WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1
      1: l1 -> l3 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ y_6^0-x_5^0<=0 && y_6^0-x_5^0<=0 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      5: l1 -> l5 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ y_6^0-x_5^0<=0 && y_6^0-x_5^0<=0 && x_5^0<=y_6^0 && y_6^0<=x_5^0 && x_5^post_6==1+x_5^0 && Result_4^0==Result_4^post_6 && y_6^0==y_6^post_6 ], cost: 1
      7: l1 -> l6 : Result_4^0'=Result_4^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ 0<=-1+y_6^0-x_5^0 && x_5^post_8==1+x_5^0 && Result_4^0==Result_4^post_8 && y_6^0==y_6^post_8 ], cost: 1
      2: l3 -> l4 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ 1+x_5^0<=y_6^0 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      3: l3 -> l4 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ 1+y_6^0<=x_5^0 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 && y_6^0==y_6^post_4 ], cost: 1
      4: l4 -> l2 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ Result_4^post_5==Result_4^post_5 && x_5^0==x_5^post_5 && y_6^0==y_6^post_5 ], cost: 1
      6: l5 -> l1 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1
      8: l6 -> l1 : Result_4^0'=Result_4^post_9, x_5^0'=x_5^post_9, y_6^0'=y_6^post_9, [ Result_4^0==Result_4^post_9 && x_5^0==x_5^post_9 && y_6^0==y_6^post_9 ], cost: 1
      9: l7 -> l0 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, [ Result_4^0==Result_4^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: l7 -> l0 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, [ Result_4^0==Result_4^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1
      5: l1 -> l5 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ y_6^0-x_5^0<=0 && y_6^0-x_5^0<=0 && x_5^0<=y_6^0 && y_6^0<=x_5^0 && x_5^post_6==1+x_5^0 && Result_4^0==Result_4^post_6 && y_6^0==y_6^post_6 ], cost: 1
      7: l1 -> l6 : Result_4^0'=Result_4^post_8, x_5^0'=x_5^post_8, y_6^0'=y_6^post_8, [ 0<=-1+y_6^0-x_5^0 && x_5^post_8==1+x_5^0 && Result_4^0==Result_4^post_8 && y_6^0==y_6^post_8 ], cost: 1
      6: l5 -> l1 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1
      8: l6 -> l1 : Result_4^0'=Result_4^post_9, x_5^0'=x_5^post_9, y_6^0'=y_6^post_9, [ Result_4^0==Result_4^post_9 && x_5^0==x_5^post_9 && y_6^0==y_6^post_9 ], cost: 1
      9: l7 -> l0 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, y_6^0'=y_6^post_10, [ Result_4^0==Result_4^post_10 && x_5^0==x_5^post_10 && y_6^0==y_6^post_10 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      0: l0 -> l1 : [], cost: 1
      5: l1 -> l5 : x_5^0'=1+x_5^0, [ y_6^0-x_5^0==0 ], cost: 1
      7: l1 -> l6 : x_5^0'=1+x_5^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 1
      6: l5 -> l1 : [], cost: 1
      8: l6 -> l1 : [], cost: 1
      9: l7 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
     11: l1 -> l1 : x_5^0'=1+x_5^0, [ y_6^0-x_5^0==0 ], cost: 2
     12: l1 -> l1 : x_5^0'=1+x_5^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 2
     10: l7 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     11: l1 -> l1 : x_5^0'=1+x_5^0, [ y_6^0-x_5^0==0 ], cost: 2
     12: l1 -> l1 : x_5^0'=1+x_5^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 2

   Accelerated rule 11 with metering function 1+y_6^0-x_5^0, yielding the new rule 13.
   Accelerated rule 12 with metering function y_6^0-x_5^0, yielding the new rule 14.
   Removing the simple loops: 11 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     13: l1 -> l1 : x_5^0'=1+y_6^0, [ y_6^0-x_5^0==0 ], cost: 2+2*y_6^0-2*x_5^0
     14: l1 -> l1 : x_5^0'=y_6^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 2*y_6^0-2*x_5^0
     10: l7 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
     10: l7 -> l1 : [], cost: 2
     15: l7 -> l1 : x_5^0'=1+y_6^0, [ y_6^0-x_5^0==0 ], cost: 4+2*y_6^0-2*x_5^0
     16: l7 -> l1 : x_5^0'=y_6^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 2+2*y_6^0-2*x_5^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     15: l7 -> l1 : x_5^0'=1+y_6^0, [ y_6^0-x_5^0==0 ], cost: 4+2*y_6^0-2*x_5^0
     16: l7 -> l1 : x_5^0'=y_6^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 2+2*y_6^0-2*x_5^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     15: l7 -> l1 : x_5^0'=1+y_6^0, [ y_6^0-x_5^0==0 ], cost: 4+2*y_6^0-2*x_5^0
     16: l7 -> l1 : x_5^0'=y_6^0, [ 0<=-1+y_6^0-x_5^0 ], cost: 2+2*y_6^0-2*x_5^0

Computing asymptotic complexity for rule 15
   Could not solve the limit problem.
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 16
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      2+2*y_6^0-2*x_5^0 (+), y_6^0-x_5^0 (+/+!) [not solved]

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

      applying transformation rule (C) using substitution {y_6^0==0,x_5^0==-n}
      resulting limit problem:
      [solved]

   Solution:
      y_6^0 / 0
      x_5^0 / -n
   Resulting cost 2+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: 2+2*n
   Rule cost:   2+2*y_6^0-2*x_5^0
   Rule guard:  [ 0<=-1+y_6^0-x_5^0 ]

WORST_CASE(Omega(n^1),?)