WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l13
      0: l0 -> l1 : __const_400^0'=__const_400^post_1, __const_5^0'=__const_5^post_1, i2^0'=i2^post_1, j3^0'=j3^post_1, k4^0'=k4^post_1, l5^0'=l5^post_1, x1^0'=x1^post_1, [ __const_5^0<=i2^0 && __const_400^0==__const_400^post_1 && __const_5^0==__const_5^post_1 && i2^0==i2^post_1 && j3^0==j3^post_1 && k4^0==k4^post_1 && l5^0==l5^post_1 && x1^0==x1^post_1 ], cost: 1
      1: l0 -> l2 : __const_400^0'=__const_400^post_2, __const_5^0'=__const_5^post_2, i2^0'=i2^post_2, j3^0'=j3^post_2, k4^0'=k4^post_2, l5^0'=l5^post_2, x1^0'=x1^post_2, [ 1+i2^0<=__const_5^0 && j3^post_2==0 && __const_400^0==__const_400^post_2 && __const_5^0==__const_5^post_2 && i2^0==i2^post_2 && k4^0==k4^post_2 && l5^0==l5^post_2 && x1^0==x1^post_2 ], cost: 1
      4: l1 -> l5 : __const_400^0'=__const_400^post_5, __const_5^0'=__const_5^post_5, i2^0'=i2^post_5, j3^0'=j3^post_5, k4^0'=k4^post_5, l5^0'=l5^post_5, x1^0'=x1^post_5, [ __const_400^0==__const_400^post_5 && __const_5^0==__const_5^post_5 && i2^0==i2^post_5 && j3^0==j3^post_5 && k4^0==k4^post_5 && l5^0==l5^post_5 && x1^0==x1^post_5 ], cost: 1
      3: l2 -> l4 : __const_400^0'=__const_400^post_4, __const_5^0'=__const_5^post_4, i2^0'=i2^post_4, j3^0'=j3^post_4, k4^0'=k4^post_4, l5^0'=l5^post_4, x1^0'=x1^post_4, [ __const_400^0==__const_400^post_4 && __const_5^0==__const_5^post_4 && i2^0==i2^post_4 && j3^0==j3^post_4 && k4^0==k4^post_4 && l5^0==l5^post_4 && x1^0==x1^post_4 ], cost: 1
      2: l3 -> l0 : __const_400^0'=__const_400^post_3, __const_5^0'=__const_5^post_3, i2^0'=i2^post_3, j3^0'=j3^post_3, k4^0'=k4^post_3, l5^0'=l5^post_3, x1^0'=x1^post_3, [ __const_400^0==__const_400^post_3 && __const_5^0==__const_5^post_3 && i2^0==i2^post_3 && j3^0==j3^post_3 && k4^0==k4^post_3 && l5^0==l5^post_3 && x1^0==x1^post_3 ], cost: 1
     15: l4 -> l3 : __const_400^0'=__const_400^post_16, __const_5^0'=__const_5^post_16, i2^0'=i2^post_16, j3^0'=j3^post_16, k4^0'=k4^post_16, l5^0'=l5^post_16, x1^0'=x1^post_16, [ __const_5^0<=j3^0 && i2^post_16==1+i2^0 && __const_400^0==__const_400^post_16 && __const_5^0==__const_5^post_16 && j3^0==j3^post_16 && k4^0==k4^post_16 && l5^0==l5^post_16 && x1^0==x1^post_16 ], cost: 1
     16: l4 -> l6 : __const_400^0'=__const_400^post_17, __const_5^0'=__const_5^post_17, i2^0'=i2^post_17, j3^0'=j3^post_17, k4^0'=k4^post_17, l5^0'=l5^post_17, x1^0'=x1^post_17, [ 1+j3^0<=__const_5^0 && k4^post_17==0 && __const_400^0==__const_400^post_17 && __const_5^0==__const_5^post_17 && i2^0==i2^post_17 && j3^0==j3^post_17 && l5^0==l5^post_17 && x1^0==x1^post_17 ], cost: 1
      5: l6 -> l7 : __const_400^0'=__const_400^post_6, __const_5^0'=__const_5^post_6, i2^0'=i2^post_6, j3^0'=j3^post_6, k4^0'=k4^post_6, l5^0'=l5^post_6, x1^0'=x1^post_6, [ __const_400^0==__const_400^post_6 && __const_5^0==__const_5^post_6 && i2^0==i2^post_6 && j3^0==j3^post_6 && k4^0==k4^post_6 && l5^0==l5^post_6 && x1^0==x1^post_6 ], cost: 1
     13: l7 -> l2 : __const_400^0'=__const_400^post_14, __const_5^0'=__const_5^post_14, i2^0'=i2^post_14, j3^0'=j3^post_14, k4^0'=k4^post_14, l5^0'=l5^post_14, x1^0'=x1^post_14, [ __const_5^0<=k4^0 && j3^post_14==1+j3^0 && __const_400^0==__const_400^post_14 && __const_5^0==__const_5^post_14 && i2^0==i2^post_14 && k4^0==k4^post_14 && l5^0==l5^post_14 && x1^0==x1^post_14 ], cost: 1
     14: l7 -> l9 : __const_400^0'=__const_400^post_15, __const_5^0'=__const_5^post_15, i2^0'=i2^post_15, j3^0'=j3^post_15, k4^0'=k4^post_15, l5^0'=l5^post_15, x1^0'=x1^post_15, [ 1+k4^0<=__const_5^0 && l5^post_15==0 && __const_400^0==__const_400^post_15 && __const_5^0==__const_5^post_15 && i2^0==i2^post_15 && j3^0==j3^post_15 && k4^0==k4^post_15 && x1^0==x1^post_15 ], cost: 1
      6: l8 -> l9 : __const_400^0'=__const_400^post_7, __const_5^0'=__const_5^post_7, i2^0'=i2^post_7, j3^0'=j3^post_7, k4^0'=k4^post_7, l5^0'=l5^post_7, x1^0'=x1^post_7, [ l5^post_7==1+l5^0 && __const_400^0==__const_400^post_7 && __const_5^0==__const_5^post_7 && i2^0==i2^post_7 && j3^0==j3^post_7 && k4^0==k4^post_7 && x1^0==x1^post_7 ], cost: 1
      7: l9 -> l10 : __const_400^0'=__const_400^post_8, __const_5^0'=__const_5^post_8, i2^0'=i2^post_8, j3^0'=j3^post_8, k4^0'=k4^post_8, l5^0'=l5^post_8, x1^0'=x1^post_8, [ __const_400^0==__const_400^post_8 && __const_5^0==__const_5^post_8 && i2^0==i2^post_8 && j3^0==j3^post_8 && k4^0==k4^post_8 && l5^0==l5^post_8 && x1^0==x1^post_8 ], cost: 1
     11: l10 -> l6 : __const_400^0'=__const_400^post_12, __const_5^0'=__const_5^post_12, i2^0'=i2^post_12, j3^0'=j3^post_12, k4^0'=k4^post_12, l5^0'=l5^post_12, x1^0'=x1^post_12, [ __const_5^0<=l5^0 && k4^post_12==1+k4^0 && __const_400^0==__const_400^post_12 && __const_5^0==__const_5^post_12 && i2^0==i2^post_12 && j3^0==j3^post_12 && l5^0==l5^post_12 && x1^0==x1^post_12 ], cost: 1
     12: l10 -> l11 : __const_400^0'=__const_400^post_13, __const_5^0'=__const_5^post_13, i2^0'=i2^post_13, j3^0'=j3^post_13, k4^0'=k4^post_13, l5^0'=l5^post_13, x1^0'=x1^post_13, [ 1+l5^0<=__const_5^0 && __const_400^0==__const_400^post_13 && __const_5^0==__const_5^post_13 && i2^0==i2^post_13 && j3^0==j3^post_13 && k4^0==k4^post_13 && l5^0==l5^post_13 && x1^0==x1^post_13 ], cost: 1
      8: l11 -> l8 : __const_400^0'=__const_400^post_9, __const_5^0'=__const_5^post_9, i2^0'=i2^post_9, j3^0'=j3^post_9, k4^0'=k4^post_9, l5^0'=l5^post_9, x1^0'=x1^post_9, [ __const_400^0==__const_400^post_9 && __const_5^0==__const_5^post_9 && i2^0==i2^post_9 && j3^0==j3^post_9 && k4^0==k4^post_9 && l5^0==l5^post_9 && x1^0==x1^post_9 ], cost: 1
      9: l11 -> l1 : __const_400^0'=__const_400^post_10, __const_5^0'=__const_5^post_10, i2^0'=i2^post_10, j3^0'=j3^post_10, k4^0'=k4^post_10, l5^0'=l5^post_10, x1^0'=x1^post_10, [ __const_400^0==__const_400^post_10 && __const_5^0==__const_5^post_10 && i2^0==i2^post_10 && j3^0==j3^post_10 && k4^0==k4^post_10 && l5^0==l5^post_10 && x1^0==x1^post_10 ], cost: 1
     10: l11 -> l8 : __const_400^0'=__const_400^post_11, __const_5^0'=__const_5^post_11, i2^0'=i2^post_11, j3^0'=j3^post_11, k4^0'=k4^post_11, l5^0'=l5^post_11, x1^0'=x1^post_11, [ __const_400^0==__const_400^post_11 && __const_5^0==__const_5^post_11 && i2^0==i2^post_11 && j3^0==j3^post_11 && k4^0==k4^post_11 && l5^0==l5^post_11 && x1^0==x1^post_11 ], cost: 1
     17: l12 -> l3 : __const_400^0'=__const_400^post_18, __const_5^0'=__const_5^post_18, i2^0'=i2^post_18, j3^0'=j3^post_18, k4^0'=k4^post_18, l5^0'=l5^post_18, x1^0'=x1^post_18, [ x1^post_18==__const_400^0 && i2^post_18==0 && __const_400^0==__const_400^post_18 && __const_5^0==__const_5^post_18 && j3^0==j3^post_18 && k4^0==k4^post_18 && l5^0==l5^post_18 ], cost: 1
     18: l13 -> l12 : __const_400^0'=__const_400^post_19, __const_5^0'=__const_5^post_19, i2^0'=i2^post_19, j3^0'=j3^post_19, k4^0'=k4^post_19, l5^0'=l5^post_19, x1^0'=x1^post_19, [ __const_400^0==__const_400^post_19 && __const_5^0==__const_5^post_19 && i2^0==i2^post_19 && j3^0==j3^post_19 && k4^0==k4^post_19 && l5^0==l5^post_19 && x1^0==x1^post_19 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     18: l13 -> l12 : __const_400^0'=__const_400^post_19, __const_5^0'=__const_5^post_19, i2^0'=i2^post_19, j3^0'=j3^post_19, k4^0'=k4^post_19, l5^0'=l5^post_19, x1^0'=x1^post_19, [ __const_400^0==__const_400^post_19 && __const_5^0==__const_5^post_19 && i2^0==i2^post_19 && j3^0==j3^post_19 && k4^0==k4^post_19 && l5^0==l5^post_19 && x1^0==x1^post_19 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l13
      1: l0 -> l2 : __const_400^0'=__const_400^post_2, __const_5^0'=__const_5^post_2, i2^0'=i2^post_2, j3^0'=j3^post_2, k4^0'=k4^post_2, l5^0'=l5^post_2, x1^0'=x1^post_2, [ 1+i2^0<=__const_5^0 && j3^post_2==0 && __const_400^0==__const_400^post_2 && __const_5^0==__const_5^post_2 && i2^0==i2^post_2 && k4^0==k4^post_2 && l5^0==l5^post_2 && x1^0==x1^post_2 ], cost: 1
      3: l2 -> l4 : __const_400^0'=__const_400^post_4, __const_5^0'=__const_5^post_4, i2^0'=i2^post_4, j3^0'=j3^post_4, k4^0'=k4^post_4, l5^0'=l5^post_4, x1^0'=x1^post_4, [ __const_400^0==__const_400^post_4 && __const_5^0==__const_5^post_4 && i2^0==i2^post_4 && j3^0==j3^post_4 && k4^0==k4^post_4 && l5^0==l5^post_4 && x1^0==x1^post_4 ], cost: 1
      2: l3 -> l0 : __const_400^0'=__const_400^post_3, __const_5^0'=__const_5^post_3, i2^0'=i2^post_3, j3^0'=j3^post_3, k4^0'=k4^post_3, l5^0'=l5^post_3, x1^0'=x1^post_3, [ __const_400^0==__const_400^post_3 && __const_5^0==__const_5^post_3 && i2^0==i2^post_3 && j3^0==j3^post_3 && k4^0==k4^post_3 && l5^0==l5^post_3 && x1^0==x1^post_3 ], cost: 1
     15: l4 -> l3 : __const_400^0'=__const_400^post_16, __const_5^0'=__const_5^post_16, i2^0'=i2^post_16, j3^0'=j3^post_16, k4^0'=k4^post_16, l5^0'=l5^post_16, x1^0'=x1^post_16, [ __const_5^0<=j3^0 && i2^post_16==1+i2^0 && __const_400^0==__const_400^post_16 && __const_5^0==__const_5^post_16 && j3^0==j3^post_16 && k4^0==k4^post_16 && l5^0==l5^post_16 && x1^0==x1^post_16 ], cost: 1
     16: l4 -> l6 : __const_400^0'=__const_400^post_17, __const_5^0'=__const_5^post_17, i2^0'=i2^post_17, j3^0'=j3^post_17, k4^0'=k4^post_17, l5^0'=l5^post_17, x1^0'=x1^post_17, [ 1+j3^0<=__const_5^0 && k4^post_17==0 && __const_400^0==__const_400^post_17 && __const_5^0==__const_5^post_17 && i2^0==i2^post_17 && j3^0==j3^post_17 && l5^0==l5^post_17 && x1^0==x1^post_17 ], cost: 1
      5: l6 -> l7 : __const_400^0'=__const_400^post_6, __const_5^0'=__const_5^post_6, i2^0'=i2^post_6, j3^0'=j3^post_6, k4^0'=k4^post_6, l5^0'=l5^post_6, x1^0'=x1^post_6, [ __const_400^0==__const_400^post_6 && __const_5^0==__const_5^post_6 && i2^0==i2^post_6 && j3^0==j3^post_6 && k4^0==k4^post_6 && l5^0==l5^post_6 && x1^0==x1^post_6 ], cost: 1
     13: l7 -> l2 : __const_400^0'=__const_400^post_14, __const_5^0'=__const_5^post_14, i2^0'=i2^post_14, j3^0'=j3^post_14, k4^0'=k4^post_14, l5^0'=l5^post_14, x1^0'=x1^post_14, [ __const_5^0<=k4^0 && j3^post_14==1+j3^0 && __const_400^0==__const_400^post_14 && __const_5^0==__const_5^post_14 && i2^0==i2^post_14 && k4^0==k4^post_14 && l5^0==l5^post_14 && x1^0==x1^post_14 ], cost: 1
     14: l7 -> l9 : __const_400^0'=__const_400^post_15, __const_5^0'=__const_5^post_15, i2^0'=i2^post_15, j3^0'=j3^post_15, k4^0'=k4^post_15, l5^0'=l5^post_15, x1^0'=x1^post_15, [ 1+k4^0<=__const_5^0 && l5^post_15==0 && __const_400^0==__const_400^post_15 && __const_5^0==__const_5^post_15 && i2^0==i2^post_15 && j3^0==j3^post_15 && k4^0==k4^post_15 && x1^0==x1^post_15 ], cost: 1
      6: l8 -> l9 : __const_400^0'=__const_400^post_7, __const_5^0'=__const_5^post_7, i2^0'=i2^post_7, j3^0'=j3^post_7, k4^0'=k4^post_7, l5^0'=l5^post_7, x1^0'=x1^post_7, [ l5^post_7==1+l5^0 && __const_400^0==__const_400^post_7 && __const_5^0==__const_5^post_7 && i2^0==i2^post_7 && j3^0==j3^post_7 && k4^0==k4^post_7 && x1^0==x1^post_7 ], cost: 1
      7: l9 -> l10 : __const_400^0'=__const_400^post_8, __const_5^0'=__const_5^post_8, i2^0'=i2^post_8, j3^0'=j3^post_8, k4^0'=k4^post_8, l5^0'=l5^post_8, x1^0'=x1^post_8, [ __const_400^0==__const_400^post_8 && __const_5^0==__const_5^post_8 && i2^0==i2^post_8 && j3^0==j3^post_8 && k4^0==k4^post_8 && l5^0==l5^post_8 && x1^0==x1^post_8 ], cost: 1
     11: l10 -> l6 : __const_400^0'=__const_400^post_12, __const_5^0'=__const_5^post_12, i2^0'=i2^post_12, j3^0'=j3^post_12, k4^0'=k4^post_12, l5^0'=l5^post_12, x1^0'=x1^post_12, [ __const_5^0<=l5^0 && k4^post_12==1+k4^0 && __const_400^0==__const_400^post_12 && __const_5^0==__const_5^post_12 && i2^0==i2^post_12 && j3^0==j3^post_12 && l5^0==l5^post_12 && x1^0==x1^post_12 ], cost: 1
     12: l10 -> l11 : __const_400^0'=__const_400^post_13, __const_5^0'=__const_5^post_13, i2^0'=i2^post_13, j3^0'=j3^post_13, k4^0'=k4^post_13, l5^0'=l5^post_13, x1^0'=x1^post_13, [ 1+l5^0<=__const_5^0 && __const_400^0==__const_400^post_13 && __const_5^0==__const_5^post_13 && i2^0==i2^post_13 && j3^0==j3^post_13 && k4^0==k4^post_13 && l5^0==l5^post_13 && x1^0==x1^post_13 ], cost: 1
      8: l11 -> l8 : __const_400^0'=__const_400^post_9, __const_5^0'=__const_5^post_9, i2^0'=i2^post_9, j3^0'=j3^post_9, k4^0'=k4^post_9, l5^0'=l5^post_9, x1^0'=x1^post_9, [ __const_400^0==__const_400^post_9 && __const_5^0==__const_5^post_9 && i2^0==i2^post_9 && j3^0==j3^post_9 && k4^0==k4^post_9 && l5^0==l5^post_9 && x1^0==x1^post_9 ], cost: 1
     10: l11 -> l8 : __const_400^0'=__const_400^post_11, __const_5^0'=__const_5^post_11, i2^0'=i2^post_11, j3^0'=j3^post_11, k4^0'=k4^post_11, l5^0'=l5^post_11, x1^0'=x1^post_11, [ __const_400^0==__const_400^post_11 && __const_5^0==__const_5^post_11 && i2^0==i2^post_11 && j3^0==j3^post_11 && k4^0==k4^post_11 && l5^0==l5^post_11 && x1^0==x1^post_11 ], cost: 1
     17: l12 -> l3 : __const_400^0'=__const_400^post_18, __const_5^0'=__const_5^post_18, i2^0'=i2^post_18, j3^0'=j3^post_18, k4^0'=k4^post_18, l5^0'=l5^post_18, x1^0'=x1^post_18, [ x1^post_18==__const_400^0 && i2^post_18==0 && __const_400^0==__const_400^post_18 && __const_5^0==__const_5^post_18 && j3^0==j3^post_18 && k4^0==k4^post_18 && l5^0==l5^post_18 ], cost: 1
     18: l13 -> l12 : __const_400^0'=__const_400^post_19, __const_5^0'=__const_5^post_19, i2^0'=i2^post_19, j3^0'=j3^post_19, k4^0'=k4^post_19, l5^0'=l5^post_19, x1^0'=x1^post_19, [ __const_400^0==__const_400^post_19 && __const_5^0==__const_5^post_19 && i2^0==i2^post_19 && j3^0==j3^post_19 && k4^0==k4^post_19 && l5^0==l5^post_19 && x1^0==x1^post_19 ], cost: 1

Simplified all rules, resulting in:
   Start location: l13
      1: l0 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 1
      3: l2 -> l4 : [], cost: 1
      2: l3 -> l0 : [], cost: 1
     15: l4 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 1
     16: l4 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 1
      5: l6 -> l7 : [], cost: 1
     13: l7 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 1
     14: l7 -> l9 : l5^0'=0, [ 1+k4^0<=__const_5^0 ], cost: 1
      6: l8 -> l9 : l5^0'=1+l5^0, [], cost: 1
      7: l9 -> l10 : [], cost: 1
     11: l10 -> l6 : k4^0'=1+k4^0, [ __const_5^0<=l5^0 ], cost: 1
     12: l10 -> l11 : [ 1+l5^0<=__const_5^0 ], cost: 1
     10: l11 -> l8 : [], cost: 1
     17: l12 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 1
     18: l13 -> l12 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l13
      3: l2 -> l4 : [], cost: 1
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     15: l4 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 1
     16: l4 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 1
      5: l6 -> l7 : [], cost: 1
     13: l7 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 1
     14: l7 -> l9 : l5^0'=0, [ 1+k4^0<=__const_5^0 ], cost: 1
      7: l9 -> l10 : [], cost: 1
     11: l10 -> l6 : k4^0'=1+k4^0, [ __const_5^0<=l5^0 ], cost: 1
     22: l10 -> l9 : l5^0'=1+l5^0, [ 1+l5^0<=__const_5^0 ], cost: 3
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     24: l2 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     25: l6 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 2
     26: l6 -> l9 : l5^0'=0, [ 1+k4^0<=__const_5^0 ], cost: 2
     27: l9 -> l6 : k4^0'=1+k4^0, [ __const_5^0<=l5^0 ], cost: 2
     28: l9 -> l9 : l5^0'=1+l5^0, [ 1+l5^0<=__const_5^0 ], cost: 4
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Accelerating simple loops of location 9.
   Accelerating the following rules:
     28: l9 -> l9 : l5^0'=1+l5^0, [ 1+l5^0<=__const_5^0 ], cost: 4

   Accelerated rule 28 with backward acceleration, yielding the new rule 29.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 28.

Accelerated all simple loops using metering functions (where possible):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     24: l2 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     25: l6 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 2
     26: l6 -> l9 : l5^0'=0, [ 1+k4^0<=__const_5^0 ], cost: 2
     27: l9 -> l6 : k4^0'=1+k4^0, [ __const_5^0<=l5^0 ], cost: 2
     29: l9 -> l9 : l5^0'=__const_5^0, [ __const_5^0-l5^0>=0 ], cost: 4*__const_5^0-4*l5^0
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     24: l2 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     25: l6 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 2
     26: l6 -> l9 : l5^0'=0, [ 1+k4^0<=__const_5^0 ], cost: 2
     30: l6 -> l9 : l5^0'=__const_5^0, [ 1+k4^0<=__const_5^0 && __const_5^0>=0 ], cost: 2+4*__const_5^0
     27: l9 -> l6 : k4^0'=1+k4^0, [ __const_5^0<=l5^0 ], cost: 2
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     24: l2 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     25: l6 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 2
     31: l6 -> l6 : k4^0'=1+k4^0, l5^0'=0, [ 1+k4^0<=__const_5^0 && __const_5^0<=0 ], cost: 4
     32: l6 -> l6 : k4^0'=1+k4^0, l5^0'=__const_5^0, [ 1+k4^0<=__const_5^0 && __const_5^0>=0 ], cost: 4+4*__const_5^0
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Accelerating simple loops of location 6.
   Accelerating the following rules:
     31: l6 -> l6 : k4^0'=1+k4^0, l5^0'=0, [ 1+k4^0<=__const_5^0 && __const_5^0<=0 ], cost: 4
     32: l6 -> l6 : k4^0'=1+k4^0, l5^0'=__const_5^0, [ 1+k4^0<=__const_5^0 && __const_5^0>=0 ], cost: 4+4*__const_5^0

   Accelerated rule 31 with backward acceleration, yielding the new rule 33.
   Accelerated rule 32 with backward acceleration, yielding the new rule 34.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 31 32.

Accelerated all simple loops using metering functions (where possible):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     24: l2 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     25: l6 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 2
     33: l6 -> l6 : k4^0'=__const_5^0, l5^0'=0, [ __const_5^0<=0 && -k4^0+__const_5^0>=1 ], cost: -4*k4^0+4*__const_5^0
     34: l6 -> l6 : k4^0'=__const_5^0, l5^0'=__const_5^0, [ __const_5^0>=0 && -k4^0+__const_5^0>=1 ], cost: -4*k4^0+4*__const_5^0-4*__const_5^0*(k4^0-__const_5^0)
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     24: l2 -> l6 : k4^0'=0, [ 1+j3^0<=__const_5^0 ], cost: 2
     35: l2 -> l6 : k4^0'=__const_5^0, l5^0'=__const_5^0, [ 1+j3^0<=__const_5^0 && __const_5^0>=1 ], cost: 2+4*__const_5^0+4*__const_5^0^2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     25: l6 -> l2 : j3^0'=1+j3^0, [ __const_5^0<=k4^0 ], cost: 2
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     36: l2 -> l2 : j3^0'=1+j3^0, k4^0'=0, [ 1+j3^0<=__const_5^0 && __const_5^0<=0 ], cost: 4
     37: l2 -> l2 : j3^0'=1+j3^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ 1+j3^0<=__const_5^0 && __const_5^0>=1 ], cost: 4+4*__const_5^0+4*__const_5^0^2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     36: l2 -> l2 : j3^0'=1+j3^0, k4^0'=0, [ 1+j3^0<=__const_5^0 && __const_5^0<=0 ], cost: 4
     37: l2 -> l2 : j3^0'=1+j3^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ 1+j3^0<=__const_5^0 && __const_5^0>=1 ], cost: 4+4*__const_5^0+4*__const_5^0^2

   Accelerated rule 36 with backward acceleration, yielding the new rule 38.
   Accelerated rule 37 with backward acceleration, yielding the new rule 39.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 36 37.

Accelerated all simple loops using metering functions (where possible):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     38: l2 -> l2 : j3^0'=__const_5^0, k4^0'=0, [ __const_5^0<=0 && __const_5^0-j3^0>=1 ], cost: 4*__const_5^0-4*j3^0
     39: l2 -> l2 : j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ __const_5^0>=1 && __const_5^0-j3^0>=1 ], cost: 4*__const_5^0^2*(__const_5^0-j3^0)+4*__const_5^0+4*__const_5^0*(__const_5^0-j3^0)-4*j3^0
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l13
     23: l2 -> l3 : i2^0'=1+i2^0, [ __const_5^0<=j3^0 ], cost: 2
     20: l3 -> l2 : j3^0'=0, [ 1+i2^0<=__const_5^0 ], cost: 2
     40: l3 -> l2 : j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ 1+i2^0<=__const_5^0 && __const_5^0>=1 ], cost: 2+4*__const_5^0+4*__const_5^0^3+4*__const_5^0^2
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l13
     41: l3 -> l3 : i2^0'=1+i2^0, j3^0'=0, [ 1+i2^0<=__const_5^0 && __const_5^0<=0 ], cost: 4
     42: l3 -> l3 : i2^0'=1+i2^0, j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ 1+i2^0<=__const_5^0 && __const_5^0>=1 ], cost: 4+4*__const_5^0+4*__const_5^0^3+4*__const_5^0^2
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     41: l3 -> l3 : i2^0'=1+i2^0, j3^0'=0, [ 1+i2^0<=__const_5^0 && __const_5^0<=0 ], cost: 4
     42: l3 -> l3 : i2^0'=1+i2^0, j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ 1+i2^0<=__const_5^0 && __const_5^0>=1 ], cost: 4+4*__const_5^0+4*__const_5^0^3+4*__const_5^0^2

   Accelerated rule 41 with backward acceleration, yielding the new rule 43.
   Accelerated rule 42 with backward acceleration, yielding the new rule 44.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 41 42.

Accelerated all simple loops using metering functions (where possible):
   Start location: l13
     43: l3 -> l3 : i2^0'=__const_5^0, j3^0'=0, [ __const_5^0<=0 && __const_5^0-i2^0>=1 ], cost: 4*__const_5^0-4*i2^0
     44: l3 -> l3 : i2^0'=__const_5^0, j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, [ __const_5^0>=1 && __const_5^0-i2^0>=1 ], cost: 4*__const_5^0^3*(__const_5^0-i2^0)+4*__const_5^0+4*__const_5^0^2*(__const_5^0-i2^0)-4*i2^0+4*__const_5^0*(__const_5^0-i2^0)
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l13
     19: l13 -> l3 : i2^0'=0, x1^0'=__const_400^0, [], cost: 2
     45: l13 -> l3 : i2^0'=__const_5^0, j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, x1^0'=__const_400^0, [ __const_5^0>=1 ], cost: 2+4*__const_5^0+4*__const_5^0^3+4*__const_5^0^2+4*__const_5^0^4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l13
     45: l13 -> l3 : i2^0'=__const_5^0, j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, x1^0'=__const_400^0, [ __const_5^0>=1 ], cost: 2+4*__const_5^0+4*__const_5^0^3+4*__const_5^0^2+4*__const_5^0^4

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l13
     45: l13 -> l3 : i2^0'=__const_5^0, j3^0'=__const_5^0, k4^0'=__const_5^0, l5^0'=__const_5^0, x1^0'=__const_400^0, [ __const_5^0>=1 ], cost: 2+4*__const_5^0+4*__const_5^0^3+4*__const_5^0^2+4*__const_5^0^4

Computing asymptotic complexity for rule 45
   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:  [ __const_400^0==__const_400^post_19 && __const_5^0==__const_5^post_19 && i2^0==i2^post_19 && j3^0==j3^post_19 && k4^0==k4^post_19 && l5^0==l5^post_19 && x1^0==x1^post_19 ]

WORST_CASE(Omega(1),?)