WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l5
      0: l0 -> l1 : __const_5000^0'=__const_5000^post_1, x_13^0'=x_13^post_1, x_27^0'=x_27^post_1, x_32^0'=x_32^post_1, y_16^0'=y_16^post_1, y_28^0'=y_28^post_1, y_33^0'=y_33^post_1, [ x_13^post_1==x_13^post_1 && y_16^post_1==y_16^post_1 && __const_5000^0==__const_5000^post_1 && x_27^0==x_27^post_1 && x_32^0==x_32^post_1 && y_28^0==y_28^post_1 && y_33^0==y_33^post_1 ], cost: 1
      1: l1 -> l2 : __const_5000^0'=__const_5000^post_2, x_13^0'=x_13^post_2, x_27^0'=x_27^post_2, x_32^0'=x_32^post_2, y_16^0'=y_16^post_2, y_28^0'=y_28^post_2, y_33^0'=y_33^post_2, [ 1<=x_13^0 && y_16^post_2==__const_5000^0 && 1<=y_16^post_2 && 1<=x_13^0 && __const_5000^0==__const_5000^post_2 && x_13^0==x_13^post_2 && x_27^0==x_27^post_2 && x_32^0==x_32^post_2 && y_28^0==y_28^post_2 && y_33^0==y_33^post_2 ], cost: 1
      3: l2 -> l1 : __const_5000^0'=__const_5000^post_4, x_13^0'=x_13^post_4, x_27^0'=x_27^post_4, x_32^0'=x_32^post_4, y_16^0'=y_16^post_4, y_28^0'=y_28^post_4, y_33^0'=y_33^post_4, [ y_16^0<=0 && y_16^0<=0 && __const_5000^0==__const_5000^post_4 && x_13^0==x_13^post_4 && x_27^0==x_27^post_4 && x_32^0==x_32^post_4 && y_16^0==y_16^post_4 && y_28^0==y_28^post_4 && y_33^0==y_33^post_4 ], cost: 1
      4: l2 -> l4 : __const_5000^0'=__const_5000^post_5, x_13^0'=x_13^post_5, x_27^0'=x_27^post_5, x_32^0'=x_32^post_5, y_16^0'=y_16^post_5, y_28^0'=y_28^post_5, y_33^0'=y_33^post_5, [ x_32^post_5==x_32^post_5 && y_33^post_5==y_33^post_5 && 1<=y_16^0 && x_13^post_5==-1+x_13^0 && y_16^post_5==-1+y_16^0 && x_13^post_5<=-1+x_32^post_5 && -1+x_32^post_5<=x_13^post_5 && y_16^post_5<=-1+y_33^post_5 && -1+y_33^post_5<=y_16^post_5 && 1<=y_33^post_5 && __const_5000^0==__const_5000^post_5 && x_27^0==x_27^post_5 && y_28^0==y_28^post_5 ], cost: 1
      2: l3 -> l2 : __const_5000^0'=__const_5000^post_3, x_13^0'=x_13^post_3, x_27^0'=x_27^post_3, x_32^0'=x_32^post_3, y_16^0'=y_16^post_3, y_28^0'=y_28^post_3, y_33^0'=y_33^post_3, [ x_27^post_3==x_27^post_3 && y_28^post_3==y_28^post_3 && 1<=y_16^0 && x_13^post_3==-1+x_13^0 && y_16^post_3==-1+y_16^0 && x_13^post_3<=-1+x_27^post_3 && -1+x_27^post_3<=x_13^post_3 && y_16^post_3<=-1+y_28^post_3 && -1+y_28^post_3<=y_16^post_3 && 1<=x_27^post_3 && 1<=y_28^post_3 && __const_5000^0==__const_5000^post_3 && x_32^0==x_32^post_3 && y_33^0==y_33^post_3 ], cost: 1
      5: l4 -> l2 : __const_5000^0'=__const_5000^post_6, x_13^0'=x_13^post_6, x_27^0'=x_27^post_6, x_32^0'=x_32^post_6, y_16^0'=y_16^post_6, y_28^0'=y_28^post_6, y_33^0'=y_33^post_6, [ __const_5000^0==__const_5000^post_6 && x_13^0==x_13^post_6 && x_27^0==x_27^post_6 && x_32^0==x_32^post_6 && y_16^0==y_16^post_6 && y_28^0==y_28^post_6 && y_33^0==y_33^post_6 ], cost: 1
      6: l5 -> l0 : __const_5000^0'=__const_5000^post_7, x_13^0'=x_13^post_7, x_27^0'=x_27^post_7, x_32^0'=x_32^post_7, y_16^0'=y_16^post_7, y_28^0'=y_28^post_7, y_33^0'=y_33^post_7, [ __const_5000^0==__const_5000^post_7 && x_13^0==x_13^post_7 && x_27^0==x_27^post_7 && x_32^0==x_32^post_7 && y_16^0==y_16^post_7 && y_28^0==y_28^post_7 && y_33^0==y_33^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l0 : __const_5000^0'=__const_5000^post_7, x_13^0'=x_13^post_7, x_27^0'=x_27^post_7, x_32^0'=x_32^post_7, y_16^0'=y_16^post_7, y_28^0'=y_28^post_7, y_33^0'=y_33^post_7, [ __const_5000^0==__const_5000^post_7 && x_13^0==x_13^post_7 && x_27^0==x_27^post_7 && x_32^0==x_32^post_7 && y_16^0==y_16^post_7 && y_28^0==y_28^post_7 && y_33^0==y_33^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      0: l0 -> l1 : __const_5000^0'=__const_5000^post_1, x_13^0'=x_13^post_1, x_27^0'=x_27^post_1, x_32^0'=x_32^post_1, y_16^0'=y_16^post_1, y_28^0'=y_28^post_1, y_33^0'=y_33^post_1, [ x_13^post_1==x_13^post_1 && y_16^post_1==y_16^post_1 && __const_5000^0==__const_5000^post_1 && x_27^0==x_27^post_1 && x_32^0==x_32^post_1 && y_28^0==y_28^post_1 && y_33^0==y_33^post_1 ], cost: 1
      1: l1 -> l2 : __const_5000^0'=__const_5000^post_2, x_13^0'=x_13^post_2, x_27^0'=x_27^post_2, x_32^0'=x_32^post_2, y_16^0'=y_16^post_2, y_28^0'=y_28^post_2, y_33^0'=y_33^post_2, [ 1<=x_13^0 && y_16^post_2==__const_5000^0 && 1<=y_16^post_2 && 1<=x_13^0 && __const_5000^0==__const_5000^post_2 && x_13^0==x_13^post_2 && x_27^0==x_27^post_2 && x_32^0==x_32^post_2 && y_28^0==y_28^post_2 && y_33^0==y_33^post_2 ], cost: 1
      3: l2 -> l1 : __const_5000^0'=__const_5000^post_4, x_13^0'=x_13^post_4, x_27^0'=x_27^post_4, x_32^0'=x_32^post_4, y_16^0'=y_16^post_4, y_28^0'=y_28^post_4, y_33^0'=y_33^post_4, [ y_16^0<=0 && y_16^0<=0 && __const_5000^0==__const_5000^post_4 && x_13^0==x_13^post_4 && x_27^0==x_27^post_4 && x_32^0==x_32^post_4 && y_16^0==y_16^post_4 && y_28^0==y_28^post_4 && y_33^0==y_33^post_4 ], cost: 1
      4: l2 -> l4 : __const_5000^0'=__const_5000^post_5, x_13^0'=x_13^post_5, x_27^0'=x_27^post_5, x_32^0'=x_32^post_5, y_16^0'=y_16^post_5, y_28^0'=y_28^post_5, y_33^0'=y_33^post_5, [ x_32^post_5==x_32^post_5 && y_33^post_5==y_33^post_5 && 1<=y_16^0 && x_13^post_5==-1+x_13^0 && y_16^post_5==-1+y_16^0 && x_13^post_5<=-1+x_32^post_5 && -1+x_32^post_5<=x_13^post_5 && y_16^post_5<=-1+y_33^post_5 && -1+y_33^post_5<=y_16^post_5 && 1<=y_33^post_5 && __const_5000^0==__const_5000^post_5 && x_27^0==x_27^post_5 && y_28^0==y_28^post_5 ], cost: 1
      5: l4 -> l2 : __const_5000^0'=__const_5000^post_6, x_13^0'=x_13^post_6, x_27^0'=x_27^post_6, x_32^0'=x_32^post_6, y_16^0'=y_16^post_6, y_28^0'=y_28^post_6, y_33^0'=y_33^post_6, [ __const_5000^0==__const_5000^post_6 && x_13^0==x_13^post_6 && x_27^0==x_27^post_6 && x_32^0==x_32^post_6 && y_16^0==y_16^post_6 && y_28^0==y_28^post_6 && y_33^0==y_33^post_6 ], cost: 1
      6: l5 -> l0 : __const_5000^0'=__const_5000^post_7, x_13^0'=x_13^post_7, x_27^0'=x_27^post_7, x_32^0'=x_32^post_7, y_16^0'=y_16^post_7, y_28^0'=y_28^post_7, y_33^0'=y_33^post_7, [ __const_5000^0==__const_5000^post_7 && x_13^0==x_13^post_7 && x_27^0==x_27^post_7 && x_32^0==x_32^post_7 && y_16^0==y_16^post_7 && y_28^0==y_28^post_7 && y_33^0==y_33^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      0: l0 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 1
      1: l1 -> l2 : y_16^0'=__const_5000^0, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 1
      3: l2 -> l1 : [ y_16^0<=0 ], cost: 1
      4: l2 -> l4 : x_13^0'=-1+x_13^0, x_32^0'=x_13^0, y_16^0'=-1+y_16^0, y_33^0'=y_16^0, [ 1<=y_16^0 ], cost: 1
      5: l4 -> l2 : [], cost: 1
      6: l5 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      1: l1 -> l2 : y_16^0'=__const_5000^0, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 1
      3: l2 -> l1 : [ y_16^0<=0 ], cost: 1
      8: l2 -> l2 : x_13^0'=-1+x_13^0, x_32^0'=x_13^0, y_16^0'=-1+y_16^0, y_33^0'=y_16^0, [ 1<=y_16^0 ], cost: 2
      7: l5 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
      8: l2 -> l2 : x_13^0'=-1+x_13^0, x_32^0'=x_13^0, y_16^0'=-1+y_16^0, y_33^0'=y_16^0, [ 1<=y_16^0 ], cost: 2

   Accelerated rule 8 with backward acceleration, yielding the new rule 9.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 8.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
      1: l1 -> l2 : y_16^0'=__const_5000^0, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 1
      3: l2 -> l1 : [ y_16^0<=0 ], cost: 1
      9: l2 -> l2 : x_13^0'=-y_16^0+x_13^0, x_32^0'=1-y_16^0+x_13^0, y_16^0'=0, y_33^0'=1, [ y_16^0>=1 ], cost: 2*y_16^0
      7: l5 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      1: l1 -> l2 : y_16^0'=__const_5000^0, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 1
     10: l1 -> l2 : x_13^0'=x_13^0-__const_5000^0, x_32^0'=1+x_13^0-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 1+2*__const_5000^0
      3: l2 -> l1 : [ y_16^0<=0 ], cost: 1
      7: l5 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l5
     11: l1 -> l1 : x_13^0'=x_13^0-__const_5000^0, x_32^0'=1+x_13^0-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 2+2*__const_5000^0
      7: l5 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     11: l1 -> l1 : x_13^0'=x_13^0-__const_5000^0, x_32^0'=1+x_13^0-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=x_13^0 && 1<=__const_5000^0 ], cost: 2+2*__const_5000^0

   Accelerated rule 11 with backward acceleration, yielding the new rule 12.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
     12: l1 -> l1 : x_13^0'=x_13^0-k_1*__const_5000^0, x_32^0'=1-(-1+k_1)*__const_5000^0+x_13^0-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=__const_5000^0 && k_1>=1 && 1<=-(-1+k_1)*__const_5000^0+x_13^0 ], cost: 2*k_1+2*k_1*__const_5000^0
      7: l5 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      7: l5 -> l1 : x_13^0'=x_13^post_1, y_16^0'=y_16^post_1, [], cost: 2
     13: l5 -> l1 : x_13^0'=x_13^post_1-k_1*__const_5000^0, x_32^0'=1-(-1+k_1)*__const_5000^0+x_13^post_1-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=__const_5000^0 && k_1>=1 && 1<=-(-1+k_1)*__const_5000^0+x_13^post_1 ], cost: 2+2*k_1+2*k_1*__const_5000^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     13: l5 -> l1 : x_13^0'=x_13^post_1-k_1*__const_5000^0, x_32^0'=1-(-1+k_1)*__const_5000^0+x_13^post_1-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=__const_5000^0 && k_1>=1 && 1<=-(-1+k_1)*__const_5000^0+x_13^post_1 ], cost: 2+2*k_1+2*k_1*__const_5000^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     13: l5 -> l1 : x_13^0'=x_13^post_1-k_1*__const_5000^0, x_32^0'=1-(-1+k_1)*__const_5000^0+x_13^post_1-__const_5000^0, y_16^0'=0, y_33^0'=1, [ 1<=__const_5000^0 && k_1>=1 && 1<=-(-1+k_1)*__const_5000^0+x_13^post_1 ], cost: 2+2*k_1+2*k_1*__const_5000^0

Computing asymptotic complexity for rule 13
   Resulting cost 0 has complexity: Unknown

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_5000^0==__const_5000^post_7 && x_13^0==x_13^post_7 && x_27^0==x_27^post_7 && x_32^0==x_32^post_7 && y_16^0==y_16^post_7 && y_28^0==y_28^post_7 && y_33^0==y_33^post_7 ]

WORST_CASE(Omega(1),?)