WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : p^0'=p^post_1, x^0'=x^post_1, y^0'=y^post_1, [ y^0<=0 && x^0<=0 && p^post_1==1 && x^0==x^post_1 && y^0==y^post_1 ], cost: 1
      1: l0 -> l2 : p^0'=p^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 1<=y^0 && y^post_2==-1+y^0 && p^0==p^post_2 && x^0==x^post_2 ], cost: 1
      2: l2 -> l0 : p^0'=p^post_3, x^0'=x^post_3, y^0'=y^post_3, [ p^0==p^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l3 -> l2 : p^0'=p^post_4, x^0'=x^post_4, y^0'=y^post_4, [ x^0<=0 && p^0==p^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1
      4: l3 -> l4 : p^0'=p^post_5, x^0'=x^post_5, y^0'=y^post_5, [ 1<=x^0 && p^post_5==1+p^0 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      5: l5 -> l3 : p^0'=p^post_6, x^0'=x^post_6, y^0'=y^post_6, [ p^post_6==0 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1
      6: l6 -> l5 : p^0'=p^post_7, x^0'=x^post_7, y^0'=y^post_7, [ p^0==p^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l6 -> l5 : p^0'=p^post_7, x^0'=x^post_7, y^0'=y^post_7, [ p^0==p^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      1: l0 -> l2 : p^0'=p^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 1<=y^0 && y^post_2==-1+y^0 && p^0==p^post_2 && x^0==x^post_2 ], cost: 1
      2: l2 -> l0 : p^0'=p^post_3, x^0'=x^post_3, y^0'=y^post_3, [ p^0==p^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l3 -> l2 : p^0'=p^post_4, x^0'=x^post_4, y^0'=y^post_4, [ x^0<=0 && p^0==p^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1
      5: l5 -> l3 : p^0'=p^post_6, x^0'=x^post_6, y^0'=y^post_6, [ p^post_6==0 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1
      6: l6 -> l5 : p^0'=p^post_7, x^0'=x^post_7, y^0'=y^post_7, [ p^0==p^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      1: l0 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 1
      2: l2 -> l0 : [], cost: 1
      3: l3 -> l2 : [ x^0<=0 ], cost: 1
      5: l5 -> l3 : p^0'=0, [], cost: 1
      6: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      9: l2 -> l2 : y^0'=-1+y^0, [ 1<=y^0 ], cost: 2
      8: l6 -> l2 : p^0'=0, [ x^0<=0 ], cost: 3

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

   Accelerated rule 9 with backward acceleration, yielding the new rule 10.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     10: l2 -> l2 : y^0'=0, [ y^0>=0 ], cost: 2*y^0
      8: l6 -> l2 : p^0'=0, [ x^0<=0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l6
      8: l6 -> l2 : p^0'=0, [ x^0<=0 ], cost: 3
     11: l6 -> l2 : p^0'=0, y^0'=0, [ x^0<=0 && y^0>=0 ], cost: 3+2*y^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     11: l6 -> l2 : p^0'=0, y^0'=0, [ x^0<=0 && y^0>=0 ], cost: 3+2*y^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     11: l6 -> l2 : p^0'=0, y^0'=0, [ x^0<=0 && y^0>=0 ], cost: 3+2*y^0

Computing asymptotic complexity for rule 11
   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:  [ p^0==p^post_7 && x^0==x^post_7 && y^0==y^post_7 ]

WORST_CASE(Omega(1),?)