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, x^0'=x^post_1, y^0'=y^post_1, [ -x^0<=0 && Result^post_1==Result^post_1 && x^0==x^post_1 && y^0==y^post_1 ], cost: 1
      1: l0 -> l3 : Result^0'=Result^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 0<=-1-x^0 && Result^0==Result^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      6: l0 -> l5 : Result^0'=Result^post_7, x^0'=x^post_7, y^0'=y^post_7, [ 0<=-1-x^0 && y^0<=-1 && -1<=y^0 && y^post_7==1+y^0 && x^post_7==-99+x^0 && Result^0==Result^post_7 ], cost: 1
      2: l3 -> l4 : Result^0'=Result^post_3, x^0'=x^post_3, y^0'=y^post_3, [ 1+y^0<=-1 && Result^0==Result^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l3 -> l4 : Result^0'=Result^post_4, x^0'=x^post_4, y^0'=y^post_4, [ 0<=y^0 && Result^0==Result^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1
      4: l4 -> l2 : Result^0'=Result^post_5, x^0'=x^post_5, y^0'=y^post_5, [ x^post_5==1+x^0 && y^post_5==1+y^0 && Result^0==Result^post_5 ], cost: 1
      5: l2 -> l0 : Result^0'=Result^post_6, x^0'=x^post_6, y^0'=y^post_6, [ Result^0==Result^post_6 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1
      7: l5 -> l0 : Result^0'=Result^post_8, x^0'=x^post_8, y^0'=y^post_8, [ Result^0==Result^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1
      8: l6 -> l0 : Result^0'=Result^post_9, x^0'=x^post_9, y^0'=y^post_9, [ Result^0==Result^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1
      9: l7 -> l6 : Result^0'=Result^post_10, x^0'=x^post_10, y^0'=y^post_10, [ Result^0==Result^post_10 && x^0==x^post_10 && y^0==y^post_10 ], cost: 1

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

Removed unreachable and leaf rules:
   Start location: l7
      1: l0 -> l3 : Result^0'=Result^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 0<=-1-x^0 && Result^0==Result^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      6: l0 -> l5 : Result^0'=Result^post_7, x^0'=x^post_7, y^0'=y^post_7, [ 0<=-1-x^0 && y^0<=-1 && -1<=y^0 && y^post_7==1+y^0 && x^post_7==-99+x^0 && Result^0==Result^post_7 ], cost: 1
      2: l3 -> l4 : Result^0'=Result^post_3, x^0'=x^post_3, y^0'=y^post_3, [ 1+y^0<=-1 && Result^0==Result^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l3 -> l4 : Result^0'=Result^post_4, x^0'=x^post_4, y^0'=y^post_4, [ 0<=y^0 && Result^0==Result^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1
      4: l4 -> l2 : Result^0'=Result^post_5, x^0'=x^post_5, y^0'=y^post_5, [ x^post_5==1+x^0 && y^post_5==1+y^0 && Result^0==Result^post_5 ], cost: 1
      5: l2 -> l0 : Result^0'=Result^post_6, x^0'=x^post_6, y^0'=y^post_6, [ Result^0==Result^post_6 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1
      7: l5 -> l0 : Result^0'=Result^post_8, x^0'=x^post_8, y^0'=y^post_8, [ Result^0==Result^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1
      8: l6 -> l0 : Result^0'=Result^post_9, x^0'=x^post_9, y^0'=y^post_9, [ Result^0==Result^post_9 && x^0==x^post_9 && y^0==y^post_9 ], cost: 1
      9: l7 -> l6 : Result^0'=Result^post_10, x^0'=x^post_10, y^0'=y^post_10, [ Result^0==Result^post_10 && x^0==x^post_10 && y^0==y^post_10 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      1: l0 -> l3 : [ 0<=-1-x^0 ], cost: 1
      6: l0 -> l5 : x^0'=-99+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 1
      2: l3 -> l4 : [ 1+y^0<=-1 ], cost: 1
      3: l3 -> l4 : [ 0<=y^0 ], cost: 1
      4: l4 -> l2 : x^0'=1+x^0, y^0'=1+y^0, [], cost: 1
      5: l2 -> l0 : [], cost: 1
      7: l5 -> 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
      1: l0 -> l3 : [ 0<=-1-x^0 ], cost: 1
     11: l0 -> l0 : x^0'=-99+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2
      2: l3 -> l4 : [ 1+y^0<=-1 ], cost: 1
      3: l3 -> l4 : [ 0<=y^0 ], cost: 1
     12: l4 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [], cost: 2
     10: l7 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     11: l0 -> l0 : x^0'=-99+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2

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

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
      1: l0 -> l3 : [ 0<=-1-x^0 ], cost: 1
     13: l0 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: -2*y^0
      2: l3 -> l4 : [ 1+y^0<=-1 ], cost: 1
      3: l3 -> l4 : [ 0<=y^0 ], cost: 1
     12: l4 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [], cost: 2
     10: l7 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
      1: l0 -> l3 : [ 0<=-1-x^0 ], cost: 1
      2: l3 -> l4 : [ 1+y^0<=-1 ], cost: 1
      3: l3 -> l4 : [ 0<=y^0 ], cost: 1
     12: l4 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [], cost: 2
     15: l4 -> l0 : x^0'=100+99*y^0+x^0, y^0'=0, [ 0<=-2-x^0 && 2+y^0==0 ], cost: -2*y^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0

Eliminated locations (on tree-shaped paths):
   Start location: l7
     16: l0 -> l4 : [ 0<=-1-x^0 && 1+y^0<=-1 ], cost: 2
     17: l0 -> l4 : [ 0<=-1-x^0 && 0<=y^0 ], cost: 2
     12: l4 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [], cost: 2
     15: l4 -> l0 : x^0'=100+99*y^0+x^0, y^0'=0, [ 0<=-2-x^0 && 2+y^0==0 ], cost: -2*y^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0

Eliminated locations (on tree-shaped paths):
   Start location: l7
     18: l0 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0<=-1 ], cost: 4
     19: l0 -> l0 : x^0'=100+99*y^0+x^0, y^0'=0, [ 0<=-2-x^0 && 2+y^0==0 ], cost: 2-2*y^0
     20: l0 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 0<=y^0 ], cost: 4
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0

Accelerating simple loops of location 0.
   Accelerating the following rules:
     18: l0 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 1+y^0<=-1 ], cost: 4
     19: l0 -> l0 : x^0'=100+99*y^0+x^0, y^0'=0, [ 0<=-2-x^0 && 2+y^0==0 ], cost: 2-2*y^0
     20: l0 -> l0 : x^0'=1+x^0, y^0'=1+y^0, [ 0<=-1-x^0 && 0<=y^0 ], cost: 4

   Accelerated rule 18 with metering function -1-x^0 (after adding x^0>=y^0), yielding the new rule 21.
   Accelerated rule 18 with metering function -1-y^0 (after adding x^0<=y^0), yielding the new rule 22.
   Accelerated rule 19 with metering function meter (where 2*meter==-1-y^0), yielding the new rule 23.
   Accelerated rule 20 with metering function -x^0, yielding the new rule 24.
   Removing the simple loops: 18 19 20.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     21: l0 -> l0 : x^0'=-1, y^0'=-1+y^0-x^0, [ 1+y^0<=-1 && x^0>=y^0 && -1-x^0>=1 ], cost: -4-4*x^0
     22: l0 -> l0 : x^0'=-1-y^0+x^0, y^0'=-1, [ 0<=-1-x^0 && 1+y^0<=-1 && x^0<=y^0 ], cost: -4-4*y^0
     23: l0 -> l0 : x^0'=99*y^0+100*meter+x^0, y^0'=0, [ 0<=-2-x^0 && 2+y^0==0 && 2*meter==-1-y^0 && meter>=1 ], cost: 2*meter
     24: l0 -> l0 : x^0'=0, y^0'=y^0-x^0, [ 0<=-1-x^0 && 0<=y^0 ], cost: -4*x^0
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0

Chained accelerated rules (with incoming rules):
   Start location: l7
     10: l7 -> l0 : [], cost: 2
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0
     25: l7 -> l0 : x^0'=-1, y^0'=-1+y^0-x^0, [ 1+y^0<=-1 && x^0>=y^0 && -1-x^0>=1 ], cost: -2-4*x^0
     26: l7 -> l0 : x^0'=-1-y^0+x^0, y^0'=-1, [ 0<=-1-x^0 && 1+y^0<=-1 && x^0<=y^0 ], cost: -2-4*y^0
     27: l7 -> l0 : x^0'=0, y^0'=y^0-x^0, [ 0<=-1-x^0 && 0<=y^0 ], cost: 2-4*x^0
     28: l7 -> l0 : x^0'=0, y^0'=-99*y^0-x^0, [ 0<=-1-x^0 && 1+y^0==0 && 0<=-1-99*y^0-x^0 ], cost: 2-398*y^0-4*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0
     25: l7 -> l0 : x^0'=-1, y^0'=-1+y^0-x^0, [ 1+y^0<=-1 && x^0>=y^0 && -1-x^0>=1 ], cost: -2-4*x^0
     26: l7 -> l0 : x^0'=-1-y^0+x^0, y^0'=-1, [ 0<=-1-x^0 && 1+y^0<=-1 && x^0<=y^0 ], cost: -2-4*y^0
     27: l7 -> l0 : x^0'=0, y^0'=y^0-x^0, [ 0<=-1-x^0 && 0<=y^0 ], cost: 2-4*x^0
     28: l7 -> l0 : x^0'=0, y^0'=-99*y^0-x^0, [ 0<=-1-x^0 && 1+y^0==0 && 0<=-1-99*y^0-x^0 ], cost: 2-398*y^0-4*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     14: l7 -> l0 : x^0'=99*y^0+x^0, y^0'=0, [ 0<=-1-x^0 && 1+y^0==0 ], cost: 2-2*y^0
     25: l7 -> l0 : x^0'=-1, y^0'=-1+y^0-x^0, [ 1+y^0<=-1 && x^0>=y^0 && -1-x^0>=1 ], cost: -2-4*x^0
     26: l7 -> l0 : x^0'=-1-y^0+x^0, y^0'=-1, [ 0<=-1-x^0 && 1+y^0<=-1 && x^0<=y^0 ], cost: -2-4*y^0
     27: l7 -> l0 : x^0'=0, y^0'=y^0-x^0, [ 0<=-1-x^0 && 0<=y^0 ], cost: 2-4*x^0
     28: l7 -> l0 : x^0'=0, y^0'=-99*y^0-x^0, [ 0<=-1-x^0 && 1+y^0==0 && 0<=-1-99*y^0-x^0 ], cost: 2-398*y^0-4*x^0

Computing asymptotic complexity for rule 14
   Could not solve the limit problem.
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 25
   Simplified the guard:
     25: l7 -> l0 : x^0'=-1, y^0'=-1+y^0-x^0, [ x^0>=y^0 && -1-x^0>=1 ], cost: -2-4*x^0
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      1-y^0+x^0 (+/+!), -2-4*x^0 (+), -1-x^0 (+/+!) [not solved]

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

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

   Solution:
      y^0 / -n
      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:  [ x^0>=y^0 && -1-x^0>=1 ]

WORST_CASE(Omega(n^1),?)