: 1
      4: l2 -> l0 : Result^0'=Result^post_5, __const_99^0'=__const_99^post_5, __disjvr_0^0'=__disjvr_0^post_5, x^0'=x^post_5, y^0'=y^post_5, [ Result^0==Result^post_5 && __const_99^0==__const_99^post_5 && __disjvr_0^0==__disjvr_0^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      6: l5 -> l0 : Result^0'=Result^post_7, __const_99^0'=__const_99^post_7, __disjvr_0^0'=__disjvr_0^post_7, x^0'=x^post_7, y^0'=y^post_7, [ Result^0==Result^post_7 && __const_99^0==__const_99^post_7 && __disjvr_0^0==__disjvr_0^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1
      7: l6 -> l0 : Result^0'=Result^post_8, __const_99^0'=__const_99^post_8, __disjvr_0^0'=__disjvr_0^post_8, x^0'=x^post_8, y^0'=y^post_8, [ Result^0==Result^post_8 && __const_99^0==__const_99^post_8 && __disjvr_0^0==__disjvr_0^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1
      8: l7 -> l6 : Result^0'=Result^post_9, __const_99^0'=__const_99^post_9, __disjvr_0^0'=__disjvr_0^post_9, x^0'=x^post_9, y^0'=y^post_9, [ Result^0==Result^post_9 && __const_99^0==__const_99^post_9 && __disjvr_0^0==__disjvr_0^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      8: l7 -> l6 : Result^0'=Result^post_9, __const_99^0'=__const_99^post_9, __disjvr_0^0'=__disjvr_0^post_9, x^0'=x^post_9, y^0'=y^post_9, [ Result^0==Result^post_9 && __const_99^0==__const_99^post_9 && __disjvr_0^0==__disjvr_0^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      1: l0 -> l3 : Result^0'=Result^post_2, __const_99^0'=__const_99^post_2, __disjvr_0^0'=__disjvr_0^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 0<=-1-x^0 && Result^0==Result^post_2 && __const_99^0==__const_99^post_2 && __disjvr_0^0==__disjvr_0^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      5: l0 -> l5 : Result^0'=Result^post_6, __const_99^0'=__const_99^post_6, __disjvr_0^0'=__disjvr_0^post_6, x^0'=x^post_6, y^0'=y^post_6, [ 0<=-1-x^0 && y^0<=-1 && -1<=y^0 && y^post_6==1+y^0 && x^post_6==x^0-__const_99^0 && Result^0==Result^post_6 && __const_99^0==__const_99^post_6 && __disjvr_0^0==__disjvr_0^post_6 ], cost: 1
      2: l3 -> l4 : Result^0'=Result^post_3, __const_99^0'=__const_99^post_3, __disjvr_0^0'=__disjvr_0^post_3, x^0'=x^post_3, y^0'=y^post_3, [ __disjvr_0^post_3==__disjvr_0^0 && Result^0==Result^post_3 && __const_99^0==__const_99^post_3 && __disjvr_0^0==__disjvr_0^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l4 -> l2 : Result^0'=Result^post_4, __const_99^0'=__const_99^post_4, __disjvr_0^0'=__disjvr_0^post_4, x^0'=x^post_4, y^0'=y^post_4, [ x^post_4==1+x^0 && y^post_4==1+y^0 && Result^0==Result^post_4 && __const_99^0==__const_99^post_4 && __disjvr_0^0==__disjvr_0^post_4 ], cost: 1
      4: l2 -> l0 : Result^0'=Result^post_5, __const_99^0'=__const_99^post_5, __disjvr_0^0'=__disjvr_0^post_5, x^0'=x^post_5, y^0'=y^post_5, [ Result^0==Result^post_5 && __const_99^0==__const_99^post_5 && __disjvr_0^0==__disjvr_0^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      6: l5 -> l0 : Result^0'=Result^post_7, __const_99^0'=__const_99^post_7, __disjvr_0^0'=__disjvr_0^post_7, x^0'=x^post_7, y^0'=y^post_7, [ Result^0==Result^post_7 && __const_99^0==__const_99^post_7 && __disjvr_0^0==__disjvr_0^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1
      7: l6 -> l0 : Result^0'=Result^post_8, __const_99^0'=__const_99^post_8, __disjvr_0^0'=__disjvr_0^post_8, x^0'=x^post_8, y^0'=y^post_8, [ Result^0==Result^post_8 && __const_99^0==__const_99^post_8 && __disjvr_0^0==__disjvr_0^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1
      8: l7 -> l6 : Result^0'=Result^post_9, __const_99^0'=__const_99^post_9, __disjvr_0^0'=__disjvr_0^post_9, x^0'=x^post_9, y^0'=y^post_9, [ Result^0==Result^post_9 && __const_99^0==__const_99^post_9 && __disjvr_0^0==__disjvr_0^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      1: l0 -> l3 : [ 0<=-1-x^0 ], cost: 1
      5: l0 -> l5 : x^0'=x^0-__const_99^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 1
      2: l3 -> l4 : [], cost: 1
      3: l4 -> l2 : x^0'=1+x^0, y^0'=1+y^0, [], cost: 1
      4: l2 -> l0 : [], cost: 1
      6: l5 -> l0 : [], cost: 1
      7: l6 -> l0 : [], cost: 1
      8: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
     11: l0 -> l0 : x^0'=x^0-__const_99^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2
     13: l0 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [ 0<=-1-x^0 ], cost: 4
      9: l7 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     11: l0 -> l0 : x^0'=x^0-__const_99^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2
     13: l0 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [ 0<=-1-x^0 ], cost: 4

   Accelerated rule 11 with metering function -1-y^0, yielding the new rule 14.
   Accelerated rule 13 with metering function -x^0, yielding the new rule 15.
   Removing the simple loops: 11 13.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     14: l0 -> l0 : x^0'=x^0+(1+y^0)*__const_99^0, y^0'=-1, [ 0<=-1-x^0 && 1+y^0==0 && -1-y^0>=1 ], cost: -2-2*y^0
     15: l0 -> l0 : x^0'=0, y^0'=-x^0+y^0, [ 0<=-1-x^0 ], cost: -4*x^0
      9: l7 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
      9: l7 -> l0 : [], cost: 2
     16: l7 -> l0 : x^0'=0, y^0'=-x^0+y^0, [ 0<=-1-x^0 ], cost: 2-4*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     16: l7 -> l0 : x^0'=0, y^0'=-x^0+y^0, [ 0<=-1-x^0 ], cost: 2-4*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     16: l7 -> l0 : x^0'=0, y^0'=-x^0+y^0, [ 0<=-1-x^0 ], cost: 2-4*x^0

Computing asymptotic complexity for rule 16
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      2-4*x^0 (+), -x^0 (+/+!) [not solved]

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

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

   Solution:
      x^0 / -n
   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*x^0
   Rule guard:  [ 0<=-1-x^0 ]

WORST_CASE(Omega(n^1),?)