WORST_CASE(Omega(1),?)

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      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

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

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l3
      0: l0 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, [], cost: 1
      1: l0 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [], cost: 1
      2: l1 -> l0 : [ 0<=x^0 && y^0<=z^0 ], cost: 1
      5: l3 -> l1 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l3
      6: l1 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, [ 0<=x^0 && y^0<=z^0 ], cost: 2
      7: l1 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [ 0<=x^0 && y^0<=z^0 ], cost: 2
      5: l3 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      6: l1 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, [ 0<=x^0 && y^0<=z^0 ], cost: 2
      7: l1 -> l1 : x^0'=-1+x^0, y^0'=-1+y^0, [ 0<=x^0 && y^0<=z^0 ], cost: 2

[test] deduced pseudo-invariant y^0<=0, also trying -y^0<=-1
   Accelerated rule 6 with backward acceleration, yielding the new rule 8.
   Accelerated rule 6 with backward acceleration, yielding the new rule 9.
   Accelerated rule 7 with backward acceleration, yielding the new rule 10.
[accelerate] Nesting with 3 inner and 2 outer candidates
   Removing the simple loops: 7.

Accelerated all simple loops using metering functions (where possible):
   Start location: l3
      6: l1 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, [ 0<=x^0 && y^0<=z^0 ], cost: 2
      8: l1 -> l1 : y^0'=y^0-k, z^0'=y^0*k-1/2*k^2+z^0-1/2*k, [ 0<=x^0 && y^0<=0 && k>=0 && 1+y^0-k<=1/2-1/2*(-1+k)^2+z^0+(-1+k)*y^0-1/2*k ], cost: 2*k
      9: l1 -> l1 : y^0'=0, z^0'=-1/2*y^0+1/2*y^0^2+z^0, [ 0<=x^0 && y^0<=z^0 && y^0>=0 ], cost: 2*y^0
     10: l1 -> l1 : x^0'=-1, y^0'=-1+y^0-x^0, [ y^0<=z^0 && 1+x^0>=0 ], cost: 2+2*x^0
      5: l3 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l3
      5: l3 -> l1 : [], cost: 2
     11: l3 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, [ 0<=x^0 && y^0<=z^0 ], cost: 4
     12: l3 -> l1 : y^0'=y^0-k, z^0'=y^0*k-1/2*k^2+z^0-1/2*k, [ 0<=x^0 && y^0<=0 && k>=0 && 1+y^0-k<=1/2-1/2*(-1+k)^2+z^0+(-1+k)*y^0-1/2*k ], cost: 2+2*k
     13: l3 -> l1 : y^0'=0, z^0'=-1/2*y^0+1/2*y^0^2+z^0, [ 0<=x^0 && y^0<=z^0 && y^0>=0 ], cost: 2+2*y^0
     14: l3 -> l1 : x^0'=-1, y^0'=-1+y^0-x^0, [ y^0<=z^0 && 1+x^0>=0 ], cost: 4+2*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l3
     12: l3 -> l1 : y^0'=y^0-k, z^0'=y^0*k-1/2*k^2+z^0-1/2*k, [ 0<=x^0 && y^0<=0 && k>=0 && 1+y^0-k<=1/2-1/2*(-1+k)^2+z^0+(-1+k)*y^0-1/2*k ], cost: 2+2*k
     13: l3 -> l1 : y^0'=0, z^0'=-1/2*y^0+1/2*y^0^2+z^0, [ 0<=x^0 && y^0<=z^0 && y^0>=0 ], cost: 2+2*y^0
     14: l3 -> l1 : x^0'=-1, y^0'=-1+y^0-x^0, [ y^0<=z^0 && 1+x^0>=0 ], cost: 4+2*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l3
     12: l3 -> l1 : y^0'=y^0-k, z^0'=y^0*k-1/2*k^2+z^0-1/2*k, [ 0<=x^0 && y^0<=0 && k>=0 && 1+y^0-k<=1/2-1/2*(-1+k)^2+z^0+(-1+k)*y^0-1/2*k ], cost: 2+2*k
     13: l3 -> l1 : y^0'=0, z^0'=-1/2*y^0+1/2*y^0^2+z^0, [ 0<=x^0 && y^0<=z^0 && y^0>=0 ], cost: 2+2*y^0
     14: l3 -> l1 : x^0'=-1, y^0'=-1+y^0-x^0, [ y^0<=z^0 && 1+x^0>=0 ], cost: 4+2*x^0

Computing asymptotic complexity for rule 12
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 14
   Resulting cost 0 has complexity: Unknown

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:  [ x^0==x^post_5 && y^0==y^post_5 && z^0==z^post_5 ]

WORST_CASE(Omega(1),?)