WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l3
      0: l0 -> l1 : __const_1000^0'=__const_1000^post_1, __const_110^0'=__const_110^post_1, __const_3000^0'=__const_3000^post_1, __const_4000^0'=__const_4000^post_1, x^0'=x^post_1, y^0'=y^post_1, [ 1+y^0<=__const_4000^0 && x^post_1==__const_1000^0+x^0 && 1+__const_110^0<=x^post_1 && __const_1000^0==__const_1000^post_1 && __const_110^0==__const_110^post_1 && __const_3000^0==__const_3000^post_1 && __const_4000^0==__const_4000^post_1 && y^0==y^post_1 ], cost: 1
      1: l1 -> l0 : __const_1000^0'=__const_1000^post_2, __const_110^0'=__const_110^post_2, __const_3000^0'=__const_3000^post_2, __const_4000^0'=__const_4000^post_2, x^0'=x^post_2, y^0'=y^post_2, [ __const_1000^0==__const_1000^post_2 && __const_110^0==__const_110^post_2 && __const_3000^0==__const_3000^post_2 && __const_4000^0==__const_4000^post_2 && x^0==x^post_2 && y^0==y^post_2 ], cost: 1
      2: l2 -> l0 : __const_1000^0'=__const_1000^post_3, __const_110^0'=__const_110^post_3, __const_3000^0'=__const_3000^post_3, __const_4000^0'=__const_4000^post_3, x^0'=x^post_3, y^0'=y^post_3, [ y^post_3==__const_3000^0 && __const_1000^0==__const_1000^post_3 && __const_110^0==__const_110^post_3 && __const_3000^0==__const_3000^post_3 && __const_4000^0==__const_4000^post_3 && x^0==x^post_3 ], cost: 1
      3: l3 -> l2 : __const_1000^0'=__const_1000^post_4, __const_110^0'=__const_110^post_4, __const_3000^0'=__const_3000^post_4, __const_4000^0'=__const_4000^post_4, x^0'=x^post_4, y^0'=y^post_4, [ __const_1000^0==__const_1000^post_4 && __const_110^0==__const_110^post_4 && __const_3000^0==__const_3000^post_4 && __const_4000^0==__const_4000^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      3: l3 -> l2 : __const_1000^0'=__const_1000^post_4, __const_110^0'=__const_110^post_4, __const_3000^0'=__const_3000^post_4, __const_4000^0'=__const_4000^post_4, x^0'=x^post_4, y^0'=y^post_4, [ __const_1000^0==__const_1000^post_4 && __const_110^0==__const_110^post_4 && __const_3000^0==__const_3000^post_4 && __const_4000^0==__const_4000^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1

Simplified all rules, resulting in:
   Start location: l3
      0: l0 -> l1 : x^0'=__const_1000^0+x^0, [ 1+y^0<=__const_4000^0 && 1+__const_110^0<=__const_1000^0+x^0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      2: l2 -> l0 : y^0'=__const_3000^0, [], 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'=__const_1000^0+x^0, [ 1+y^0<=__const_4000^0 && 1+__const_110^0<=__const_1000^0+x^0 ], cost: 2
      4: l3 -> l0 : y^0'=__const_3000^0, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      5: l0 -> l0 : x^0'=__const_1000^0+x^0, [ 1+y^0<=__const_4000^0 && 1+__const_110^0<=__const_1000^0+x^0 ], cost: 2

   Found no metering function for rule 5.
   Removing the simple loops:.

Accelerated all simple loops using metering functions (where possible):
   Start location: l3
      5: l0 -> l0 : x^0'=__const_1000^0+x^0, [ 1+y^0<=__const_4000^0 && 1+__const_110^0<=__const_1000^0+x^0 ], cost: 2
      4: l3 -> l0 : y^0'=__const_3000^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l3
      4: l3 -> l0 : y^0'=__const_3000^0, [], cost: 2
      6: l3 -> l0 : x^0'=__const_1000^0+x^0, y^0'=__const_3000^0, [ 1+__const_3000^0<=__const_4000^0 && 1+__const_110^0<=__const_1000^0+x^0 ], cost: 4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l3
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l3
     <empty>

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Constant
   Cpx degree:  0
   Solved cost: 1
   Rule cost:   1
   Rule guard:  [ __const_1000^0==__const_1000^post_4 && __const_110^0==__const_110^post_4 && __const_3000^0==__const_3000^post_4 && __const_4000^0==__const_4000^post_4 && x^0==x^post_4 && y^0==y^post_4 ]

WORST_CASE(Omega(1),?)