WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : nI6^0'=nI6^post_1, nX4^0'=nX4^post_1, nX9^0'=nX9^post_1, nX^0'=nX^post_1, res10^0'=res10^post_1, res5^0'=res5^post_1, ret_nBC18^0'=ret_nBC18^post_1, ret_nBC211^0'=ret_nBC211^post_1, tmp7^0'=tmp7^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, [ res5^post_1==tmp7^0+res5^0 && nI6^post_1==1+nI6^0 && nX^0==nX^post_1 && nX4^0==nX4^post_1 && nX9^0==nX9^post_1 && res10^0==res10^post_1 && ret_nBC18^0==ret_nBC18^post_1 && ret_nBC211^0==ret_nBC211^post_1 && tmp^0==tmp^post_1 && tmp7^0==tmp7^post_1 && tmp___0^0==tmp___0^post_1 ], cost: 1
      5: l1 -> l3 : nI6^0'=nI6^post_6, nX4^0'=nX4^post_6, nX9^0'=nX9^post_6, nX^0'=nX^post_6, res10^0'=res10^post_6, res5^0'=res5^post_6, ret_nBC18^0'=ret_nBC18^post_6, ret_nBC211^0'=ret_nBC211^post_6, tmp7^0'=tmp7^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, [ nI6^0==nI6^post_6 && nX^0==nX^post_6 && nX4^0==nX4^post_6 && nX9^0==nX9^post_6 && res10^0==res10^post_6 && res5^0==res5^post_6 && ret_nBC18^0==ret_nBC18^post_6 && ret_nBC211^0==ret_nBC211^post_6 && tmp^0==tmp^post_6 && tmp7^0==tmp7^post_6 && tmp___0^0==tmp___0^post_6 ], cost: 1
      1: l2 -> l0 : nI6^0'=nI6^post_2, nX4^0'=nX4^post_2, nX9^0'=nX9^post_2, nX^0'=nX^post_2, res10^0'=res10^post_2, res5^0'=res5^post_2, ret_nBC18^0'=ret_nBC18^post_2, ret_nBC211^0'=ret_nBC211^post_2, tmp7^0'=tmp7^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ tmp7^post_2==0 && nI6^0==nI6^post_2 && nX^0==nX^post_2 && nX4^0==nX4^post_2 && nX9^0==nX9^post_2 && res10^0==res10^post_2 && res5^0==res5^post_2 && ret_nBC18^0==ret_nBC18^post_2 && ret_nBC211^0==ret_nBC211^post_2 && tmp^0==tmp^post_2 && tmp___0^0==tmp___0^post_2 ], cost: 1
      2: l2 -> l0 : nI6^0'=nI6^post_3, nX4^0'=nX4^post_3, nX9^0'=nX9^post_3, nX^0'=nX^post_3, res10^0'=res10^post_3, res5^0'=res5^post_3, ret_nBC18^0'=ret_nBC18^post_3, ret_nBC211^0'=ret_nBC211^post_3, tmp7^0'=tmp7^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, [ tmp7^post_3==1 && nI6^0==nI6^post_3 && nX^0==nX^post_3 && nX4^0==nX4^post_3 && nX9^0==nX9^post_3 && res10^0==res10^post_3 && res5^0==res5^post_3 && ret_nBC18^0==ret_nBC18^post_3 && ret_nBC211^0==ret_nBC211^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 ], cost: 1
      3: l3 -> l4 : nI6^0'=nI6^post_4, nX4^0'=nX4^post_4, nX9^0'=nX9^post_4, nX^0'=nX^post_4, res10^0'=res10^post_4, res5^0'=res5^post_4, ret_nBC18^0'=ret_nBC18^post_4, ret_nBC211^0'=ret_nBC211^post_4, tmp7^0'=tmp7^post_4, tmp^0'=tmp^post_4, tmp___0^0'=tmp___0^post_4, [ 32<=nI6^0 && ret_nBC18^post_4==res5^0 && tmp^post_4==ret_nBC18^post_4 && nX9^post_4==nX^0 && res10^1_1==nX9^post_4 && res10^2_1==res10^2_1 && res10^3_1==res10^3_1 && res10^4_1==res10^4_1 && res10^5_1==res10^5_1 && res10^post_4==res10^post_4 && ret_nBC211^post_4==res10^post_4 && tmp___0^post_4==ret_nBC211^post_4 && nI6^0==nI6^post_4 && nX^0==nX^post_4 && nX4^0==nX4^post_4 && res5^0==res5^post_4 && tmp7^0==tmp7^post_4 ], cost: 1
      4: l3 -> l2 : nI6^0'=nI6^post_5, nX4^0'=nX4^post_5, nX9^0'=nX9^post_5, nX^0'=nX^post_5, res10^0'=res10^post_5, res5^0'=res5^post_5, ret_nBC18^0'=ret_nBC18^post_5, ret_nBC211^0'=ret_nBC211^post_5, tmp7^0'=tmp7^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, [ 1+nI6^0<=32 && nI6^0==nI6^post_5 && nX^0==nX^post_5 && nX4^0==nX4^post_5 && nX9^0==nX9^post_5 && res10^0==res10^post_5 && res5^0==res5^post_5 && ret_nBC18^0==ret_nBC18^post_5 && ret_nBC211^0==ret_nBC211^post_5 && tmp^0==tmp^post_5 && tmp7^0==tmp7^post_5 && tmp___0^0==tmp___0^post_5 ], cost: 1
      6: l5 -> l1 : nI6^0'=nI6^post_7, nX4^0'=nX4^post_7, nX9^0'=nX9^post_7, nX^0'=nX^post_7, res10^0'=res10^post_7, res5^0'=res5^post_7, ret_nBC18^0'=ret_nBC18^post_7, ret_nBC211^0'=ret_nBC211^post_7, tmp7^0'=tmp7^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, [ nX4^post_7==nX^0 && res5^post_7==0 && nI6^post_7==0 && nX^0==nX^post_7 && nX9^0==nX9^post_7 && res10^0==res10^post_7 && ret_nBC18^0==ret_nBC18^post_7 && ret_nBC211^0==ret_nBC211^post_7 && tmp^0==tmp^post_7 && tmp7^0==tmp7^post_7 && tmp___0^0==tmp___0^post_7 ], cost: 1
      7: l6 -> l5 : nI6^0'=nI6^post_8, nX4^0'=nX4^post_8, nX9^0'=nX9^post_8, nX^0'=nX^post_8, res10^0'=res10^post_8, res5^0'=res5^post_8, ret_nBC18^0'=ret_nBC18^post_8, ret_nBC211^0'=ret_nBC211^post_8, tmp7^0'=tmp7^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ nI6^0==nI6^post_8 && nX^0==nX^post_8 && nX4^0==nX4^post_8 && nX9^0==nX9^post_8 && res10^0==res10^post_8 && res5^0==res5^post_8 && ret_nBC18^0==ret_nBC18^post_8 && ret_nBC211^0==ret_nBC211^post_8 && tmp^0==tmp^post_8 && tmp7^0==tmp7^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : nI6^0'=nI6^post_8, nX4^0'=nX4^post_8, nX9^0'=nX9^post_8, nX^0'=nX^post_8, res10^0'=res10^post_8, res5^0'=res5^post_8, ret_nBC18^0'=ret_nBC18^post_8, ret_nBC211^0'=ret_nBC211^post_8, tmp7^0'=tmp7^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ nI6^0==nI6^post_8 && nX^0==nX^post_8 && nX4^0==nX4^post_8 && nX9^0==nX9^post_8 && res10^0==res10^post_8 && res5^0==res5^post_8 && ret_nBC18^0==ret_nBC18^post_8 && ret_nBC211^0==ret_nBC211^post_8 && tmp^0==tmp^post_8 && tmp7^0==tmp7^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      0: l0 -> l1 : nI6^0'=nI6^post_1, nX4^0'=nX4^post_1, nX9^0'=nX9^post_1, nX^0'=nX^post_1, res10^0'=res10^post_1, res5^0'=res5^post_1, ret_nBC18^0'=ret_nBC18^post_1, ret_nBC211^0'=ret_nBC211^post_1, tmp7^0'=tmp7^post_1, tmp^0'=tmp^post_1, tmp___0^0'=tmp___0^post_1, [ res5^post_1==tmp7^0+res5^0 && nI6^post_1==1+nI6^0 && nX^0==nX^post_1 && nX4^0==nX4^post_1 && nX9^0==nX9^post_1 && res10^0==res10^post_1 && ret_nBC18^0==ret_nBC18^post_1 && ret_nBC211^0==ret_nBC211^post_1 && tmp^0==tmp^post_1 && tmp7^0==tmp7^post_1 && tmp___0^0==tmp___0^post_1 ], cost: 1
      5: l1 -> l3 : nI6^0'=nI6^post_6, nX4^0'=nX4^post_6, nX9^0'=nX9^post_6, nX^0'=nX^post_6, res10^0'=res10^post_6, res5^0'=res5^post_6, ret_nBC18^0'=ret_nBC18^post_6, ret_nBC211^0'=ret_nBC211^post_6, tmp7^0'=tmp7^post_6, tmp^0'=tmp^post_6, tmp___0^0'=tmp___0^post_6, [ nI6^0==nI6^post_6 && nX^0==nX^post_6 && nX4^0==nX4^post_6 && nX9^0==nX9^post_6 && res10^0==res10^post_6 && res5^0==res5^post_6 && ret_nBC18^0==ret_nBC18^post_6 && ret_nBC211^0==ret_nBC211^post_6 && tmp^0==tmp^post_6 && tmp7^0==tmp7^post_6 && tmp___0^0==tmp___0^post_6 ], cost: 1
      1: l2 -> l0 : nI6^0'=nI6^post_2, nX4^0'=nX4^post_2, nX9^0'=nX9^post_2, nX^0'=nX^post_2, res10^0'=res10^post_2, res5^0'=res5^post_2, ret_nBC18^0'=ret_nBC18^post_2, ret_nBC211^0'=ret_nBC211^post_2, tmp7^0'=tmp7^post_2, tmp^0'=tmp^post_2, tmp___0^0'=tmp___0^post_2, [ tmp7^post_2==0 && nI6^0==nI6^post_2 && nX^0==nX^post_2 && nX4^0==nX4^post_2 && nX9^0==nX9^post_2 && res10^0==res10^post_2 && res5^0==res5^post_2 && ret_nBC18^0==ret_nBC18^post_2 && ret_nBC211^0==ret_nBC211^post_2 && tmp^0==tmp^post_2 && tmp___0^0==tmp___0^post_2 ], cost: 1
      2: l2 -> l0 : nI6^0'=nI6^post_3, nX4^0'=nX4^post_3, nX9^0'=nX9^post_3, nX^0'=nX^post_3, res10^0'=res10^post_3, res5^0'=res5^post_3, ret_nBC18^0'=ret_nBC18^post_3, ret_nBC211^0'=ret_nBC211^post_3, tmp7^0'=tmp7^post_3, tmp^0'=tmp^post_3, tmp___0^0'=tmp___0^post_3, [ tmp7^post_3==1 && nI6^0==nI6^post_3 && nX^0==nX^post_3 && nX4^0==nX4^post_3 && nX9^0==nX9^post_3 && res10^0==res10^post_3 && res5^0==res5^post_3 && ret_nBC18^0==ret_nBC18^post_3 && ret_nBC211^0==ret_nBC211^post_3 && tmp^0==tmp^post_3 && tmp___0^0==tmp___0^post_3 ], cost: 1
      4: l3 -> l2 : nI6^0'=nI6^post_5, nX4^0'=nX4^post_5, nX9^0'=nX9^post_5, nX^0'=nX^post_5, res10^0'=res10^post_5, res5^0'=res5^post_5, ret_nBC18^0'=ret_nBC18^post_5, ret_nBC211^0'=ret_nBC211^post_5, tmp7^0'=tmp7^post_5, tmp^0'=tmp^post_5, tmp___0^0'=tmp___0^post_5, [ 1+nI6^0<=32 && nI6^0==nI6^post_5 && nX^0==nX^post_5 && nX4^0==nX4^post_5 && nX9^0==nX9^post_5 && res10^0==res10^post_5 && res5^0==res5^post_5 && ret_nBC18^0==ret_nBC18^post_5 && ret_nBC211^0==ret_nBC211^post_5 && tmp^0==tmp^post_5 && tmp7^0==tmp7^post_5 && tmp___0^0==tmp___0^post_5 ], cost: 1
      6: l5 -> l1 : nI6^0'=nI6^post_7, nX4^0'=nX4^post_7, nX9^0'=nX9^post_7, nX^0'=nX^post_7, res10^0'=res10^post_7, res5^0'=res5^post_7, ret_nBC18^0'=ret_nBC18^post_7, ret_nBC211^0'=ret_nBC211^post_7, tmp7^0'=tmp7^post_7, tmp^0'=tmp^post_7, tmp___0^0'=tmp___0^post_7, [ nX4^post_7==nX^0 && res5^post_7==0 && nI6^post_7==0 && nX^0==nX^post_7 && nX9^0==nX9^post_7 && res10^0==res10^post_7 && ret_nBC18^0==ret_nBC18^post_7 && ret_nBC211^0==ret_nBC211^post_7 && tmp^0==tmp^post_7 && tmp7^0==tmp7^post_7 && tmp___0^0==tmp___0^post_7 ], cost: 1
      7: l6 -> l5 : nI6^0'=nI6^post_8, nX4^0'=nX4^post_8, nX9^0'=nX9^post_8, nX^0'=nX^post_8, res10^0'=res10^post_8, res5^0'=res5^post_8, ret_nBC18^0'=ret_nBC18^post_8, ret_nBC211^0'=ret_nBC211^post_8, tmp7^0'=tmp7^post_8, tmp^0'=tmp^post_8, tmp___0^0'=tmp___0^post_8, [ nI6^0==nI6^post_8 && nX^0==nX^post_8 && nX4^0==nX4^post_8 && nX9^0==nX9^post_8 && res10^0==res10^post_8 && res5^0==res5^post_8 && ret_nBC18^0==ret_nBC18^post_8 && ret_nBC211^0==ret_nBC211^post_8 && tmp^0==tmp^post_8 && tmp7^0==tmp7^post_8 && tmp___0^0==tmp___0^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : nI6^0'=1+nI6^0, res5^0'=tmp7^0+res5^0, [], cost: 1
      5: l1 -> l3 : [], cost: 1
      1: l2 -> l0 : tmp7^0'=0, [], cost: 1
      2: l2 -> l0 : tmp7^0'=1, [], cost: 1
      4: l3 -> l2 : [ 1+nI6^0<=32 ], cost: 1
      6: l5 -> l1 : nI6^0'=0, nX4^0'=nX^0, res5^0'=0, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      0: l0 -> l1 : nI6^0'=1+nI6^0, res5^0'=tmp7^0+res5^0, [], cost: 1
      9: l1 -> l2 : [ 1+nI6^0<=32 ], cost: 2
      1: l2 -> l0 : tmp7^0'=0, [], cost: 1
      2: l2 -> l0 : tmp7^0'=1, [], cost: 1
      8: l6 -> l1 : nI6^0'=0, nX4^0'=nX^0, res5^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
      0: l0 -> l1 : nI6^0'=1+nI6^0, res5^0'=tmp7^0+res5^0, [], cost: 1
     10: l1 -> l0 : tmp7^0'=0, [ 1+nI6^0<=32 ], cost: 3
     11: l1 -> l0 : tmp7^0'=1, [ 1+nI6^0<=32 ], cost: 3
      8: l6 -> l1 : nI6^0'=0, nX4^0'=nX^0, res5^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
     12: l1 -> l1 : nI6^0'=1+nI6^0, res5^0'=res5^0, tmp7^0'=0, [ 1+nI6^0<=32 ], cost: 4
     13: l1 -> l1 : nI6^0'=1+nI6^0, res5^0'=1+res5^0, tmp7^0'=1, [ 1+nI6^0<=32 ], cost: 4
      8: l6 -> l1 : nI6^0'=0, nX4^0'=nX^0, res5^0'=0, [], cost: 2

Accelerating simple loops of location 1.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     12: l1 -> l1 : nI6^0'=1+nI6^0, tmp7^0'=0, [ 1+nI6^0<=32 ], cost: 4
     13: l1 -> l1 : nI6^0'=1+nI6^0, res5^0'=1+res5^0, tmp7^0'=1, [ 1+nI6^0<=32 ], cost: 4

   Accelerated rule 12 with backward acceleration, yielding the new rule 14.
   Accelerated rule 13 with backward acceleration, yielding the new rule 15.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 12 13.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     14: l1 -> l1 : nI6^0'=32, tmp7^0'=0, [ 32-nI6^0>=1 ], cost: 128-4*nI6^0
     15: l1 -> l1 : nI6^0'=32, res5^0'=32+res5^0-nI6^0, tmp7^0'=1, [ 32-nI6^0>=1 ], cost: 128-4*nI6^0
      8: l6 -> l1 : nI6^0'=0, nX4^0'=nX^0, res5^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      8: l6 -> l1 : nI6^0'=0, nX4^0'=nX^0, res5^0'=0, [], cost: 2
     16: l6 -> l1 : nI6^0'=32, nX4^0'=nX^0, res5^0'=0, tmp7^0'=0, [], cost: 130
     17: l6 -> l1 : nI6^0'=32, nX4^0'=nX^0, res5^0'=32, tmp7^0'=1, [], cost: 130

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     <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:  [ nI6^0==nI6^post_8 && nX^0==nX^post_8 && nX4^0==nX4^post_8 && nX9^0==nX9^post_8 && res10^0==res10^post_8 && res5^0==res5^post_8 && ret_nBC18^0==ret_nBC18^post_8 && ret_nBC211^0==ret_nBC211^post_8 && tmp^0==tmp^post_8 && tmp7^0==tmp7^post_8 && tmp___0^0==tmp___0^post_8 ]

WORST_CASE(Omega(1),?)