WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l8
      0: l0 -> l1 : i2^0'=i2^post_1, size1010^0'=size1010^post_1, size1^0'=size1^post_1, size77^0'=size77^post_1, tmp1111^0'=tmp1111^post_1, tmp88^0'=tmp88^post_1, [ i2^0==i2^post_1 && size1^0==size1^post_1 && size1010^0==size1010^post_1 && size77^0==size77^post_1 && tmp1111^0==tmp1111^post_1 && tmp88^0==tmp88^post_1 ], cost: 1
      7: l1 -> l5 : i2^0'=i2^post_8, size1010^0'=size1010^post_8, size1^0'=size1^post_8, size77^0'=size77^post_8, tmp1111^0'=tmp1111^post_8, tmp88^0'=tmp88^post_8, [ size1^0<=i2^0 && i2^post_8==0 && size1^0==size1^post_8 && size1010^0==size1010^post_8 && size77^0==size77^post_8 && tmp1111^0==tmp1111^post_8 && tmp88^0==tmp88^post_8 ], cost: 1
      8: l1 -> l0 : i2^0'=i2^post_9, size1010^0'=size1010^post_9, size1^0'=size1^post_9, size77^0'=size77^post_9, tmp1111^0'=tmp1111^post_9, tmp88^0'=tmp88^post_9, [ 1+i2^0<=size1^0 && i2^post_9==1+i2^0 && size1^0==size1^post_9 && size1010^0==size1010^post_9 && size77^0==size77^post_9 && tmp1111^0==tmp1111^post_9 && tmp88^0==tmp88^post_9 ], cost: 1
      1: l2 -> l3 : i2^0'=i2^post_2, size1010^0'=size1010^post_2, size1^0'=size1^post_2, size77^0'=size77^post_2, tmp1111^0'=tmp1111^post_2, tmp88^0'=tmp88^post_2, [ size1^0<=i2^0 && i2^0==i2^post_2 && size1^0==size1^post_2 && size1010^0==size1010^post_2 && size77^0==size77^post_2 && tmp1111^0==tmp1111^post_2 && tmp88^0==tmp88^post_2 ], cost: 1
      2: l2 -> l4 : i2^0'=i2^post_3, size1010^0'=size1010^post_3, size1^0'=size1^post_3, size77^0'=size77^post_3, tmp1111^0'=tmp1111^post_3, tmp88^0'=tmp88^post_3, [ 1+i2^0<=size1^0 && i2^post_3==1+i2^0 && size1^0==size1^post_3 && size1010^0==size1010^post_3 && size77^0==size77^post_3 && tmp1111^0==tmp1111^post_3 && tmp88^0==tmp88^post_3 ], cost: 1
      6: l4 -> l2 : i2^0'=i2^post_7, size1010^0'=size1010^post_7, size1^0'=size1^post_7, size77^0'=size77^post_7, tmp1111^0'=tmp1111^post_7, tmp88^0'=tmp88^post_7, [ i2^0==i2^post_7 && size1^0==size1^post_7 && size1010^0==size1010^post_7 && size77^0==size77^post_7 && tmp1111^0==tmp1111^post_7 && tmp88^0==tmp88^post_7 ], cost: 1
      3: l5 -> l6 : i2^0'=i2^post_4, size1010^0'=size1010^post_4, size1^0'=size1^post_4, size77^0'=size77^post_4, tmp1111^0'=tmp1111^post_4, tmp88^0'=tmp88^post_4, [ i2^0==i2^post_4 && size1^0==size1^post_4 && size1010^0==size1010^post_4 && size77^0==size77^post_4 && tmp1111^0==tmp1111^post_4 && tmp88^0==tmp88^post_4 ], cost: 1
      4: l6 -> l4 : i2^0'=i2^post_5, size1010^0'=size1010^post_5, size1^0'=size1^post_5, size77^0'=size77^post_5, tmp1111^0'=tmp1111^post_5, tmp88^0'=tmp88^post_5, [ size1^0<=i2^0 && i2^post_5==0 && size1^0==size1^post_5 && size1010^0==size1010^post_5 && size77^0==size77^post_5 && tmp1111^0==tmp1111^post_5 && tmp88^0==tmp88^post_5 ], cost: 1
      5: l6 -> l5 : i2^0'=i2^post_6, size1010^0'=size1010^post_6, size1^0'=size1^post_6, size77^0'=size77^post_6, tmp1111^0'=tmp1111^post_6, tmp88^0'=tmp88^post_6, [ 1+i2^0<=size1^0 && i2^post_6==1+i2^0 && size1^0==size1^post_6 && size1010^0==size1010^post_6 && size77^0==size77^post_6 && tmp1111^0==tmp1111^post_6 && tmp88^0==tmp88^post_6 ], cost: 1
      9: l7 -> l0 : i2^0'=i2^post_10, size1010^0'=size1010^post_10, size1^0'=size1^post_10, size77^0'=size77^post_10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [ size1^post_10==10 && size77^post_10==size1^post_10 && tmp88^post_10==tmp88^post_10 && size1010^post_10==size1^post_10 && tmp1111^post_10==tmp1111^post_10 && i2^post_10==0 ], cost: 1
     10: l8 -> l7 : i2^0'=i2^post_11, size1010^0'=size1010^post_11, size1^0'=size1^post_11, size77^0'=size77^post_11, tmp1111^0'=tmp1111^post_11, tmp88^0'=tmp88^post_11, [ i2^0==i2^post_11 && size1^0==size1^post_11 && size1010^0==size1010^post_11 && size77^0==size77^post_11 && tmp1111^0==tmp1111^post_11 && tmp88^0==tmp88^post_11 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: l8 -> l7 : i2^0'=i2^post_11, size1010^0'=size1010^post_11, size1^0'=size1^post_11, size77^0'=size77^post_11, tmp1111^0'=tmp1111^post_11, tmp88^0'=tmp88^post_11, [ i2^0==i2^post_11 && size1^0==size1^post_11 && size1010^0==size1010^post_11 && size77^0==size77^post_11 && tmp1111^0==tmp1111^post_11 && tmp88^0==tmp88^post_11 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l8
      0: l0 -> l1 : i2^0'=i2^post_1, size1010^0'=size1010^post_1, size1^0'=size1^post_1, size77^0'=size77^post_1, tmp1111^0'=tmp1111^post_1, tmp88^0'=tmp88^post_1, [ i2^0==i2^post_1 && size1^0==size1^post_1 && size1010^0==size1010^post_1 && size77^0==size77^post_1 && tmp1111^0==tmp1111^post_1 && tmp88^0==tmp88^post_1 ], cost: 1
      7: l1 -> l5 : i2^0'=i2^post_8, size1010^0'=size1010^post_8, size1^0'=size1^post_8, size77^0'=size77^post_8, tmp1111^0'=tmp1111^post_8, tmp88^0'=tmp88^post_8, [ size1^0<=i2^0 && i2^post_8==0 && size1^0==size1^post_8 && size1010^0==size1010^post_8 && size77^0==size77^post_8 && tmp1111^0==tmp1111^post_8 && tmp88^0==tmp88^post_8 ], cost: 1
      8: l1 -> l0 : i2^0'=i2^post_9, size1010^0'=size1010^post_9, size1^0'=size1^post_9, size77^0'=size77^post_9, tmp1111^0'=tmp1111^post_9, tmp88^0'=tmp88^post_9, [ 1+i2^0<=size1^0 && i2^post_9==1+i2^0 && size1^0==size1^post_9 && size1010^0==size1010^post_9 && size77^0==size77^post_9 && tmp1111^0==tmp1111^post_9 && tmp88^0==tmp88^post_9 ], cost: 1
      2: l2 -> l4 : i2^0'=i2^post_3, size1010^0'=size1010^post_3, size1^0'=size1^post_3, size77^0'=size77^post_3, tmp1111^0'=tmp1111^post_3, tmp88^0'=tmp88^post_3, [ 1+i2^0<=size1^0 && i2^post_3==1+i2^0 && size1^0==size1^post_3 && size1010^0==size1010^post_3 && size77^0==size77^post_3 && tmp1111^0==tmp1111^post_3 && tmp88^0==tmp88^post_3 ], cost: 1
      6: l4 -> l2 : i2^0'=i2^post_7, size1010^0'=size1010^post_7, size1^0'=size1^post_7, size77^0'=size77^post_7, tmp1111^0'=tmp1111^post_7, tmp88^0'=tmp88^post_7, [ i2^0==i2^post_7 && size1^0==size1^post_7 && size1010^0==size1010^post_7 && size77^0==size77^post_7 && tmp1111^0==tmp1111^post_7 && tmp88^0==tmp88^post_7 ], cost: 1
      3: l5 -> l6 : i2^0'=i2^post_4, size1010^0'=size1010^post_4, size1^0'=size1^post_4, size77^0'=size77^post_4, tmp1111^0'=tmp1111^post_4, tmp88^0'=tmp88^post_4, [ i2^0==i2^post_4 && size1^0==size1^post_4 && size1010^0==size1010^post_4 && size77^0==size77^post_4 && tmp1111^0==tmp1111^post_4 && tmp88^0==tmp88^post_4 ], cost: 1
      4: l6 -> l4 : i2^0'=i2^post_5, size1010^0'=size1010^post_5, size1^0'=size1^post_5, size77^0'=size77^post_5, tmp1111^0'=tmp1111^post_5, tmp88^0'=tmp88^post_5, [ size1^0<=i2^0 && i2^post_5==0 && size1^0==size1^post_5 && size1010^0==size1010^post_5 && size77^0==size77^post_5 && tmp1111^0==tmp1111^post_5 && tmp88^0==tmp88^post_5 ], cost: 1
      5: l6 -> l5 : i2^0'=i2^post_6, size1010^0'=size1010^post_6, size1^0'=size1^post_6, size77^0'=size77^post_6, tmp1111^0'=tmp1111^post_6, tmp88^0'=tmp88^post_6, [ 1+i2^0<=size1^0 && i2^post_6==1+i2^0 && size1^0==size1^post_6 && size1010^0==size1010^post_6 && size77^0==size77^post_6 && tmp1111^0==tmp1111^post_6 && tmp88^0==tmp88^post_6 ], cost: 1
      9: l7 -> l0 : i2^0'=i2^post_10, size1010^0'=size1010^post_10, size1^0'=size1^post_10, size77^0'=size77^post_10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [ size1^post_10==10 && size77^post_10==size1^post_10 && tmp88^post_10==tmp88^post_10 && size1010^post_10==size1^post_10 && tmp1111^post_10==tmp1111^post_10 && i2^post_10==0 ], cost: 1
     10: l8 -> l7 : i2^0'=i2^post_11, size1010^0'=size1010^post_11, size1^0'=size1^post_11, size77^0'=size77^post_11, tmp1111^0'=tmp1111^post_11, tmp88^0'=tmp88^post_11, [ i2^0==i2^post_11 && size1^0==size1^post_11 && size1010^0==size1010^post_11 && size77^0==size77^post_11 && tmp1111^0==tmp1111^post_11 && tmp88^0==tmp88^post_11 ], cost: 1

Simplified all rules, resulting in:
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      8: l1 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
      2: l2 -> l4 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
      6: l4 -> l2 : [], cost: 1
      3: l5 -> l6 : [], cost: 1
      4: l6 -> l4 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      5: l6 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
      9: l7 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 1
     10: l8 -> l7 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      8: l1 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
     12: l4 -> l4 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 2
      3: l5 -> l6 : [], cost: 1
      4: l6 -> l4 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      5: l6 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2

Accelerating simple loops of location 4.
   Accelerating the following rules:
     12: l4 -> l4 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 2

   Accelerated rule 12 with metering function size1^0-i2^0, yielding the new rule 13.
   Removing the simple loops: 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      8: l1 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
     13: l4 -> l4 : i2^0'=size1^0, [ 1+i2^0<=size1^0 ], cost: 2*size1^0-2*i2^0
      3: l5 -> l6 : [], cost: 1
      4: l6 -> l4 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      5: l6 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      8: l1 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
      3: l5 -> l6 : [], cost: 1
      4: l6 -> l4 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      5: l6 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
     14: l6 -> l4 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 1+2*size1^0
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l8
      0: l0 -> l1 : [], cost: 1
      7: l1 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 1
      8: l1 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
      3: l5 -> l6 : [], cost: 1
      5: l6 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 1
     14: l6 -> l4 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 1+2*size1^0
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l8
     15: l0 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 2
     16: l0 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 2
     17: l5 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 2
     18: l5 -> l4 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 2+2*size1^0
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     16: l0 -> l0 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 2

   Accelerated rule 16 with metering function size1^0-i2^0, yielding the new rule 19.
   Removing the simple loops: 16.

Accelerating simple loops of location 5.
   Accelerating the following rules:
     17: l5 -> l5 : i2^0'=1+i2^0, [ 1+i2^0<=size1^0 ], cost: 2

   Accelerated rule 17 with metering function size1^0-i2^0, yielding the new rule 20.
   Removing the simple loops: 17.

Accelerated all simple loops using metering functions (where possible):
   Start location: l8
     15: l0 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 2
     19: l0 -> l0 : i2^0'=size1^0, [ 1+i2^0<=size1^0 ], cost: 2*size1^0-2*i2^0
     18: l5 -> l4 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 2+2*size1^0
     20: l5 -> l5 : i2^0'=size1^0, [ 1+i2^0<=size1^0 ], cost: 2*size1^0-2*i2^0
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l8
     15: l0 -> l5 : i2^0'=0, [ size1^0<=i2^0 ], cost: 2
     22: l0 -> l5 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 2+2*size1^0
     18: l5 -> l4 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 2+2*size1^0
     11: l8 -> l0 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 2
     21: l8 -> l0 : i2^0'=10, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 22

Eliminated locations (on tree-shaped paths):
   Start location: l8
     18: l5 -> l4 : i2^0'=size1^0, [ size1^0<=i2^0 && 1<=size1^0 ], cost: 2+2*size1^0
     23: l8 -> l5 : i2^0'=0, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 24
     24: l8 -> l5 : i2^0'=10, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 44

Eliminated locations (on tree-shaped paths):
   Start location: l8
     25: l8 -> l4 : i2^0'=10, size1010^0'=10, size1^0'=10, size77^0'=10, tmp1111^0'=tmp1111^post_10, tmp88^0'=tmp88^post_10, [], cost: 66

Applied pruning (of leafs and parallel rules):
   Start location: l8
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l8
     <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:  [ i2^0==i2^post_11 && size1^0==size1^post_11 && size1010^0==size1010^post_11 && size77^0==size77^post_11 && tmp1111^0==tmp1111^post_11 && tmp88^0==tmp88^post_11 ]

WORST_CASE(Omega(1),?)