WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l9
      0: l0 -> l1 : x^0'=x^post_1, y^0'=y^post_1, z^0'=z^post_1, [ 1<=x^0 && x^post_1==-1+x^0 && y^0==y^post_1 && z^0==z^post_1 ], cost: 1
      1: l1 -> l0 : x^0'=x^post_2, y^0'=y^post_2, z^0'=z^post_2, [ x^0==x^post_2 && y^0==y^post_2 && z^0==z^post_2 ], cost: 1
      2: l2 -> l0 : x^0'=x^post_3, y^0'=y^post_3, z^0'=z^post_3, [ y^0<=0 && x^0==x^post_3 && y^0==y^post_3 && z^0==z^post_3 ], cost: 1
      3: l2 -> l3 : x^0'=x^post_4, y^0'=y^post_4, z^0'=z^post_4, [ 1<=y^0 && y^post_4==-1+y^0 && x^0==x^post_4 && z^0==z^post_4 ], cost: 1
      4: l3 -> l2 : x^0'=x^post_5, y^0'=y^post_5, z^0'=z^post_5, [ x^0==x^post_5 && y^0==y^post_5 && z^0==z^post_5 ], cost: 1
      5: l4 -> l2 : x^0'=x^post_6, y^0'=y^post_6, z^0'=z^post_6, [ z^0<=x^0 && x^0==x^post_6 && y^0==y^post_6 && z^0==z^post_6 ], cost: 1
      6: l4 -> l5 : x^0'=x^post_7, y^0'=y^post_7, z^0'=z^post_7, [ 1+x^0<=z^0 && x^post_7==1+x^0 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1
      7: l5 -> l4 : x^0'=x^post_8, y^0'=y^post_8, z^0'=z^post_8, [ x^0==x^post_8 && y^0==y^post_8 && z^0==z^post_8 ], cost: 1
      8: l6 -> l4 : x^0'=x^post_9, y^0'=y^post_9, z^0'=z^post_9, [ y^0<=z^0 && x^0==x^post_9 && y^0==y^post_9 && z^0==z^post_9 ], cost: 1
      9: l6 -> l7 : x^0'=x^post_10, y^0'=y^post_10, z^0'=z^post_10, [ 1+z^0<=y^0 && y^post_10==-1+y^0 && x^0==x^post_10 && z^0==z^post_10 ], cost: 1
     10: l7 -> l6 : x^0'=x^post_11, y^0'=y^post_11, z^0'=z^post_11, [ x^0==x^post_11 && y^0==y^post_11 && z^0==z^post_11 ], cost: 1
     11: l8 -> l6 : x^0'=x^post_12, y^0'=y^post_12, z^0'=z^post_12, [ x^post_12==0 && y^0==y^post_12 && z^0==z^post_12 ], cost: 1
     12: l9 -> l8 : x^0'=x^post_13, y^0'=y^post_13, z^0'=z^post_13, [ x^0==x^post_13 && y^0==y^post_13 && z^0==z^post_13 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     12: l9 -> l8 : x^0'=x^post_13, y^0'=y^post_13, z^0'=z^post_13, [ x^0==x^post_13 && y^0==y^post_13 && z^0==z^post_13 ], cost: 1

Simplified all rules, resulting in:
   Start location: l9
      0: l0 -> l1 : x^0'=-1+x^0, [ 1<=x^0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      2: l2 -> l0 : [ y^0<=0 ], cost: 1
      3: l2 -> l3 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 1
      4: l3 -> l2 : [], cost: 1
      5: l4 -> l2 : [ z^0<=x^0 ], cost: 1
      6: l4 -> l5 : x^0'=1+x^0, [ 1+x^0<=z^0 ], cost: 1
      7: l5 -> l4 : [], cost: 1
      8: l6 -> l4 : [ y^0<=z^0 ], cost: 1
      9: l6 -> l7 : y^0'=-1+y^0, [ 1+z^0<=y^0 ], cost: 1
     10: l7 -> l6 : [], cost: 1
     11: l8 -> l6 : x^0'=0, [], cost: 1
     12: l9 -> l8 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l9
     17: l0 -> l0 : x^0'=-1+x^0, [ 1<=x^0 ], cost: 2
      2: l2 -> l0 : [ y^0<=0 ], cost: 1
     16: l2 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2
      5: l4 -> l2 : [ z^0<=x^0 ], cost: 1
     15: l4 -> l4 : x^0'=1+x^0, [ 1+x^0<=z^0 ], cost: 2
      8: l6 -> l4 : [ y^0<=z^0 ], cost: 1
     14: l6 -> l6 : y^0'=-1+y^0, [ 1+z^0<=y^0 ], cost: 2
     13: l9 -> l6 : x^0'=0, [], cost: 2

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

   Accelerated rule 17 with backward acceleration, yielding the new rule 18.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 17.

Accelerating simple loops of location 2.
   Accelerating the following rules:
     16: l2 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2

   Accelerated rule 16 with backward acceleration, yielding the new rule 19.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 16.

Accelerating simple loops of location 4.
   Accelerating the following rules:
     15: l4 -> l4 : x^0'=1+x^0, [ 1+x^0<=z^0 ], cost: 2

   Accelerated rule 15 with backward acceleration, yielding the new rule 20.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 15.

Accelerating simple loops of location 6.
   Accelerating the following rules:
     14: l6 -> l6 : y^0'=-1+y^0, [ 1+z^0<=y^0 ], cost: 2

   Accelerated rule 14 with backward acceleration, yielding the new rule 21.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 14.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     18: l0 -> l0 : x^0'=0, [ x^0>=0 ], cost: 2*x^0
      2: l2 -> l0 : [ y^0<=0 ], cost: 1
     19: l2 -> l2 : y^0'=0, [ y^0>=0 ], cost: 2*y^0
      5: l4 -> l2 : [ z^0<=x^0 ], cost: 1
     20: l4 -> l4 : x^0'=z^0, [ z^0-x^0>=0 ], cost: 2*z^0-2*x^0
      8: l6 -> l4 : [ y^0<=z^0 ], cost: 1
     21: l6 -> l6 : y^0'=z^0, [ y^0-z^0>=0 ], cost: 2*y^0-2*z^0
     13: l9 -> l6 : x^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
      2: l2 -> l0 : [ y^0<=0 ], cost: 1
     22: l2 -> l0 : x^0'=0, [ y^0<=0 && x^0>=0 ], cost: 1+2*x^0
      5: l4 -> l2 : [ z^0<=x^0 ], cost: 1
     23: l4 -> l2 : y^0'=0, [ z^0<=x^0 && y^0>=0 ], cost: 1+2*y^0
      8: l6 -> l4 : [ y^0<=z^0 ], cost: 1
     24: l6 -> l4 : x^0'=z^0, [ y^0<=z^0 && z^0-x^0>=0 ], cost: 1+2*z^0-2*x^0
     13: l9 -> l6 : x^0'=0, [], cost: 2
     25: l9 -> l6 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 ], cost: 2+2*y^0-2*z^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l9
     22: l2 -> l0 : x^0'=0, [ y^0<=0 && x^0>=0 ], cost: 1+2*x^0
      5: l4 -> l2 : [ z^0<=x^0 ], cost: 1
     23: l4 -> l2 : y^0'=0, [ z^0<=x^0 && y^0>=0 ], cost: 1+2*y^0
      8: l6 -> l4 : [ y^0<=z^0 ], cost: 1
     24: l6 -> l4 : x^0'=z^0, [ y^0<=z^0 && z^0-x^0>=0 ], cost: 1+2*z^0-2*x^0
     13: l9 -> l6 : x^0'=0, [], cost: 2
     25: l9 -> l6 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 ], cost: 2+2*y^0-2*z^0

Eliminated locations (on tree-shaped paths):
   Start location: l9
     30: l4 -> l0 : x^0'=0, [ z^0<=x^0 && y^0<=0 && x^0>=0 ], cost: 2+2*x^0
     31: l4 -> l0 : x^0'=0, y^0'=0, [ z^0<=x^0 && y^0>=0 && x^0>=0 ], cost: 2+2*y^0+2*x^0
     26: l9 -> l4 : x^0'=0, [ y^0<=z^0 ], cost: 3
     27: l9 -> l4 : x^0'=z^0, [ y^0<=z^0 && z^0>=0 ], cost: 3+2*z^0
     28: l9 -> l4 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 ], cost: 3+2*y^0-2*z^0
     29: l9 -> l4 : x^0'=z^0, y^0'=z^0, [ y^0-z^0>=0 && z^0>=0 ], cost: 3+2*y^0

Eliminated locations (on tree-shaped paths):
   Start location: l9
     32: l9 -> l0 : x^0'=0, [ y^0<=z^0 && z^0<=0 && y^0<=0 ], cost: 5
     33: l9 -> l0 : x^0'=0, y^0'=0, [ y^0<=z^0 && z^0<=0 && y^0>=0 ], cost: 5+2*y^0
     34: l9 -> l0 : x^0'=0, [ y^0<=z^0 && z^0>=0 && y^0<=0 ], cost: 5+4*z^0
     35: l9 -> l0 : x^0'=0, y^0'=0, [ y^0<=z^0 && z^0>=0 && y^0>=0 ], cost: 5+2*y^0+4*z^0
     36: l9 -> l0 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 && z^0<=0 ], cost: 5+2*y^0-2*z^0
     37: l9 -> l0 : x^0'=0, y^0'=0, [ y^0-z^0>=0 && z^0<=0 && z^0>=0 ], cost: 5+2*y^0
     38: l9 -> l0 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 && z^0>=0 && z^0<=0 ], cost: 5+2*y^0+2*z^0
     39: l9 -> l0 : x^0'=0, y^0'=0, [ y^0-z^0>=0 && z^0>=0 ], cost: 5+2*y^0+4*z^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l9
     32: l9 -> l0 : x^0'=0, [ y^0<=z^0 && z^0<=0 && y^0<=0 ], cost: 5
     33: l9 -> l0 : x^0'=0, y^0'=0, [ y^0<=z^0 && z^0<=0 && y^0>=0 ], cost: 5+2*y^0
     34: l9 -> l0 : x^0'=0, [ y^0<=z^0 && z^0>=0 && y^0<=0 ], cost: 5+4*z^0
     35: l9 -> l0 : x^0'=0, y^0'=0, [ y^0<=z^0 && z^0>=0 && y^0>=0 ], cost: 5+2*y^0+4*z^0
     36: l9 -> l0 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 && z^0<=0 ], cost: 5+2*y^0-2*z^0
     37: l9 -> l0 : x^0'=0, y^0'=0, [ y^0-z^0>=0 && z^0<=0 && z^0>=0 ], cost: 5+2*y^0
     38: l9 -> l0 : x^0'=0, y^0'=z^0, [ y^0-z^0>=0 && z^0>=0 && z^0<=0 ], cost: 5+2*y^0+2*z^0
     39: l9 -> l0 : x^0'=0, y^0'=0, [ y^0-z^0>=0 && z^0>=0 ], cost: 5+2*y^0+4*z^0

Computing asymptotic complexity for rule 36
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 39
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 33
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 34
   Simplified the guard:
     34: l9 -> l0 : x^0'=0, [ z^0>=0 && y^0<=0 ], cost: 5+4*z^0
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 35
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 37
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 38
   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:  [ x^0==x^post_13 && y^0==y^post_13 && z^0==z^post_13 ]

WORST_CASE(Omega(1),?)