WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_1, __disjvr_1^0'=__disjvr_1^post_1, x^0'=x^post_1, y^0'=y^post_1, [ -x^0<=y^0 && 1+x^0<=y^0 && x^post_1==1+x^0 && __disjvr_0^0==__disjvr_0^post_1 && __disjvr_1^0==__disjvr_1^post_1 && y^0==y^post_1 ], cost: 1
      1: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_2, __disjvr_1^0'=__disjvr_1^post_2, x^0'=x^post_2, y^0'=y^post_2, [ x^0<=y^0 && 1+x^0<=-y^0 && y^post_2==1+y^0 && __disjvr_0^0==__disjvr_0^post_2 && __disjvr_1^0==__disjvr_1^post_2 && x^0==x^post_2 ], cost: 1
      2: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_3, __disjvr_1^0'=__disjvr_1^post_3, x^0'=x^post_3, y^0'=y^post_3, [ y^0<=1-x^0 && 1+y^0<=x^0 && x^post_3==-1+x^0 && __disjvr_0^0==__disjvr_0^post_3 && __disjvr_1^0==__disjvr_1^post_3 && y^0==y^post_3 ], cost: 1
      3: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_4, __disjvr_1^0'=__disjvr_1^post_4, x^0'=x^post_4, y^0'=y^post_4, [ y^0<=x^0 && 2-y^0<=x^0 && y^post_4==-1+y^0 && __disjvr_0^0==__disjvr_0^post_4 && __disjvr_1^0==__disjvr_1^post_4 && x^0==x^post_4 ], cost: 1
      4: l1 -> l2 : __disjvr_0^0'=__disjvr_0^post_5, __disjvr_1^0'=__disjvr_1^post_5, x^0'=x^post_5, y^0'=y^post_5, [ __disjvr_0^post_5==__disjvr_0^0 && __disjvr_0^0==__disjvr_0^post_5 && __disjvr_1^0==__disjvr_1^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      5: l2 -> l0 : __disjvr_0^0'=__disjvr_0^post_6, __disjvr_1^0'=__disjvr_1^post_6, x^0'=x^post_6, y^0'=y^post_6, [ __disjvr_1^post_6==__disjvr_1^0 && __disjvr_0^0==__disjvr_0^post_6 && __disjvr_1^0==__disjvr_1^post_6 && x^0==x^post_6 && y^0==y^post_6 ], cost: 1
      6: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post_7, __disjvr_1^0'=__disjvr_1^post_7, x^0'=x^post_7, y^0'=y^post_7, [ __disjvr_0^0==__disjvr_0^post_7 && __disjvr_1^0==__disjvr_1^post_7 && x^0==x^post_7 && y^0==y^post_7 ], cost: 1
      7: l4 -> l3 : __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, x^0'=x^post_8, y^0'=y^post_8, [ __disjvr_0^0==__disjvr_0^post_8 && __disjvr_1^0==__disjvr_1^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l4 -> l3 : __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, x^0'=x^post_8, y^0'=y^post_8, [ __disjvr_0^0==__disjvr_0^post_8 && __disjvr_1^0==__disjvr_1^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : x^0'=1+x^0, [ -x^0<=y^0 && 1+x^0<=y^0 ], cost: 1
      1: l0 -> l1 : y^0'=1+y^0, [ x^0<=y^0 && 1+x^0<=-y^0 ], cost: 1
      2: l0 -> l1 : x^0'=-1+x^0, [ y^0<=1-x^0 && 1+y^0<=x^0 ], cost: 1
      3: l0 -> l1 : y^0'=-1+y^0, [ y^0<=x^0 && 2-y^0<=x^0 ], cost: 1
      4: l1 -> l2 : [], cost: 1
      5: l2 -> l0 : [], cost: 1
      6: l3 -> l1 : [], cost: 1
      7: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      0: l0 -> l1 : x^0'=1+x^0, [ -x^0<=y^0 && 1+x^0<=y^0 ], cost: 1
      1: l0 -> l1 : y^0'=1+y^0, [ x^0<=y^0 && 1+x^0<=-y^0 ], cost: 1
      2: l0 -> l1 : x^0'=-1+x^0, [ y^0<=1-x^0 && 1+y^0<=x^0 ], cost: 1
      3: l0 -> l1 : y^0'=-1+y^0, [ y^0<=x^0 && 2-y^0<=x^0 ], cost: 1
      9: l1 -> l0 : [], cost: 2
      8: l4 -> l1 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l4
     10: l1 -> l1 : x^0'=1+x^0, [ -x^0<=y^0 && 1+x^0<=y^0 ], cost: 3
     11: l1 -> l1 : y^0'=1+y^0, [ x^0<=y^0 && 1+x^0<=-y^0 ], cost: 3
     12: l1 -> l1 : x^0'=-1+x^0, [ y^0<=1-x^0 && 1+y^0<=x^0 ], cost: 3
     13: l1 -> l1 : y^0'=-1+y^0, [ y^0<=x^0 && 2-y^0<=x^0 ], cost: 3
      8: l4 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     10: l1 -> l1 : x^0'=1+x^0, [ -x^0<=y^0 && 1+x^0<=y^0 ], cost: 3
     11: l1 -> l1 : y^0'=1+y^0, [ x^0<=y^0 && 1+x^0<=-y^0 ], cost: 3
     12: l1 -> l1 : x^0'=-1+x^0, [ y^0<=1-x^0 && 1+y^0<=x^0 ], cost: 3
     13: l1 -> l1 : y^0'=-1+y^0, [ y^0<=x^0 && 2-y^0<=x^0 ], cost: 3

   Accelerated rule 10 with backward acceleration, yielding the new rule 14.
   Accelerated rule 11 with backward acceleration, yielding the new rule 15.
   Accelerated rule 12 with backward acceleration, yielding the new rule 16.
   Accelerated rule 13 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 10 11 12 13.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
     14: l1 -> l1 : x^0'=y^0, [ -x^0<=y^0 && -x^0+y^0>=0 ], cost: -3*x^0+3*y^0
     15: l1 -> l1 : y^0'=-x^0, [ x^0<=y^0 && -x^0-y^0>=0 ], cost: -3*x^0-3*y^0
     16: l1 -> l1 : x^0'=y^0, [ y^0<=1-x^0 && x^0-y^0>=0 ], cost: 3*x^0-3*y^0
     17: l1 -> l1 : y^0'=1-x^0, [ y^0<=x^0 && -1+x^0+y^0>=0 ], cost: -3+3*x^0+3*y^0
      8: l4 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      8: l4 -> l1 : [], cost: 2
     18: l4 -> l1 : x^0'=y^0, [ -x^0<=y^0 && -x^0+y^0>=0 ], cost: 2-3*x^0+3*y^0
     19: l4 -> l1 : y^0'=-x^0, [ x^0<=y^0 && -x^0-y^0>=0 ], cost: 2-3*x^0-3*y^0
     20: l4 -> l1 : x^0'=y^0, [ y^0<=1-x^0 && x^0-y^0>=0 ], cost: 2+3*x^0-3*y^0
     21: l4 -> l1 : y^0'=1-x^0, [ y^0<=x^0 && -1+x^0+y^0>=0 ], cost: -1+3*x^0+3*y^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     18: l4 -> l1 : x^0'=y^0, [ -x^0<=y^0 && -x^0+y^0>=0 ], cost: 2-3*x^0+3*y^0
     19: l4 -> l1 : y^0'=-x^0, [ x^0<=y^0 && -x^0-y^0>=0 ], cost: 2-3*x^0-3*y^0
     20: l4 -> l1 : x^0'=y^0, [ y^0<=1-x^0 && x^0-y^0>=0 ], cost: 2+3*x^0-3*y^0
     21: l4 -> l1 : y^0'=1-x^0, [ y^0<=x^0 && -1+x^0+y^0>=0 ], cost: -1+3*x^0+3*y^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     18: l4 -> l1 : x^0'=y^0, [ -x^0<=y^0 && -x^0+y^0>=0 ], cost: 2-3*x^0+3*y^0
     19: l4 -> l1 : y^0'=-x^0, [ x^0<=y^0 && -x^0-y^0>=0 ], cost: 2-3*x^0-3*y^0
     20: l4 -> l1 : x^0'=y^0, [ y^0<=1-x^0 && x^0-y^0>=0 ], cost: 2+3*x^0-3*y^0
     21: l4 -> l1 : y^0'=1-x^0, [ y^0<=x^0 && -1+x^0+y^0>=0 ], cost: -1+3*x^0+3*y^0

Computing asymptotic complexity for rule 18
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 19
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 20
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 21
   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:  [ __disjvr_0^0==__disjvr_0^post_8 && __disjvr_1^0==__disjvr_1^post_8 && x^0==x^post_8 && y^0==y^post_8 ]

WORST_CASE(Omega(1),?)