WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, __cil_tmp4_8^0'=__cil_tmp4_8^post_1, __const_1000^0'=__const_1000^post_1, __const_101^0'=__const_101^post_1, __const_9^0'=__const_9^post_1, __retres3_7^0'=__retres3_7^post_1, i_5^0'=i_5^post_1, x_6^0'=x_6^post_1, [ 1-x_6^0+__const_9^0<=0 && __retres3_7^post_1==0 && __cil_tmp4_8^post_1==__retres3_7^post_1 && Result_4^post_1==__cil_tmp4_8^post_1 && __const_1000^0==__const_1000^post_1 && __const_101^0==__const_101^post_1 && __const_9^0==__const_9^post_1 && i_5^0==i_5^post_1 && x_6^0==x_6^post_1 ], cost: 1
      1: l0 -> l1 : Result_4^0'=Result_4^post_2, __cil_tmp4_8^0'=__cil_tmp4_8^post_2, __const_1000^0'=__const_1000^post_2, __const_101^0'=__const_101^post_2, __const_9^0'=__const_9^post_2, __retres3_7^0'=__retres3_7^post_2, i_5^0'=i_5^post_2, x_6^0'=x_6^post_2, [ 0<=-x_6^0+__const_9^0 && 1+i_5^0-__const_101^0<=0 && __retres3_7^post_2==0 && __cil_tmp4_8^post_2==__retres3_7^post_2 && Result_4^post_2==__cil_tmp4_8^post_2 && __const_1000^0==__const_1000^post_2 && __const_101^0==__const_101^post_2 && __const_9^0==__const_9^post_2 && i_5^0==i_5^post_2 && x_6^0==x_6^post_2 ], cost: 1
      2: l0 -> l2 : Result_4^0'=Result_4^post_3, __cil_tmp4_8^0'=__cil_tmp4_8^post_3, __const_1000^0'=__const_1000^post_3, __const_101^0'=__const_101^post_3, __const_9^0'=__const_9^post_3, __retres3_7^0'=__retres3_7^post_3, i_5^0'=i_5^post_3, x_6^0'=x_6^post_3, [ 0<=-x_6^0+__const_9^0 && 0<=i_5^0-__const_101^0 && i_5^post_3==-1+i_5^0 && Result_4^0==Result_4^post_3 && __cil_tmp4_8^0==__cil_tmp4_8^post_3 && __const_1000^0==__const_1000^post_3 && __const_101^0==__const_101^post_3 && __const_9^0==__const_9^post_3 && __retres3_7^0==__retres3_7^post_3 && x_6^0==x_6^post_3 ], cost: 1
      3: l2 -> l0 : Result_4^0'=Result_4^post_4, __cil_tmp4_8^0'=__cil_tmp4_8^post_4, __const_1000^0'=__const_1000^post_4, __const_101^0'=__const_101^post_4, __const_9^0'=__const_9^post_4, __retres3_7^0'=__retres3_7^post_4, i_5^0'=i_5^post_4, x_6^0'=x_6^post_4, [ Result_4^0==Result_4^post_4 && __cil_tmp4_8^0==__cil_tmp4_8^post_4 && __const_1000^0==__const_1000^post_4 && __const_101^0==__const_101^post_4 && __const_9^0==__const_9^post_4 && __retres3_7^0==__retres3_7^post_4 && i_5^0==i_5^post_4 && x_6^0==x_6^post_4 ], cost: 1
      4: l3 -> l0 : Result_4^0'=Result_4^post_5, __cil_tmp4_8^0'=__cil_tmp4_8^post_5, __const_1000^0'=__const_1000^post_5, __const_101^0'=__const_101^post_5, __const_9^0'=__const_9^post_5, __retres3_7^0'=__retres3_7^post_5, i_5^0'=i_5^post_5, x_6^0'=x_6^post_5, [ i_5^post_5==__const_1000^0 && Result_4^0==Result_4^post_5 && __cil_tmp4_8^0==__cil_tmp4_8^post_5 && __const_1000^0==__const_1000^post_5 && __const_101^0==__const_101^post_5 && __const_9^0==__const_9^post_5 && __retres3_7^0==__retres3_7^post_5 && x_6^0==x_6^post_5 ], cost: 1
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, __cil_tmp4_8^0'=__cil_tmp4_8^post_6, __const_1000^0'=__const_1000^post_6, __const_101^0'=__const_101^post_6, __const_9^0'=__const_9^post_6, __retres3_7^0'=__retres3_7^post_6, i_5^0'=i_5^post_6, x_6^0'=x_6^post_6, [ Result_4^0==Result_4^post_6 && __cil_tmp4_8^0==__cil_tmp4_8^post_6 && __const_1000^0==__const_1000^post_6 && __const_101^0==__const_101^post_6 && __const_9^0==__const_9^post_6 && __retres3_7^0==__retres3_7^post_6 && i_5^0==i_5^post_6 && x_6^0==x_6^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, __cil_tmp4_8^0'=__cil_tmp4_8^post_6, __const_1000^0'=__const_1000^post_6, __const_101^0'=__const_101^post_6, __const_9^0'=__const_9^post_6, __retres3_7^0'=__retres3_7^post_6, i_5^0'=i_5^post_6, x_6^0'=x_6^post_6, [ Result_4^0==Result_4^post_6 && __cil_tmp4_8^0==__cil_tmp4_8^post_6 && __const_1000^0==__const_1000^post_6 && __const_101^0==__const_101^post_6 && __const_9^0==__const_9^post_6 && __retres3_7^0==__retres3_7^post_6 && i_5^0==i_5^post_6 && x_6^0==x_6^post_6 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      2: l0 -> l2 : Result_4^0'=Result_4^post_3, __cil_tmp4_8^0'=__cil_tmp4_8^post_3, __const_1000^0'=__const_1000^post_3, __const_101^0'=__const_101^post_3, __const_9^0'=__const_9^post_3, __retres3_7^0'=__retres3_7^post_3, i_5^0'=i_5^post_3, x_6^0'=x_6^post_3, [ 0<=-x_6^0+__const_9^0 && 0<=i_5^0-__const_101^0 && i_5^post_3==-1+i_5^0 && Result_4^0==Result_4^post_3 && __cil_tmp4_8^0==__cil_tmp4_8^post_3 && __const_1000^0==__const_1000^post_3 && __const_101^0==__const_101^post_3 && __const_9^0==__const_9^post_3 && __retres3_7^0==__retres3_7^post_3 && x_6^0==x_6^post_3 ], cost: 1
      3: l2 -> l0 : Result_4^0'=Result_4^post_4, __cil_tmp4_8^0'=__cil_tmp4_8^post_4, __const_1000^0'=__const_1000^post_4, __const_101^0'=__const_101^post_4, __const_9^0'=__const_9^post_4, __retres3_7^0'=__retres3_7^post_4, i_5^0'=i_5^post_4, x_6^0'=x_6^post_4, [ Result_4^0==Result_4^post_4 && __cil_tmp4_8^0==__cil_tmp4_8^post_4 && __const_1000^0==__const_1000^post_4 && __const_101^0==__const_101^post_4 && __const_9^0==__const_9^post_4 && __retres3_7^0==__retres3_7^post_4 && i_5^0==i_5^post_4 && x_6^0==x_6^post_4 ], cost: 1
      4: l3 -> l0 : Result_4^0'=Result_4^post_5, __cil_tmp4_8^0'=__cil_tmp4_8^post_5, __const_1000^0'=__const_1000^post_5, __const_101^0'=__const_101^post_5, __const_9^0'=__const_9^post_5, __retres3_7^0'=__retres3_7^post_5, i_5^0'=i_5^post_5, x_6^0'=x_6^post_5, [ i_5^post_5==__const_1000^0 && Result_4^0==Result_4^post_5 && __cil_tmp4_8^0==__cil_tmp4_8^post_5 && __const_1000^0==__const_1000^post_5 && __const_101^0==__const_101^post_5 && __const_9^0==__const_9^post_5 && __retres3_7^0==__retres3_7^post_5 && x_6^0==x_6^post_5 ], cost: 1
      5: l4 -> l3 : Result_4^0'=Result_4^post_6, __cil_tmp4_8^0'=__cil_tmp4_8^post_6, __const_1000^0'=__const_1000^post_6, __const_101^0'=__const_101^post_6, __const_9^0'=__const_9^post_6, __retres3_7^0'=__retres3_7^post_6, i_5^0'=i_5^post_6, x_6^0'=x_6^post_6, [ Result_4^0==Result_4^post_6 && __cil_tmp4_8^0==__cil_tmp4_8^post_6 && __const_1000^0==__const_1000^post_6 && __const_101^0==__const_101^post_6 && __const_9^0==__const_9^post_6 && __retres3_7^0==__retres3_7^post_6 && i_5^0==i_5^post_6 && x_6^0==x_6^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      2: l0 -> l2 : i_5^0'=-1+i_5^0, [ 0<=-x_6^0+__const_9^0 && 0<=i_5^0-__const_101^0 ], cost: 1
      3: l2 -> l0 : [], cost: 1
      4: l3 -> l0 : i_5^0'=__const_1000^0, [], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      7: l0 -> l0 : i_5^0'=-1+i_5^0, [ 0<=-x_6^0+__const_9^0 && 0<=i_5^0-__const_101^0 ], cost: 2
      6: l4 -> l0 : i_5^0'=__const_1000^0, [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      7: l0 -> l0 : i_5^0'=-1+i_5^0, [ 0<=-x_6^0+__const_9^0 && 0<=i_5^0-__const_101^0 ], cost: 2

   Accelerated rule 7 with metering function 1+i_5^0-__const_101^0, yielding the new rule 8.
   Removing the simple loops: 7.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      8: l0 -> l0 : i_5^0'=-1+__const_101^0, [ 0<=-x_6^0+__const_9^0 && 0<=i_5^0-__const_101^0 ], cost: 2+2*i_5^0-2*__const_101^0
      6: l4 -> l0 : i_5^0'=__const_1000^0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l0 : i_5^0'=__const_1000^0, [], cost: 2
      9: l4 -> l0 : i_5^0'=-1+__const_101^0, [ 0<=-x_6^0+__const_9^0 && 0<=__const_1000^0-__const_101^0 ], cost: 4+2*__const_1000^0-2*__const_101^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
      9: l4 -> l0 : i_5^0'=-1+__const_101^0, [ 0<=-x_6^0+__const_9^0 && 0<=__const_1000^0-__const_101^0 ], cost: 4+2*__const_1000^0-2*__const_101^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
      9: l4 -> l0 : i_5^0'=-1+__const_101^0, [ 0<=-x_6^0+__const_9^0 && 0<=__const_1000^0-__const_101^0 ], cost: 4+2*__const_1000^0-2*__const_101^0

Computing asymptotic complexity for rule 9
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      1+__const_1000^0-__const_101^0 (+/+!), 4+2*__const_1000^0-2*__const_101^0 (+), 1-x_6^0+__const_9^0 (+/+!) [not solved]

      removing all constraints (solved by SMT)
      resulting limit problem: [solved]

      applying transformation rule (C) using substitution {__const_1000^0==0,__const_101^0==-n,x_6^0==-n,__const_9^0==0}
      resulting limit problem:
      [solved]

   Solution:
      __const_1000^0 / 0
      __const_101^0 / -n
      x_6^0 / -n
      __const_9^0 / 0
   Resulting cost 4+2*n has complexity: Poly(n^1)

Found new complexity Poly(n^1).

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Poly(n^1)
   Cpx degree:  1
   Solved cost: 4+2*n
   Rule cost:   4+2*__const_1000^0-2*__const_101^0
   Rule guard:  [ 0<=-x_6^0+__const_9^0 && 0<=__const_1000^0-__const_101^0 ]

WORST_CASE(Omega(n^1),?)