WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      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: l0 -> l2 : 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==-1+oldX0^post_2 && x1^post_2==-1+oldX1^post_2 && oldX2^0==oldX2^post_2 && oldX3^0==oldX3^post_2 ], cost: 1
     10: l2 -> l4 : 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^post_11==x0^0 && oldX1^post_11==x1^0 && x0^post_11==oldX0^post_11 && x1^post_11==oldX1^post_11 && oldX2^0==oldX2^post_11 && oldX3^0==oldX3^post_11 ], cost: 1
      2: l3 -> l1 : 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 && oldX3^post_3==oldX3^post_3 && oldX0^post_3<=0 && 0<=oldX0^post_3 && oldX1^post_3<=0 && 0<=oldX1^post_3 && x0^post_3==oldX2^post_3 && x1^post_3==oldX3^post_3 ], cost: 1
      3: l3 -> l1 : 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 && oldX2^post_4==oldX2^post_4 && oldX3^post_4==oldX3^post_4 && 1<=oldX1^post_4 && x0^post_4==oldX2^post_4 && x1^post_4==oldX3^post_4 ], cost: 1
      4: l3 -> l1 : 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 && oldX2^post_5==oldX2^post_5 && oldX3^post_5==oldX3^post_5 && 1+oldX1^post_5<=0 && x0^post_5==oldX2^post_5 && x1^post_5==oldX3^post_5 ], cost: 1
      5: l3 -> l1 : 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 && oldX2^post_6==oldX2^post_6 && oldX3^post_6==oldX3^post_6 && 1<=oldX0^post_6 && x0^post_6==oldX2^post_6 && x1^post_6==oldX3^post_6 ], cost: 1
      6: l3 -> l1 : 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 && oldX3^post_7==oldX3^post_7 && 1+oldX0^post_7<=0 && x0^post_7==oldX2^post_7 && x1^post_7==oldX3^post_7 ], cost: 1
      7: l4 -> l0 : 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 && 1<=oldX0^post_8 && 1<=oldX1^post_8 && x0^post_8==oldX0^post_8 && x1^post_8==oldX1^post_8 && oldX2^0==oldX2^post_8 && oldX3^0==oldX3^post_8 ], cost: 1
      8: l4 -> l3 : 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^post_9==x0^0 && oldX1^post_9==x1^0 && oldX1^post_9<=0 && x0^post_9==oldX0^post_9 && x1^post_9==oldX1^post_9 && oldX2^0==oldX2^post_9 && oldX3^0==oldX3^post_9 ], cost: 1
      9: l4 -> l3 : 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^post_10==x0^0 && oldX1^post_10==x1^0 && oldX0^post_10<=0 && x0^post_10==oldX0^post_10 && x1^post_10==oldX1^post_10 && oldX2^0==oldX2^post_10 && oldX3^0==oldX3^post_10 ], cost: 1
     11: l5 -> l1 : 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: l5 -> l0 : 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: l5 -> l3 : 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: l5 -> 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: l5 -> l2 : 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
     16: l6 -> l5 : oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, oldX2^0'=oldX2^post_17, oldX3^0'=oldX3^post_17, x0^0'=x0^post_17, x1^0'=x1^post_17, [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     16: l6 -> l5 : oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, oldX2^0'=oldX2^post_17, oldX3^0'=oldX3^post_17, x0^0'=x0^post_17, x1^0'=x1^post_17, [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      1: l0 -> l2 : 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==-1+oldX0^post_2 && x1^post_2==-1+oldX1^post_2 && oldX2^0==oldX2^post_2 && oldX3^0==oldX3^post_2 ], cost: 1
     10: l2 -> l4 : 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^post_11==x0^0 && oldX1^post_11==x1^0 && x0^post_11==oldX0^post_11 && x1^post_11==oldX1^post_11 && oldX2^0==oldX2^post_11 && oldX3^0==oldX3^post_11 ], cost: 1
      7: l4 -> l0 : 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 && 1<=oldX0^post_8 && 1<=oldX1^post_8 && x0^post_8==oldX0^post_8 && x1^post_8==oldX1^post_8 && oldX2^0==oldX2^post_8 && oldX3^0==oldX3^post_8 ], cost: 1
     12: l5 -> l0 : 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
     14: l5 -> 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: l5 -> l2 : 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
     16: l6 -> l5 : oldX0^0'=oldX0^post_17, oldX1^0'=oldX1^post_17, oldX2^0'=oldX2^post_17, oldX3^0'=oldX3^post_17, x0^0'=x0^post_17, x1^0'=x1^post_17, [ oldX0^0==oldX0^post_17 && oldX1^0==oldX1^post_17 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      1: l0 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [], cost: 1
     10: l2 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, [], cost: 1
      7: l4 -> l0 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ 1<=x0^0 && 1<=x1^0 ], cost: 1
     12: l5 -> l0 : [], cost: 1
     14: l5 -> l4 : [], cost: 1
     15: l5 -> l2 : [], cost: 1
     16: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on tree-shaped paths):
   Start location: l6
      1: l0 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [], cost: 1
     10: l2 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, [], cost: 1
      7: l4 -> l0 : oldX0^0'=x0^0, oldX1^0'=x1^0, [ 1<=x0^0 && 1<=x1^0 ], cost: 1
     17: l6 -> l0 : [], cost: 2
     18: l6 -> l4 : [], cost: 2
     19: l6 -> l2 : [], cost: 2

Eliminated location l0 (as a last resort):
   Start location: l6
     10: l2 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, [], cost: 1
     20: l4 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [ 1<=x0^0 && 1<=x1^0 ], cost: 2
     18: l6 -> l4 : [], cost: 2
     19: l6 -> l2 : [], cost: 2
     21: l6 -> l2 : oldX0^0'=x0^0, oldX1^0'=x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [], cost: 3

Eliminated location l2 (as a last resort):
   Start location: l6
     23: l4 -> l4 : oldX0^0'=-1+x0^0, oldX1^0'=-1+x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [ 1<=x0^0 && 1<=x1^0 ], cost: 3
     18: l6 -> l4 : [], cost: 2
     22: l6 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, [], cost: 3
     24: l6 -> l4 : oldX0^0'=-1+x0^0, oldX1^0'=-1+x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [], cost: 4

Accelerating simple loops of location 4.
   Accelerating the following rules:
     23: l4 -> l4 : oldX0^0'=-1+x0^0, oldX1^0'=-1+x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [ 1<=x0^0 && 1<=x1^0 ], cost: 3

   Accelerated rule 23 with backward acceleration, yielding the new rule 25.
   Accelerated rule 23 with backward acceleration, yielding the new rule 26.
[accelerate] Nesting with 2 inner and 1 outer candidates
   Removing the simple loops: 23.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     25: l4 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 3*x0^0
     26: l4 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 3*x1^0
     18: l6 -> l4 : [], cost: 2
     22: l6 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, [], cost: 3
     24: l6 -> l4 : oldX0^0'=-1+x0^0, oldX1^0'=-1+x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: l6
     18: l6 -> l4 : [], cost: 2
     22: l6 -> l4 : oldX0^0'=x0^0, oldX1^0'=x1^0, [], cost: 3
     24: l6 -> l4 : oldX0^0'=-1+x0^0, oldX1^0'=-1+x1^0, x0^0'=-1+x0^0, x1^0'=-1+x1^0, [], cost: 4
     27: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 2+3*x0^0
     28: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 3+3*x0^0
     29: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ -1+x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 1+3*x0^0
     30: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 2+3*x1^0
     31: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 3+3*x1^0
     32: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ -1+x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 1+3*x1^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     27: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 2+3*x0^0
     28: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 3+3*x0^0
     29: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ -1+x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 1+3*x0^0
     30: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 2+3*x1^0
     31: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 3+3*x1^0
     32: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ -1+x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 1+3*x1^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     28: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 3+3*x0^0
     29: l6 -> l4 : oldX0^0'=0, oldX1^0'=-x0^0+x1^0, x0^0'=0, x1^0'=-x0^0+x1^0, [ -1+x0^0>=1 && 1<=1-x0^0+x1^0 ], cost: 1+3*x0^0
     31: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 3+3*x1^0
     32: l6 -> l4 : oldX0^0'=x0^0-x1^0, oldX1^0'=0, x0^0'=x0^0-x1^0, x1^0'=0, [ -1+x1^0>=1 && 1<=1+x0^0-x1^0 ], cost: 1+3*x1^0

Computing asymptotic complexity for rule 28
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 29
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 31
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 32
   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 && oldX2^0==oldX2^post_17 && oldX3^0==oldX3^post_17 && x0^0==x0^post_17 && x1^0==x1^post_17 ]

WORST_CASE(Omega(1),?)