WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : oldX0^0'=oldX0^post_1, oldX1^0'=oldX1^post_1, x0^0'=x0^post_1, [ oldX0^post_1==x0^0 && oldX1^post_1==oldX1^post_1 && x0^post_1==oldX1^post_1 ], cost: 1
      1: l0 -> l2 : oldX0^0'=oldX0^post_2, oldX1^0'=oldX1^post_2, x0^0'=x0^post_2, [ oldX0^post_2==x0^0 && x0^post_2==-2+oldX0^post_2 && oldX1^0==oldX1^post_2 ], cost: 1
      2: l0 -> l2 : oldX0^0'=oldX0^post_3, oldX1^0'=oldX1^post_3, x0^0'=x0^post_3, [ oldX0^post_3==x0^0 && x0^post_3==-1+oldX0^post_3 && oldX1^0==oldX1^post_3 ], cost: 1
      9: l2 -> l5 : oldX0^0'=oldX0^post_10, oldX1^0'=oldX1^post_10, x0^0'=x0^post_10, [ oldX0^post_10==x0^0 && x0^post_10==oldX0^post_10 && oldX1^0==oldX1^post_10 ], cost: 1
      3: l3 -> l0 : oldX0^0'=oldX0^post_4, oldX1^0'=oldX1^post_4, x0^0'=x0^post_4, [ oldX0^post_4==x0^0 && 2<=oldX0^post_4 && x0^post_4==oldX0^post_4 && oldX1^0==oldX1^post_4 ], cost: 1
      4: l3 -> l0 : oldX0^0'=oldX0^post_5, oldX1^0'=oldX1^post_5, x0^0'=x0^post_5, [ oldX0^post_5==x0^0 && 1+oldX0^post_5<=1 && x0^post_5==oldX0^post_5 && oldX1^0==oldX1^post_5 ], cost: 1
      5: l3 -> l4 : oldX0^0'=oldX0^post_6, oldX1^0'=oldX1^post_6, x0^0'=x0^post_6, [ oldX0^post_6==x0^0 && oldX0^post_6<=1 && 1<=oldX0^post_6 && x0^post_6==oldX0^post_6 && oldX1^0==oldX1^post_6 ], cost: 1
      6: l4 -> l1 : oldX0^0'=oldX0^post_7, oldX1^0'=oldX1^post_7, x0^0'=x0^post_7, [ oldX0^post_7==x0^0 && oldX1^post_7==oldX1^post_7 && x0^post_7==oldX1^post_7 ], cost: 1
      7: l5 -> l3 : oldX0^0'=oldX0^post_8, oldX1^0'=oldX1^post_8, x0^0'=x0^post_8, [ oldX0^post_8==x0^0 && 1<=oldX0^post_8 && x0^post_8==oldX0^post_8 && oldX1^0==oldX1^post_8 ], cost: 1
      8: l5 -> l4 : oldX0^0'=oldX0^post_9, oldX1^0'=oldX1^post_9, x0^0'=x0^post_9, [ oldX0^post_9==x0^0 && oldX0^post_9<=0 && x0^post_9==oldX0^post_9 && oldX1^0==oldX1^post_9 ], cost: 1
     10: l6 -> l1 : oldX0^0'=oldX0^post_11, oldX1^0'=oldX1^post_11, x0^0'=x0^post_11, [ oldX0^0==oldX0^post_11 && oldX1^0==oldX1^post_11 && x0^0==x0^post_11 ], cost: 1
     11: l6 -> l0 : oldX0^0'=oldX0^post_12, oldX1^0'=oldX1^post_12, x0^0'=x0^post_12, [ oldX0^0==oldX0^post_12 && oldX1^0==oldX1^post_12 && x0^0==x0^post_12 ], cost: 1
     12: l6 -> l3 : oldX0^0'=oldX0^post_13, oldX1^0'=oldX1^post_13, x0^0'=x0^post_13, [ oldX0^0==oldX0^post_13 && oldX1^0==oldX1^post_13 && x0^0==x0^post_13 ], cost: 1
     13: l6 -> l4 : oldX0^0'=oldX0^post_14, oldX1^0'=oldX1^post_14, x0^0'=x0^post_14, [ oldX0^0==oldX0^post_14 && oldX1^0==oldX1^post_14 && x0^0==x0^post_14 ], cost: 1
     14: l6 -> l5 : oldX0^0'=oldX0^post_15, oldX1^0'=oldX1^post_15, x0^0'=x0^post_15, [ oldX0^0==oldX0^post_15 && oldX1^0==oldX1^post_15 && x0^0==x0^post_15 ], cost: 1
     15: l6 -> l2 : oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, x0^0'=x0^post_16, [ oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && x0^0==x0^post_16 ], cost: 1
     16: l7 -> l6 : oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, x0^0'=x0^post_17, [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && x0^0==x0^post_17 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     16: l7 -> l6 : oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, x0^0'=x0^post_17, [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && x0^0==x0^post_17 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      1: l0 -> l2 : oldX0^0'=oldX0^post_2, oldX1^0'=oldX1^post_2, x0^0'=x0^post_2, [ oldX0^post_2==x0^0 && x0^post_2==-2+oldX0^post_2 && oldX1^0==oldX1^post_2 ], cost: 1
      2: l0 -> l2 : oldX0^0'=oldX0^post_3, oldX1^0'=oldX1^post_3, x0^0'=x0^post_3, [ oldX0^post_3==x0^0 && x0^post_3==-1+oldX0^post_3 && oldX1^0==oldX1^post_3 ], cost: 1
      9: l2 -> l5 : oldX0^0'=oldX0^post_10, oldX1^0'=oldX1^post_10, x0^0'=x0^post_10, [ oldX0^post_10==x0^0 && x0^post_10==oldX0^post_10 && oldX1^0==oldX1^post_10 ], cost: 1
      3: l3 -> l0 : oldX0^0'=oldX0^post_4, oldX1^0'=oldX1^post_4, x0^0'=x0^post_4, [ oldX0^post_4==x0^0 && 2<=oldX0^post_4 && x0^post_4==oldX0^post_4 && oldX1^0==oldX1^post_4 ], cost: 1
      4: l3 -> l0 : oldX0^0'=oldX0^post_5, oldX1^0'=oldX1^post_5, x0^0'=x0^post_5, [ oldX0^post_5==x0^0 && 1+oldX0^post_5<=1 && x0^post_5==oldX0^post_5 && oldX1^0==oldX1^post_5 ], cost: 1
      7: l5 -> l3 : oldX0^0'=oldX0^post_8, oldX1^0'=oldX1^post_8, x0^0'=x0^post_8, [ oldX0^post_8==x0^0 && 1<=oldX0^post_8 && x0^post_8==oldX0^post_8 && oldX1^0==oldX1^post_8 ], cost: 1
     11: l6 -> l0 : oldX0^0'=oldX0^post_12, oldX1^0'=oldX1^post_12, x0^0'=x0^post_12, [ oldX0^0==oldX0^post_12 && oldX1^0==oldX1^post_12 && x0^0==x0^post_12 ], cost: 1
     12: l6 -> l3 : oldX0^0'=oldX0^post_13, oldX1^0'=oldX1^post_13, x0^0'=x0^post_13, [ oldX0^0==oldX0^post_13 && oldX1^0==oldX1^post_13 && x0^0==x0^post_13 ], cost: 1
     14: l6 -> l5 : oldX0^0'=oldX0^post_15, oldX1^0'=oldX1^post_15, x0^0'=x0^post_15, [ oldX0^0==oldX0^post_15 && oldX1^0==oldX1^post_15 && x0^0==x0^post_15 ], cost: 1
     15: l6 -> l2 : oldX0^0'=oldX0^post_16, oldX1^0'=oldX1^post_16, x0^0'=x0^post_16, [ oldX0^0==oldX0^post_16 && oldX1^0==oldX1^post_16 && x0^0==x0^post_16 ], cost: 1
     16: l7 -> l6 : oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, x0^0'=x0^post_17, [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && x0^0==x0^post_17 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      1: l0 -> l2 : oldX0^0'=x0^0, x0^0'=-2+x0^0, [], cost: 1
      2: l0 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, [], cost: 1
      9: l2 -> l5 : oldX0^0'=x0^0, [], cost: 1
      3: l3 -> l0 : oldX0^0'=x0^0, [ 2<=x0^0 ], cost: 1
      4: l3 -> l0 : oldX0^0'=x0^0, [ 1+x0^0<=1 ], cost: 1
      7: l5 -> l3 : oldX0^0'=x0^0, [ 1<=x0^0 ], cost: 1
     11: l6 -> l0 : [], cost: 1
     12: l6 -> l3 : [], cost: 1
     14: l6 -> l5 : [], cost: 1
     15: l6 -> l2 : [], cost: 1
     16: l7 -> l6 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on tree-shaped paths):
   Start location: l7
      1: l0 -> l2 : oldX0^0'=x0^0, x0^0'=-2+x0^0, [], cost: 1
      2: l0 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, [], cost: 1
      9: l2 -> l5 : oldX0^0'=x0^0, [], cost: 1
      3: l3 -> l0 : oldX0^0'=x0^0, [ 2<=x0^0 ], cost: 1
      4: l3 -> l0 : oldX0^0'=x0^0, [ 1+x0^0<=1 ], cost: 1
      7: l5 -> l3 : oldX0^0'=x0^0, [ 1<=x0^0 ], cost: 1
     17: l7 -> l0 : [], cost: 2
     18: l7 -> l3 : [], cost: 2
     19: l7 -> l5 : [], cost: 2
     20: l7 -> l2 : [], cost: 2

Eliminated location l0 (as a last resort):
   Start location: l7
      9: l2 -> l5 : oldX0^0'=x0^0, [], cost: 1
     21: l3 -> l2 : oldX0^0'=x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 2
     22: l3 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 2
     23: l3 -> l2 : oldX0^0'=x0^0, x0^0'=-2+x0^0, [ 1+x0^0<=1 ], cost: 2
     24: l3 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, [ 1+x0^0<=1 ], cost: 2
      7: l5 -> l3 : oldX0^0'=x0^0, [ 1<=x0^0 ], cost: 1
     18: l7 -> l3 : [], cost: 2
     19: l7 -> l5 : [], cost: 2
     20: l7 -> l2 : [], cost: 2
     25: l7 -> l2 : oldX0^0'=x0^0, x0^0'=-2+x0^0, [], cost: 3
     26: l7 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, [], cost: 3

Eliminated location l2 (as a last resort):
   Start location: l7
     28: l3 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 3
     29: l3 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 3
     30: l3 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 1+x0^0<=1 ], cost: 3
     31: l3 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 1+x0^0<=1 ], cost: 3
      7: l5 -> l3 : oldX0^0'=x0^0, [ 1<=x0^0 ], cost: 1
     18: l7 -> l3 : [], cost: 2
     19: l7 -> l5 : [], cost: 2
     27: l7 -> l5 : oldX0^0'=x0^0, [], cost: 3
     32: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [], cost: 4
     33: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [], cost: 4

Eliminated location l3 (as a last resort):
   Start location: l7
     34: l5 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 4
     35: l5 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 4
     19: l7 -> l5 : [], cost: 2
     27: l7 -> l5 : oldX0^0'=x0^0, [], cost: 3
     32: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [], cost: 4
     33: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [], cost: 4
     36: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 5
     37: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 5
     38: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 1+x0^0<=1 ], cost: 5
     39: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 1+x0^0<=1 ], cost: 5

Accelerating simple loops of location 5.
   Accelerating the following rules:
     34: l5 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 4
     35: l5 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 4

   Accelerated rule 34 with backward acceleration, yielding the new rule 40.
   Accelerated rule 35 with backward acceleration, yielding the new rule 41.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 34 35.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     40: l5 -> l5 : oldX0^0'=x0^0-2*k, x0^0'=x0^0-2*k, [ k>=1 && 2<=2+x0^0-2*k ], cost: 4*k
     41: l5 -> l5 : oldX0^0'=1, x0^0'=1, [ -1+x0^0>=1 ], cost: -4+4*x0^0
     19: l7 -> l5 : [], cost: 2
     27: l7 -> l5 : oldX0^0'=x0^0, [], cost: 3
     32: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [], cost: 4
     33: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [], cost: 4
     36: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 5
     37: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 5
     38: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 1+x0^0<=1 ], cost: 5
     39: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 1+x0^0<=1 ], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: l7
     19: l7 -> l5 : [], cost: 2
     27: l7 -> l5 : oldX0^0'=x0^0, [], cost: 3
     32: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [], cost: 4
     33: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [], cost: 4
     36: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 2<=x0^0 ], cost: 5
     37: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 2<=x0^0 ], cost: 5
     38: l7 -> l5 : oldX0^0'=-2+x0^0, x0^0'=-2+x0^0, [ 1+x0^0<=1 ], cost: 5
     39: l7 -> l5 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, [ 1+x0^0<=1 ], cost: 5
     42: l7 -> l5 : oldX0^0'=x0^0-2*k, x0^0'=x0^0-2*k, [ k>=1 && 2<=2+x0^0-2*k ], cost: 2+4*k
     43: l7 -> l5 : oldX0^0'=x0^0-2*k, x0^0'=x0^0-2*k, [ k>=1 && 2<=2+x0^0-2*k ], cost: 3+4*k
     44: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ k>=1 && 2<=x0^0-2*k ], cost: 4+4*k
     45: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ k>=1 && 2<=1+x0^0-2*k ], cost: 4+4*k
     46: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ 2<=x0^0 && k>=1 && 2<=x0^0-2*k ], cost: 5+4*k
     47: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ 2<=x0^0 && k>=1 && 2<=1+x0^0-2*k ], cost: 5+4*k
     48: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -1+x0^0>=1 ], cost: -2+4*x0^0
     49: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -1+x0^0>=1 ], cost: -1+4*x0^0
     50: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -3+x0^0>=1 ], cost: -8+4*x0^0
     51: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -2+x0^0>=1 ], cost: -4+4*x0^0
     52: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -3+x0^0>=1 ], cost: -7+4*x0^0
     53: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -2+x0^0>=1 ], cost: -3+4*x0^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     42: l7 -> l5 : oldX0^0'=x0^0-2*k, x0^0'=x0^0-2*k, [ k>=1 && 2<=2+x0^0-2*k ], cost: 2+4*k
     43: l7 -> l5 : oldX0^0'=x0^0-2*k, x0^0'=x0^0-2*k, [ k>=1 && 2<=2+x0^0-2*k ], cost: 3+4*k
     44: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ k>=1 && 2<=x0^0-2*k ], cost: 4+4*k
     45: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ k>=1 && 2<=1+x0^0-2*k ], cost: 4+4*k
     46: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ 2<=x0^0 && k>=1 && 2<=x0^0-2*k ], cost: 5+4*k
     47: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ 2<=x0^0 && k>=1 && 2<=1+x0^0-2*k ], cost: 5+4*k
     48: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -1+x0^0>=1 ], cost: -2+4*x0^0
     49: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -1+x0^0>=1 ], cost: -1+4*x0^0
     50: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -3+x0^0>=1 ], cost: -8+4*x0^0
     51: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -2+x0^0>=1 ], cost: -4+4*x0^0
     52: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -3+x0^0>=1 ], cost: -7+4*x0^0
     53: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -2+x0^0>=1 ], cost: -3+4*x0^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     43: l7 -> l5 : oldX0^0'=x0^0-2*k, x0^0'=x0^0-2*k, [ k>=1 && 2<=2+x0^0-2*k ], cost: 3+4*k
     44: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ k>=1 && 2<=x0^0-2*k ], cost: 4+4*k
     45: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ k>=1 && 2<=1+x0^0-2*k ], cost: 4+4*k
     46: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ 2<=x0^0 && k>=1 && 2<=x0^0-2*k ], cost: 5+4*k
     47: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ 2<=x0^0 && k>=1 && 2<=1+x0^0-2*k ], cost: 5+4*k
     49: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -1+x0^0>=1 ], cost: -1+4*x0^0
     52: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -3+x0^0>=1 ], cost: -7+4*x0^0
     53: l7 -> l5 : oldX0^0'=1, x0^0'=1, [ -2+x0^0>=1 ], cost: -3+4*x0^0

Computing asymptotic complexity for rule 43
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 44
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 45
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 46
   Simplified the guard:
     46: l7 -> l5 : oldX0^0'=-2+x0^0-2*k, x0^0'=-2+x0^0-2*k, [ k>=1 && 2<=x0^0-2*k ], cost: 5+4*k
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 47
   Simplified the guard:
     47: l7 -> l5 : oldX0^0'=-1+x0^0-2*k, x0^0'=-1+x0^0-2*k, [ k>=1 && 2<=1+x0^0-2*k ], cost: 5+4*k
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 49
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 52
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 53
   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:  [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && x0^0==x0^post_17 ]

WORST_CASE(Omega(1),?)