WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l3
      0: l0 -> l1 : x^0'=x^post_1, [ x^post_1==-1000+x^0 && 201<=x^post_1 ], cost: 1
      1: l1 -> l0 : x^0'=x^post_2, [ x^0==x^post_2 ], cost: 1
      2: l2 -> l0 : x^0'=x^post_3, [ x^0==x^post_3 ], cost: 1
      3: l3 -> l2 : x^0'=x^post_4, [ x^0==x^post_4 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      3: l3 -> l2 : x^0'=x^post_4, [ x^0==x^post_4 ], cost: 1

Simplified all rules, resulting in:
   Start location: l3
      0: l0 -> l1 : x^0'=-1000+x^0, [ 201<=-1000+x^0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      3: l3 -> l2 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l3
      5: l0 -> l0 : x^0'=-1000+x^0, [ 201<=-1000+x^0 ], cost: 2
      4: l3 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      5: l0 -> l0 : x^0'=-1000+x^0, [ 201<=-1000+x^0 ], cost: 2

   Accelerated rule 5 with metering function meter (where 1000*meter==-1200+x^0), yielding the new rule 6.
   Removing the simple loops: 5.

Accelerated all simple loops using metering functions (where possible):
   Start location: l3
      6: l0 -> l0 : x^0'=x^0-1000*meter, [ 201<=-1000+x^0 && 1000*meter==-1200+x^0 && meter>=1 ], cost: 2*meter
      4: l3 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l3
      4: l3 -> l0 : [], cost: 2
      7: l3 -> l0 : x^0'=x^0-1000*meter, [ 201<=-1000+x^0 && 1000*meter==-1200+x^0 && meter>=1 ], cost: 2+2*meter

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l3
      7: l3 -> l0 : x^0'=x^0-1000*meter, [ 201<=-1000+x^0 && 1000*meter==-1200+x^0 && meter>=1 ], cost: 2+2*meter

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l3
      7: l3 -> l0 : x^0'=x^0-1000*meter, [ 201<=-1000+x^0 && 1000*meter==-1200+x^0 && meter>=1 ], cost: 2+2*meter

Computing asymptotic complexity for rule 7
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -1200+x^0 (+/+!), 2+2*meter (+), -1199+x^0-1000*meter (+/+!), 1201-x^0+1000*meter (+/+!) [not solved]

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

      applying transformation rule (C) using substitution {x^0==-800+1000*n,meter==-2+n}
      resulting limit problem:
      [solved]

   Solution:
      x^0 / -800+1000*n
      meter / -2+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*meter
   Rule guard:  [ 201<=-1000+x^0 && 1000*meter==-1200+x^0 ]

WORST_CASE(Omega(n^1),?)