WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_1, __disjvr_1^0'=__disjvr_1^post_1, __disjvr_2^0'=__disjvr_2^post_1, x^0'=x^post_1, y^0'=y^post_1, [ 1+2*y^0<=x^0 && x^0<=1+2*y^0 && x^post_1==1+3*x^0 && __disjvr_0^0==__disjvr_0^post_1 && __disjvr_1^0==__disjvr_1^post_1 && __disjvr_2^0==__disjvr_2^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, __disjvr_2^0'=__disjvr_2^post_2, x^0'=x^post_2, y^0'=y^post_2, [ 2*y^0<=x^0 && x^0<=2*y^0 && x^post_2==y^0 && __disjvr_0^0==__disjvr_0^post_2 && __disjvr_1^0==__disjvr_1^post_2 && __disjvr_2^0==__disjvr_2^post_2 && y^0==y^post_2 ], cost: 1
      2: l1 -> l2 : __disjvr_0^0'=__disjvr_0^post_3, __disjvr_1^0'=__disjvr_1^post_3, __disjvr_2^0'=__disjvr_2^post_3, x^0'=x^post_3, y^0'=y^post_3, [ __disjvr_0^post_3==__disjvr_0^0 && __disjvr_0^0==__disjvr_0^post_3 && __disjvr_1^0==__disjvr_1^post_3 && __disjvr_2^0==__disjvr_2^post_3 && x^0==x^post_3 && y^0==y^post_3 ], cost: 1
      3: l2 -> l3 : __disjvr_0^0'=__disjvr_0^post_4, __disjvr_1^0'=__disjvr_1^post_4, __disjvr_2^0'=__disjvr_2^post_4, x^0'=x^post_4, y^0'=y^post_4, [ __disjvr_1^post_4==__disjvr_1^0 && __disjvr_0^0==__disjvr_0^post_4 && __disjvr_1^0==__disjvr_1^post_4 && __disjvr_2^0==__disjvr_2^post_4 && x^0==x^post_4 && y^0==y^post_4 ], cost: 1
      4: l3 -> l4 : __disjvr_0^0'=__disjvr_0^post_5, __disjvr_1^0'=__disjvr_1^post_5, __disjvr_2^0'=__disjvr_2^post_5, x^0'=x^post_5, y^0'=y^post_5, [ __disjvr_2^post_5==__disjvr_2^0 && __disjvr_0^0==__disjvr_0^post_5 && __disjvr_1^0==__disjvr_1^post_5 && __disjvr_2^0==__disjvr_2^post_5 && x^0==x^post_5 && y^0==y^post_5 ], cost: 1
      5: l4 -> l0 : __disjvr_0^0'=__disjvr_0^post_6, __disjvr_1^0'=__disjvr_1^post_6, __disjvr_2^0'=__disjvr_2^post_6, x^0'=x^post_6, y^0'=y^post_6, [ y^post_6==y^post_6 && __disjvr_0^0==__disjvr_0^post_6 && __disjvr_1^0==__disjvr_1^post_6 && __disjvr_2^0==__disjvr_2^post_6 && x^0==x^post_6 ], cost: 1
      6: l5 -> l1 : __disjvr_0^0'=__disjvr_0^post_7, __disjvr_1^0'=__disjvr_1^post_7, __disjvr_2^0'=__disjvr_2^post_7, x^0'=x^post_7, y^0'=y^post_7, [ x^post_7==x^post_7 && 1<=x^post_7 && __disjvr_0^0==__disjvr_0^post_7 && __disjvr_1^0==__disjvr_1^post_7 && __disjvr_2^0==__disjvr_2^post_7 && y^0==y^post_7 ], cost: 1
      7: l6 -> l5 : __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, __disjvr_2^0'=__disjvr_2^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 && __disjvr_2^0==__disjvr_2^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: l6 -> l5 : __disjvr_0^0'=__disjvr_0^post_8, __disjvr_1^0'=__disjvr_1^post_8, __disjvr_2^0'=__disjvr_2^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 && __disjvr_2^0==__disjvr_2^post_8 && x^0==x^post_8 && y^0==y^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : x^0'=1+3*x^0, [ 1+2*y^0-x^0==0 ], cost: 1
      1: l0 -> l1 : x^0'=y^0, [ 2*y^0-x^0==0 ], cost: 1
      2: l1 -> l2 : [], cost: 1
      3: l2 -> l3 : [], cost: 1
      4: l3 -> l4 : [], cost: 1
      5: l4 -> l0 : y^0'=y^post_6, [], cost: 1
      6: l5 -> l1 : x^0'=x^post_7, [ 1<=x^post_7 ], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      0: l0 -> l1 : x^0'=1+3*x^0, [ 1+2*y^0-x^0==0 ], cost: 1
      1: l0 -> l1 : x^0'=y^0, [ 2*y^0-x^0==0 ], cost: 1
     11: l1 -> l0 : y^0'=y^post_6, [], cost: 4
      8: l6 -> l1 : x^0'=x^post_7, [ 1<=x^post_7 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
     12: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_6, [ 1-x^0+2*y^post_6==0 ], cost: 5
     13: l1 -> l1 : x^0'=y^post_6, y^0'=y^post_6, [ -x^0+2*y^post_6==0 ], cost: 5
      8: l6 -> l1 : x^0'=x^post_7, [ 1<=x^post_7 ], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     12: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_6, [ 1-x^0+2*y^post_6==0 ], cost: 5
     13: l1 -> l1 : x^0'=y^post_6, y^0'=y^post_6, [ -x^0+2*y^post_6==0 ], cost: 5

[test] deduced invariant 1-x^0<=0
[test] deduced invariant -x^0<=0
   Failed to prove monotonicity of the guard of rule 12.
[test] deduced pseudo-invariant -x^0+y^post_6<=0, also trying x^0-y^post_6<=-1
   Accelerated rule 13 with non-termination, yielding the new rule 14.
   Accelerated rule 13 with non-termination, yielding the new rule 15.
[accelerate] Nesting with 1 inner and 2 outer candidates
   Nested simple loops 13 (outer loop) and 12 (inner loop) with Rule(1 | 1-x^0+2*y^post_6==0, -1-3*x^0+2*y^post_6==0, | NONTERM || 7 | ), resulting in the new rules: 16, 17.
   Removing the simple loops: 13.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     12: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_6, [ 1-x^0+2*y^post_6==0 ], cost: 5
     14: l1 -> [7] : [ -x^0+2*y^post_6==0 && y^post_6==0 ], cost: NONTERM
     15: l1 -> [7] : [ -x^0+2*y^post_6==0 && -x^0+y^post_6<=0 && y^post_6==0 ], cost: NONTERM
     16: l1 -> [7] : [ 1-x^0+2*y^post_6==0 && -1-3*x^0+2*y^post_6==0 ], cost: NONTERM
     17: l1 -> [7] : [ -x^0+2*y^post_6==0 && 1+y^post_6==0 && -1-y^post_6==0 ], cost: NONTERM
      8: l6 -> l1 : x^0'=x^post_7, [ 1<=x^post_7 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      8: l6 -> l1 : x^0'=x^post_7, [ 1<=x^post_7 ], cost: 2
     18: l6 -> l1 : x^0'=4+6*y^post_6, y^0'=y^post_6, [ 1<=1+2*y^post_6 ], cost: 7

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     <empty>

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 && __disjvr_2^0==__disjvr_2^post_8 && x^0==x^post_8 && y^0==y^post_8 ]

WORST_CASE(Omega(1),?)