WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l5
      0: l0 -> l1 : x^0'=x^post_1, [ x^0<=0 && x^post_1==1 ], cost: 1
      1: l0 -> l1 : x^0'=x^post_2, [ 1<=x^0 && x^post_2==1+x^0 ], cost: 1
      4: l1 -> l2 : x^0'=x^post_5, [ x^0==x^post_5 ], cost: 1
      2: l2 -> l3 : x^0'=x^post_3, [ 4<=x^0 && x^0==x^post_3 ], cost: 1
      3: l2 -> l0 : x^0'=x^post_4, [ 1+x^0<=4 && x^0==x^post_4 ], cost: 1
      5: l4 -> l1 : x^0'=x^post_6, [ x^1_1==5 && x^post_6==x^post_6 ], cost: 1
      6: l5 -> l4 : x^0'=x^post_7, [ x^0==x^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l4 : x^0'=x^post_7, [ x^0==x^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      0: l0 -> l1 : x^0'=x^post_1, [ x^0<=0 && x^post_1==1 ], cost: 1
      1: l0 -> l1 : x^0'=x^post_2, [ 1<=x^0 && x^post_2==1+x^0 ], cost: 1
      4: l1 -> l2 : x^0'=x^post_5, [ x^0==x^post_5 ], cost: 1
      3: l2 -> l0 : x^0'=x^post_4, [ 1+x^0<=4 && x^0==x^post_4 ], cost: 1
      5: l4 -> l1 : x^0'=x^post_6, [ x^1_1==5 && x^post_6==x^post_6 ], cost: 1
      6: l5 -> l4 : x^0'=x^post_7, [ x^0==x^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      0: l0 -> l1 : x^0'=1, [ x^0<=0 ], cost: 1
      1: l0 -> l1 : x^0'=1+x^0, [ 1<=x^0 ], cost: 1
      4: l1 -> l2 : [], cost: 1
      3: l2 -> l0 : [ 1+x^0<=4 ], cost: 1
      5: l4 -> l1 : x^0'=x^post_6, [], cost: 1
      6: l5 -> l4 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      0: l0 -> l1 : x^0'=1, [ x^0<=0 ], cost: 1
      1: l0 -> l1 : x^0'=1+x^0, [ 1<=x^0 ], cost: 1
      8: l1 -> l0 : [ 1+x^0<=4 ], cost: 2
      7: l5 -> l1 : x^0'=x^post_6, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l5
      9: l1 -> l1 : x^0'=1, [ x^0<=0 ], cost: 3
     10: l1 -> l1 : x^0'=1+x^0, [ 1+x^0<=4 && 1<=x^0 ], cost: 3
      7: l5 -> l1 : x^0'=x^post_6, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      9: l1 -> l1 : x^0'=1, [ x^0<=0 ], cost: 3
     10: l1 -> l1 : x^0'=1+x^0, [ 1+x^0<=4 && 1<=x^0 ], cost: 3

   Failed to prove monotonicity of the guard of rule 9.
   Accelerated rule 10 with backward acceleration, yielding the new rule 11.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
      9: l1 -> l1 : x^0'=1, [ x^0<=0 ], cost: 3
     11: l1 -> l1 : x^0'=4, [ 1<=x^0 && 4-x^0>=0 ], cost: 12-3*x^0
      7: l5 -> l1 : x^0'=x^post_6, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      7: l5 -> l1 : x^0'=x^post_6, [], cost: 2
     12: l5 -> l1 : x^0'=1, [], cost: 5
     13: l5 -> l1 : x^0'=4, [ 1<=x^post_6 && 4-x^post_6>=0 ], cost: 14-3*x^post_6

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     13: l5 -> l1 : x^0'=4, [ 1<=x^post_6 && 4-x^post_6>=0 ], cost: 14-3*x^post_6

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     13: l5 -> l1 : x^0'=4, [ 1<=x^post_6 && 4-x^post_6>=0 ], cost: 14-3*x^post_6

Computing asymptotic complexity for rule 13
   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:  [ x^0==x^post_7 ]

WORST_CASE(Omega(1),?)