WORST_CASE(Omega(1),?)

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l6 -> l5 : x^0'=x^post_11, y^0'=y^post_11, [ x^0==x^post_11 && y^0==y^post_11 ], 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 : [ 1+x^0<=1 ], cost: 1
      3: l1 -> l2 : [ 2<=x^0 ], cost: 1
      4: l2 -> l3 : [ 1+x^0<=2 ], cost: 1
      5: l2 -> l3 : [ 3<=x^0 ], cost: 1
      6: l3 -> l4 : [ 1+x^0<=4 ], cost: 1
      7: l3 -> l4 : [ 5<=x^0 ], cost: 1
      8: l4 -> l0 : y^0'=y^post_9, [], cost: 1
      9: l5 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 1
     10: 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
      2: l1 -> l2 : [ 1+x^0<=1 ], cost: 1
      3: l1 -> l2 : [ 2<=x^0 ], cost: 1
      4: l2 -> l3 : [ 1+x^0<=2 ], cost: 1
      5: l2 -> l3 : [ 3<=x^0 ], cost: 1
      6: l3 -> l4 : [ 1+x^0<=4 ], cost: 1
      7: l3 -> l4 : [ 5<=x^0 ], cost: 1
      8: l4 -> l0 : y^0'=y^post_9, [], cost: 1
     11: l6 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 2

Eliminated locations (on tree-shaped 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
     12: l1 -> l3 : [ 1+x^0<=1 ], cost: 2
     13: l1 -> l3 : [ 3<=x^0 ], cost: 2
     14: l3 -> l0 : y^0'=y^post_9, [ 1+x^0<=4 ], cost: 2
     15: l3 -> l0 : y^0'=y^post_9, [ 5<=x^0 ], cost: 2
     11: l6 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 2

Eliminated locations (on tree-shaped 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
     16: l1 -> l0 : y^0'=y^post_9, [ 1+x^0<=1 ], cost: 4
     17: l1 -> l0 : y^0'=y^post_9, [ 3<=x^0 && 1+x^0<=4 ], cost: 4
     18: l1 -> l0 : y^0'=y^post_9, [ 5<=x^0 ], cost: 4
     11: l6 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
     19: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 1+x^0<=1 && 1+2*y^post_9-x^0==0 ], cost: 5
     20: l1 -> l1 : x^0'=y^post_9, y^0'=y^post_9, [ 1+x^0<=1 && 2*y^post_9-x^0==0 ], cost: 5
     21: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 3<=x^0 && 1+x^0<=4 && 1+2*y^post_9-x^0==0 ], cost: 5
     22: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 5<=x^0 && 1+2*y^post_9-x^0==0 ], cost: 5
     23: l1 -> l1 : x^0'=y^post_9, y^0'=y^post_9, [ 5<=x^0 && 2*y^post_9-x^0==0 ], cost: 5
     11: l6 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 2

Accelerating simple loops of location 1.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     19: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 1+x^0<=1 && 1+2*y^post_9-x^0==0 ], cost: 5
     20: l1 -> l1 : x^0'=y^post_9, y^0'=y^post_9, [ 1+x^0<=1 && 2*y^post_9-x^0==0 ], cost: 5
     21: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 3-x^0==0 && 1+2*y^post_9-x^0==0 ], cost: 5
     22: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 5<=x^0 && 1+2*y^post_9-x^0==0 ], cost: 5
     23: l1 -> l1 : x^0'=y^post_9, y^0'=y^post_9, [ 5<=x^0 && 2*y^post_9-x^0==0 ], cost: 5

   Failed to prove monotonicity of the guard of rule 19.
   Accelerated rule 20 with non-termination, yielding the new rule 24.
   Failed to prove monotonicity of the guard of rule 21.
   Failed to prove monotonicity of the guard of rule 22.
   Failed to prove monotonicity of the guard of rule 23.
[accelerate] Nesting with 4 inner and 5 outer candidates
   Nested simple loops 20 (outer loop) and 19 (inner loop) with Rule(1 | 1+x^0<=1, 1+2*y^post_9-x^0==0, 2+3*x^0<=1, -1+2*y^post_9-3*x^0==0, | NONTERM || 7 | ), resulting in the new rules: 25, 26.
   Removing the simple loops: 20.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     19: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 1+x^0<=1 && 1+2*y^post_9-x^0==0 ], cost: 5
     21: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 3-x^0==0 && 1+2*y^post_9-x^0==0 ], cost: 5
     22: l1 -> l1 : x^0'=1+3*x^0, y^0'=y^post_9, [ 5<=x^0 && 1+2*y^post_9-x^0==0 ], cost: 5
     23: l1 -> l1 : x^0'=y^post_9, y^0'=y^post_9, [ 5<=x^0 && 2*y^post_9-x^0==0 ], cost: 5
     24: l1 -> [7] : [ 1+x^0<=1 && 2*y^post_9-x^0==0 && y^post_9==0 ], cost: NONTERM
     25: l1 -> [7] : [ 1+x^0<=1 && 1+2*y^post_9-x^0==0 && 2+3*x^0<=1 && -1+2*y^post_9-3*x^0==0 ], cost: NONTERM
     26: l1 -> [7] : [ 1+x^0<=1 && 2*y^post_9-x^0==0 && 1+y^post_9==0 && 2+3*y^post_9<=1 && -1-y^post_9==0 ], cost: NONTERM
     11: l6 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
     11: l6 -> l1 : x^0'=x^post_10, [ 1<=x^post_10 ], cost: 2
     27: l6 -> l1 : x^0'=10, y^0'=1, [], cost: 7
     28: l6 -> l1 : x^0'=4+6*y^post_9, y^0'=y^post_9, [ 5<=1+2*y^post_9 ], cost: 7
     29: l6 -> l1 : x^0'=y^post_9, y^0'=y^post_9, [ 5<=2*y^post_9 ], 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:  [ x^0==x^post_11 && y^0==y^post_11 ]

WORST_CASE(Omega(1),?)