WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l8
      0: l0 -> l1 : oldX0^0'=oldX0^post_1, oldX1^0'=oldX1^post_1, oldX2^0'=oldX2^post_1, oldX3^0'=oldX3^post_1, x0^0'=x0^post_1, x1^0'=x1^post_1, [ oldX0^post_1==x0^0 && oldX1^post_1==x1^0 && oldX2^post_1==oldX2^post_1 && oldX3^post_1==oldX3^post_1 && x0^post_1==oldX2^post_1 && x1^post_1==oldX3^post_1 ], cost: 1
      1: l2 -> l3 : oldX0^0'=oldX0^post_2, oldX1^0'=oldX1^post_2, oldX2^0'=oldX2^post_2, oldX3^0'=oldX3^post_2, x0^0'=x0^post_2, x1^0'=x1^post_2, [ oldX0^post_2==x0^0 && oldX1^post_2==x1^0 && x0^post_2==oldX0^post_2 && x1^post_2==1+oldX1^post_2 && oldX2^0==oldX2^post_2 && oldX3^0==oldX3^post_2 ], cost: 1
      2: l2 -> l4 : oldX0^0'=oldX0^post_3, oldX1^0'=oldX1^post_3, oldX2^0'=oldX2^post_3, oldX3^0'=oldX3^post_3, x0^0'=x0^post_3, x1^0'=x1^post_3, [ oldX0^post_3==x0^0 && oldX1^post_3==x1^0 && oldX2^post_3==oldX2^post_3 && x0^post_3==oldX1^post_3 && x1^post_3==oldX2^post_3 && oldX3^0==oldX3^post_3 ], cost: 1
      3: l3 -> l0 : oldX0^0'=oldX0^post_4, oldX1^0'=oldX1^post_4, oldX2^0'=oldX2^post_4, oldX3^0'=oldX3^post_4, x0^0'=x0^post_4, x1^0'=x1^post_4, [ oldX0^post_4==x0^0 && oldX1^post_4==x1^0 && oldX0^post_4<=oldX1^post_4 && x0^post_4==oldX0^post_4 && x1^post_4==oldX1^post_4 && oldX2^0==oldX2^post_4 && oldX3^0==oldX3^post_4 ], cost: 1
      4: l3 -> l2 : oldX0^0'=oldX0^post_5, oldX1^0'=oldX1^post_5, oldX2^0'=oldX2^post_5, oldX3^0'=oldX3^post_5, x0^0'=x0^post_5, x1^0'=x1^post_5, [ oldX0^post_5==x0^0 && oldX1^post_5==x1^0 && 1+oldX1^post_5<=oldX0^post_5 && x0^post_5==oldX0^post_5 && x1^post_5==oldX1^post_5 && oldX2^0==oldX2^post_5 && oldX3^0==oldX3^post_5 ], cost: 1
      6: l4 -> l5 : oldX0^0'=oldX0^post_7, oldX1^0'=oldX1^post_7, oldX2^0'=oldX2^post_7, oldX3^0'=oldX3^post_7, x0^0'=x0^post_7, x1^0'=x1^post_7, [ oldX0^post_7==x0^0 && oldX1^post_7==x1^0 && oldX2^post_7==oldX2^post_7 && x0^post_7==oldX0^post_7 && x1^post_7==oldX2^post_7 && oldX3^0==oldX3^post_7 ], cost: 1
      5: l5 -> l3 : oldX0^0'=oldX0^post_6, oldX1^0'=oldX1^post_6, oldX2^0'=oldX2^post_6, oldX3^0'=oldX3^post_6, x0^0'=x0^post_6, x1^0'=x1^post_6, [ oldX0^post_6==x0^0 && oldX1^post_6==x1^0 && x0^post_6==oldX0^post_6 && x1^post_6==0 && oldX2^0==oldX2^post_6 && oldX3^0==oldX3^post_6 ], cost: 1
      7: l6 -> l7 : oldX0^0'=oldX0^post_8, oldX1^0'=oldX1^post_8, oldX2^0'=oldX2^post_8, oldX3^0'=oldX3^post_8, x0^0'=x0^post_8, x1^0'=x1^post_8, [ oldX0^post_8==x0^0 && oldX1^post_8==x1^0 && oldX2^post_8==oldX2^post_8 && oldX3^post_8==oldX3^post_8 && x0^post_8==oldX2^post_8 && x1^post_8==oldX3^post_8 ], cost: 1
      8: l6 -> l7 : oldX0^0'=oldX0^post_9, oldX1^0'=oldX1^post_9, oldX2^0'=oldX2^post_9, oldX3^0'=oldX3^post_9, x0^0'=x0^post_9, x1^0'=x1^post_9, [ oldX0^0==oldX0^post_9 && oldX1^0==oldX1^post_9 && oldX2^0==oldX2^post_9 && oldX3^0==oldX3^post_9 && x0^0==x0^post_9 && x1^0==x1^post_9 ], cost: 1
      9: l6 -> l1 : oldX0^0'=oldX0^post_10, oldX1^0'=oldX1^post_10, oldX2^0'=oldX2^post_10, oldX3^0'=oldX3^post_10, x0^0'=x0^post_10, x1^0'=x1^post_10, [ oldX0^0==oldX0^post_10 && oldX1^0==oldX1^post_10 && oldX2^0==oldX2^post_10 && oldX3^0==oldX3^post_10 && x0^0==x0^post_10 && x1^0==x1^post_10 ], cost: 1
     10: l6 -> l0 : oldX0^0'=oldX0^post_11, oldX1^0'=oldX1^post_11, oldX2^0'=oldX2^post_11, oldX3^0'=oldX3^post_11, x0^0'=x0^post_11, x1^0'=x1^post_11, [ oldX0^0==oldX0^post_11 && oldX1^0==oldX1^post_11 && oldX2^0==oldX2^post_11 && oldX3^0==oldX3^post_11 && x0^0==x0^post_11 && x1^0==x1^post_11 ], cost: 1
     11: l6 -> l2 : oldX0^0'=oldX0^post_12, oldX1^0'=oldX1^post_12, oldX2^0'=oldX2^post_12, oldX3^0'=oldX3^post_12, x0^0'=x0^post_12, x1^0'=x1^post_12, [ oldX0^0==oldX0^post_12 && oldX1^0==oldX1^post_12 && oldX2^0==oldX2^post_12 && oldX3^0==oldX3^post_12 && x0^0==x0^post_12 && x1^0==x1^post_12 ], cost: 1
     12: l6 -> l3 : oldX0^0'=oldX0^post_13, oldX1^0'=oldX1^post_13, oldX2^0'=oldX2^post_13, oldX3^0'=oldX3^post_13, x0^0'=x0^post_13, x1^0'=x1^post_13, [ oldX0^0==oldX0^post_13 && oldX1^0==oldX1^post_13 && oldX2^0==oldX2^post_13 && oldX3^0==oldX3^post_13 && x0^0==x0^post_13 && x1^0==x1^post_13 ], cost: 1
     13: l6 -> l5 : oldX0^0'=oldX0^post_14, oldX1^0'=oldX1^post_14, oldX2^0'=oldX2^post_14, oldX3^0'=oldX3^post_14, x0^0'=x0^post_14, x1^0'=x1^post_14, [ oldX0^0==oldX0^post_14 && oldX1^0==oldX1^post_14 && oldX2^0==oldX2^post_14 && oldX3^0==oldX3^post_14 && x0^0==x0^post_14 && x1^0==x1^post_14 ], cost: 1
     14: l6 -> l4 : oldX0^0'=oldX0^post_15, oldX1^0'=oldX1^post_15, oldX2^0'=oldX2^post_15, oldX3^0'=oldX3^post_15, x0^0'=x0^post_15, x1^0'=x1^post_15, [ oldX0^0==oldX0^post_15 && oldX1^0==oldX1^post_15 && oldX2^0==oldX2^post_15 && oldX3^0==oldX3^post_15 && x0^0==x0^post_15 && x1^0==x1^post_15 ], cost: 1
     15: l8 -> l6 : oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, oldX2^0'=oldX2^post_16, oldX3^0'=oldX3^post_16, x0^0'=x0^post_16, x1^0'=x1^post_16, [ oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && oldX2^0==oldX2^post_16 && oldX3^0==oldX3^post_16 && x0^0==x0^post_16 && x1^0==x1^post_16 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     15: l8 -> l6 : oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, oldX2^0'=oldX2^post_16, oldX3^0'=oldX3^post_16, x0^0'=x0^post_16, x1^0'=x1^post_16, [ oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && oldX2^0==oldX2^post_16 && oldX3^0==oldX3^post_16 && x0^0==x0^post_16 && x1^0==x1^post_16 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l8
      1: l2 -> l3 : oldX0^0'=oldX0^post_2, oldX1^0'=oldX1^post_2, oldX2^0'=oldX2^post_2, oldX3^0'=oldX3^post_2, x0^0'=x0^post_2, x1^0'=x1^post_2, [ oldX0^post_2==x0^0 && oldX1^post_2==x1^0 && x0^post_2==oldX0^post_2 && x1^post_2==1+oldX1^post_2 && oldX2^0==oldX2^post_2 && oldX3^0==oldX3^post_2 ], cost: 1
      2: l2 -> l4 : oldX0^0'=oldX0^post_3, oldX1^0'=oldX1^post_3, oldX2^0'=oldX2^post_3, oldX3^0'=oldX3^post_3, x0^0'=x0^post_3, x1^0'=x1^post_3, [ oldX0^post_3==x0^0 && oldX1^post_3==x1^0 && oldX2^post_3==oldX2^post_3 && x0^post_3==oldX1^post_3 && x1^post_3==oldX2^post_3 && oldX3^0==oldX3^post_3 ], cost: 1
      4: l3 -> l2 : oldX0^0'=oldX0^post_5, oldX1^0'=oldX1^post_5, oldX2^0'=oldX2^post_5, oldX3^0'=oldX3^post_5, x0^0'=x0^post_5, x1^0'=x1^post_5, [ oldX0^post_5==x0^0 && oldX1^post_5==x1^0 && 1+oldX1^post_5<=oldX0^post_5 && x0^post_5==oldX0^post_5 && x1^post_5==oldX1^post_5 && oldX2^0==oldX2^post_5 && oldX3^0==oldX3^post_5 ], cost: 1
      6: l4 -> l5 : oldX0^0'=oldX0^post_7, oldX1^0'=oldX1^post_7, oldX2^0'=oldX2^post_7, oldX3^0'=oldX3^post_7, x0^0'=x0^post_7, x1^0'=x1^post_7, [ oldX0^post_7==x0^0 && oldX1^post_7==x1^0 && oldX2^post_7==oldX2^post_7 && x0^post_7==oldX0^post_7 && x1^post_7==oldX2^post_7 && oldX3^0==oldX3^post_7 ], cost: 1
      5: l5 -> l3 : oldX0^0'=oldX0^post_6, oldX1^0'=oldX1^post_6, oldX2^0'=oldX2^post_6, oldX3^0'=oldX3^post_6, x0^0'=x0^post_6, x1^0'=x1^post_6, [ oldX0^post_6==x0^0 && oldX1^post_6==x1^0 && x0^post_6==oldX0^post_6 && x1^post_6==0 && oldX2^0==oldX2^post_6 && oldX3^0==oldX3^post_6 ], cost: 1
     11: l6 -> l2 : oldX0^0'=oldX0^post_12, oldX1^0'=oldX1^post_12, oldX2^0'=oldX2^post_12, oldX3^0'=oldX3^post_12, x0^0'=x0^post_12, x1^0'=x1^post_12, [ oldX0^0==oldX0^post_12 && oldX1^0==oldX1^post_12 && oldX2^0==oldX2^post_12 && oldX3^0==oldX3^post_12 && x0^0==x0^post_12 && x1^0==x1^post_12 ], cost: 1
     12: l6 -> l3 : oldX0^0'=oldX0^post_13, oldX1^0'=oldX1^post_13, oldX2^0'=oldX2^post_13, oldX3^0'=oldX3^post_13, x0^0'=x0^post_13, x1^0'=x1^post_13, [ oldX0^0==oldX0^post_13 && oldX1^0==oldX1^post_13 && oldX2^0==oldX2^post_13 && oldX3^0==oldX3^post_13 && x0^0==x0^post_13 && x1^0==x1^post_13 ], cost: 1
     13: l6 -> l5 : oldX0^0'=oldX0^post_14, oldX1^0'=oldX1^post_14, oldX2^0'=oldX2^post_14, oldX3^0'=oldX3^post_14, x0^0'=x0^post_14, x1^0'=x1^post_14, [ oldX0^0==oldX0^post_14 && oldX1^0==oldX1^post_14 && oldX2^0==oldX2^post_14 && oldX3^0==oldX3^post_14 && x0^0==x0^post_14 && x1^0==x1^post_14 ], cost: 1
     14: l6 -> l4 : oldX0^0'=oldX0^post_15, oldX1^0'=oldX1^post_15, oldX2^0'=oldX2^post_15, oldX3^0'=oldX3^post_15, x0^0'=x0^post_15, x1^0'=x1^post_15, [ oldX0^0==oldX0^post_15 && oldX1^0==oldX1^post_15 && oldX2^0==oldX2^post_15 && oldX3^0==oldX3^post_15 && x0^0==x0^post_15 && x1^0==x1^post_15 ], cost: 1
     15: l8 -> l6 : oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, oldX2^0'=oldX2^post_16, oldX3^0'=oldX3^post_16, x0^0'=x0^post_16, x1^0'=x1^post_16, [ oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && oldX2^0==oldX2^post_16 && oldX3^0==oldX3^post_16 && x0^0==x0^post_16 && x1^0==x1^post_16 ], cost: 1

Simplified all rules, resulting in:
   Start location: l8
      1: l2 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [], cost: 1
      2: l2 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [], cost: 1
      4: l3 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ 1+x1^0<=x0^0 ], cost: 1
      6: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 1
      5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=0, [], cost: 1
     11: l6 -> l2 : [], cost: 1
     12: l6 -> l3 : [], cost: 1
     13: l6 -> l5 : [], cost: 1
     14: l6 -> l4 : [], cost: 1
     15: l8 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on tree-shaped paths):
   Start location: l8
      1: l2 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [], cost: 1
      2: l2 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [], cost: 1
      4: l3 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ 1+x1^0<=x0^0 ], cost: 1
      6: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 1
      5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=0, [], cost: 1
     16: l8 -> l2 : [], cost: 2
     17: l8 -> l3 : [], cost: 2
     18: l8 -> l5 : [], cost: 2
     19: l8 -> l4 : [], cost: 2

Eliminated location l2 (as a last resort):
   Start location: l8
     20: l3 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [ 1+x1^0<=x0^0 ], cost: 2
     21: l3 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [ 1+x1^0<=x0^0 ], cost: 2
      6: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 1
      5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=0, [], cost: 1
     17: l8 -> l3 : [], cost: 2
     18: l8 -> l5 : [], cost: 2
     19: l8 -> l4 : [], cost: 2
     22: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [], cost: 3
     23: l8 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [], cost: 3

Accelerating simple loops of location 3.
   Accelerating the following rules:
     20: l3 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [ 1+x1^0<=x0^0 ], cost: 2

   Accelerated rule 20 with metering function -x1^0+x0^0, yielding the new rule 24.
   Removing the simple loops: 20.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     21: l3 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [ 1+x1^0<=x0^0 ], cost: 2
     24: l3 -> l3 : oldX0^0'=x0^0, oldX1^0'=-1+x0^0, x1^0'=x0^0, [ 1+x1^0<=x0^0 ], cost: -2*x1^0+2*x0^0
      6: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 1
      5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=0, [], cost: 1
     17: l8 -> l3 : [], cost: 2
     18: l8 -> l5 : [], cost: 2
     19: l8 -> l4 : [], cost: 2
     22: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [], cost: 3
     23: l8 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l8
     21: l3 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [ 1+x1^0<=x0^0 ], cost: 2
      6: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 1
      5: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=0, [], cost: 1
     25: l5 -> l3 : oldX0^0'=x0^0, oldX1^0'=-1+x0^0, x1^0'=x0^0, [ 1<=x0^0 ], cost: 1+2*x0^0
     17: l8 -> l3 : [], cost: 2
     18: l8 -> l5 : [], cost: 2
     19: l8 -> l4 : [], cost: 2
     22: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=x1^0, x1^0'=1+x1^0, [], cost: 3
     23: l8 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [], cost: 3
     26: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-1+x0^0, x1^0'=x0^0, [ 1+x1^0<=x0^0 ], cost: 2-2*x1^0+2*x0^0
     27: l8 -> l3 : oldX0^0'=x0^0, oldX1^0'=-1+x0^0, x1^0'=x0^0, [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0

Eliminated location l3 (as a last resort):
   Start location: l8
      6: l4 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 1
     28: l5 -> l4 : oldX0^0'=x0^0, oldX1^0'=0, oldX2^0'=oldX2^post_3, x0^0'=0, x1^0'=oldX2^post_3, [ 1<=x0^0 ], cost: 3
     31: l5 -> [10] : [ 1<=x0^0 ], cost: 1+2*x0^0
     18: l8 -> l5 : [], cost: 2
     19: l8 -> l4 : [], cost: 2
     23: l8 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [], cost: 3
     29: l8 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_3, x0^0'=x1^0, x1^0'=oldX2^post_3, [ 1+x1^0<=x0^0 ], cost: 4
     30: l8 -> l4 : oldX0^0'=x0^0, oldX1^0'=1+x1^0, oldX2^0'=oldX2^post_3, x0^0'=1+x1^0, x1^0'=oldX2^post_3, [ 2+x1^0<=x0^0 ], cost: 5
     32: l8 -> [10] : [ 1+x1^0<=x0^0 ], cost: 2-2*x1^0+2*x0^0
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0

Eliminated location l4 (as a last resort):
   Start location: l8
     31: l5 -> [10] : [ 1<=x0^0 ], cost: 1+2*x0^0
     36: l5 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 4
     18: l8 -> l5 : [], cost: 2
     32: l8 -> [10] : [ 1+x1^0<=x0^0 ], cost: 2-2*x1^0+2*x0^0
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0
     34: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 3
     35: l8 -> l5 : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [], cost: 4
     37: l8 -> l5 : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 ], cost: 5
     38: l8 -> l5 : oldX0^0'=1+x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=1+x1^0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 ], cost: 6

Accelerating simple loops of location 5.
   Accelerating the following rules:
     36: l5 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 4

   Found no metering function for rule 36.
   Removing the simple loops:.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     31: l5 -> [10] : [ 1<=x0^0 ], cost: 1+2*x0^0
     36: l5 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 4
     18: l8 -> l5 : [], cost: 2
     32: l8 -> [10] : [ 1+x1^0<=x0^0 ], cost: 2-2*x1^0+2*x0^0
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0
     34: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 3
     35: l8 -> l5 : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [], cost: 4
     37: l8 -> l5 : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 ], cost: 5
     38: l8 -> l5 : oldX0^0'=1+x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=1+x1^0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 ], cost: 6

Chained accelerated rules (with incoming rules):
   Start location: l8
     31: l5 -> [10] : [ 1<=x0^0 ], cost: 1+2*x0^0
     18: l8 -> l5 : [], cost: 2
     32: l8 -> [10] : [ 1+x1^0<=x0^0 ], cost: 2-2*x1^0+2*x0^0
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0
     34: l8 -> l5 : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [], cost: 3
     35: l8 -> l5 : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [], cost: 4
     37: l8 -> l5 : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 ], cost: 5
     38: l8 -> l5 : oldX0^0'=1+x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=1+x1^0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 ], cost: 6
     39: l8 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 6
     40: l8 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 7
     41: l8 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1<=x1^0 ], cost: 8
     42: l8 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 && 1<=x1^0 ], cost: 9
     43: l8 -> l5 : oldX0^0'=0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 && 1<=1+x1^0 ], cost: 10

Eliminated locations (on tree-shaped paths):
   Start location: l8
     32: l8 -> [10] : [ 1+x1^0<=x0^0 ], cost: 2-2*x1^0+2*x0^0
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0
     44: l8 -> [10] : [ 1<=x0^0 ], cost: 3+2*x0^0
     45: l8 -> [10] : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 4+2*x0^0
     46: l8 -> [10] : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1<=x1^0 ], cost: 5+2*x1^0
     47: l8 -> [10] : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 && 1<=x1^0 ], cost: 6+2*x1^0
     48: l8 -> [10] : oldX0^0'=1+x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=1+x1^0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 && 1<=1+x1^0 ], cost: 9+2*x1^0

Applied pruning (of leafs and parallel rules):
   Start location: l8
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0
     45: l8 -> [10] : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 4+2*x0^0
     46: l8 -> [10] : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1<=x1^0 ], cost: 5+2*x1^0
     47: l8 -> [10] : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 && 1<=x1^0 ], cost: 6+2*x1^0
     48: l8 -> [10] : oldX0^0'=1+x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=1+x1^0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 && 1<=1+x1^0 ], cost: 9+2*x1^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l8
     33: l8 -> [10] : [ 2+x1^0<=x0^0 ], cost: 1-2*x1^0+2*x0^0
     45: l8 -> [10] : oldX0^0'=x0^0, oldX1^0'=x1^0, oldX2^0'=oldX2^post_7, x1^0'=oldX2^post_7, [ 1<=x0^0 ], cost: 4+2*x0^0
     46: l8 -> [10] : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1<=x1^0 ], cost: 5+2*x1^0
     47: l8 -> [10] : oldX0^0'=x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=x1^0, x1^0'=oldX2^post_7, [ 1+x1^0<=x0^0 && 1<=x1^0 ], cost: 6+2*x1^0
     48: l8 -> [10] : oldX0^0'=1+x1^0, oldX1^0'=oldX2^post_3, oldX2^0'=oldX2^post_7, x0^0'=1+x1^0, x1^0'=oldX2^post_7, [ 2+x1^0<=x0^0 && 1<=1+x1^0 ], cost: 9+2*x1^0

Computing asymptotic complexity for rule 33
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -1-x1^0+x0^0 (+/+!), 1-2*x1^0+2*x0^0 (+) [not solved]

      removing all constraints (solved by SMT)
      resulting limit problem: [solved]

      applying transformation rule (C) using substitution {x1^0==0,x0^0==n}
      resulting limit problem:
      [solved]

   Solution:
      x1^0 / 0
      x0^0 / n
   Resulting cost 1+2*n has complexity: Poly(n^1)

Found new complexity Poly(n^1).

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Poly(n^1)
   Cpx degree:  1
   Solved cost: 1+2*n
   Rule cost:   1-2*x1^0+2*x0^0
   Rule guard:  [ 2+x1^0<=x0^0 ]

WORST_CASE(Omega(n^1),?)