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-x^0+2*y^0==0 ], cost: 1
      1: l0 -> l1 : x^0'=y^0, [ -x^0+2*y^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-x^0+2*y^0==0 ], cost: 1
      1: l0 -> l1 : x^0'=y^0, [ -x^0+2*y^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-x^0+2*y^0==0 ], cost: 1
      1: l0 -> l1 : x^0'=y^0, [ -x^0+2*y^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-x^0+2*y^0==0 ], cost: 1
      1: l0 -> l1 : x^0'=y^0, [ -x^0+2*y^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

   Found no metering function for rule 19.
   Accelerated rule 20 with NONTERM (after strengthening guard), yielding the new rule 24.
   Accelerated rule 21 with metering function meter (where 7*meter==1+2*y^post_9-x^0), yielding the new rule 25.
   Found no metering function for rule 22.
   Accelerated rule 23 with NONTERM (after strengthening guard), yielding the new rule 26.
   Removing the simple loops: 21.

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
     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
     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 -> l1 : x^0'=-1/2+3^meter*x^0+1/2*3^meter, y^0'=y^post_9, [ 3-x^0==0 && 1+2*y^post_9-x^0==0 && 7*meter==1+2*y^post_9-x^0 && meter>=1 ], cost: 5*meter
     26: l1 -> [7] : [ 5<=x^0 && 2*y^post_9-x^0==0 && 5<=y^post_9 && 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'=4+6*y^post_9, y^0'=y^post_9, [ 5<=1+2*y^post_9 ], cost: 7
     28: 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),?)