WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : rt_11^0'=rt_11^post_1, st_14^0'=st_14^post_1, x_13^0'=x_13^post_1, y_15^0'=y_15^post_1, [ rt_11^0==rt_11^post_1 && st_14^0==st_14^post_1 && x_13^0==x_13^post_1 && y_15^0==y_15^post_1 ], cost: 1
      1: l1 -> l2 : rt_11^0'=rt_11^post_2, st_14^0'=st_14^post_2, x_13^0'=x_13^post_2, y_15^0'=y_15^post_2, [ x_13^0<=0 && rt_11^post_2==st_14^0 && st_14^0==st_14^post_2 && x_13^0==x_13^post_2 && y_15^0==y_15^post_2 ], cost: 1
      2: l1 -> l3 : rt_11^0'=rt_11^post_3, st_14^0'=st_14^post_3, x_13^0'=x_13^post_3, y_15^0'=y_15^post_3, [ 1<=x_13^0 && x_13^post_3==x_13^0+y_15^0 && y_15^post_3==-1+y_15^0 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 ], cost: 1
      3: l3 -> l1 : rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, x_13^0'=x_13^post_4, y_15^0'=y_15^post_4, [ rt_11^0==rt_11^post_4 && st_14^0==st_14^post_4 && x_13^0==x_13^post_4 && y_15^0==y_15^post_4 ], cost: 1
      4: l4 -> l0 : rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, x_13^0'=x_13^post_5, y_15^0'=y_15^post_5, [ rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && x_13^0==x_13^post_5 && y_15^0==y_15^post_5 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: l4 -> l0 : rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, x_13^0'=x_13^post_5, y_15^0'=y_15^post_5, [ rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && x_13^0==x_13^post_5 && y_15^0==y_15^post_5 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      0: l0 -> l1 : rt_11^0'=rt_11^post_1, st_14^0'=st_14^post_1, x_13^0'=x_13^post_1, y_15^0'=y_15^post_1, [ rt_11^0==rt_11^post_1 && st_14^0==st_14^post_1 && x_13^0==x_13^post_1 && y_15^0==y_15^post_1 ], cost: 1
      2: l1 -> l3 : rt_11^0'=rt_11^post_3, st_14^0'=st_14^post_3, x_13^0'=x_13^post_3, y_15^0'=y_15^post_3, [ 1<=x_13^0 && x_13^post_3==x_13^0+y_15^0 && y_15^post_3==-1+y_15^0 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 ], cost: 1
      3: l3 -> l1 : rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, x_13^0'=x_13^post_4, y_15^0'=y_15^post_4, [ rt_11^0==rt_11^post_4 && st_14^0==st_14^post_4 && x_13^0==x_13^post_4 && y_15^0==y_15^post_4 ], cost: 1
      4: l4 -> l0 : rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, x_13^0'=x_13^post_5, y_15^0'=y_15^post_5, [ rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && x_13^0==x_13^post_5 && y_15^0==y_15^post_5 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : [], cost: 1
      2: l1 -> l3 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, [ 1<=x_13^0 ], cost: 1
      3: l3 -> l1 : [], cost: 1
      4: l4 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      6: l1 -> l1 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, [ 1<=x_13^0 ], cost: 2
      5: l4 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      6: l1 -> l1 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, [ 1<=x_13^0 ], cost: 2

[test] deduced pseudo-invariant y_15^0<=0, also trying -y_15^0<=-1
   Accelerated rule 6 with backward acceleration, yielding the new rule 7.
   Accelerated rule 6 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 2 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      6: l1 -> l1 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, [ 1<=x_13^0 ], cost: 2
      7: l1 -> l1 : x_13^0'=1/2*k+x_13^0-1/2*k^2+k*y_15^0, y_15^0'=-k+y_15^0, [ y_15^0<=0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2+1/2*k+x_13^0+(-1+k)*y_15^0 ], cost: 2*k
      8: l1 -> l1 : x_13^0'=x_13^0+1/2*y_15^0^2+1/2*y_15^0, y_15^0'=0, [ 1<=x_13^0 && y_15^0>=0 ], cost: 2*y_15^0
      5: l4 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      5: l4 -> l1 : [], cost: 2
      9: l4 -> l1 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, [ 1<=x_13^0 ], cost: 4
     10: l4 -> l1 : x_13^0'=1/2*k+x_13^0-1/2*k^2+k*y_15^0, y_15^0'=-k+y_15^0, [ y_15^0<=0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2+1/2*k+x_13^0+(-1+k)*y_15^0 ], cost: 2+2*k
     11: l4 -> l1 : x_13^0'=x_13^0+1/2*y_15^0^2+1/2*y_15^0, y_15^0'=0, [ 1<=x_13^0 && y_15^0>=0 ], cost: 2+2*y_15^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     10: l4 -> l1 : x_13^0'=1/2*k+x_13^0-1/2*k^2+k*y_15^0, y_15^0'=-k+y_15^0, [ y_15^0<=0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2+1/2*k+x_13^0+(-1+k)*y_15^0 ], cost: 2+2*k
     11: l4 -> l1 : x_13^0'=x_13^0+1/2*y_15^0^2+1/2*y_15^0, y_15^0'=0, [ 1<=x_13^0 && y_15^0>=0 ], cost: 2+2*y_15^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     10: l4 -> l1 : x_13^0'=1/2*k+x_13^0-1/2*k^2+k*y_15^0, y_15^0'=-k+y_15^0, [ y_15^0<=0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2+1/2*k+x_13^0+(-1+k)*y_15^0 ], cost: 2+2*k
     11: l4 -> l1 : x_13^0'=x_13^0+1/2*y_15^0^2+1/2*y_15^0, y_15^0'=0, [ 1<=x_13^0 && y_15^0>=0 ], cost: 2+2*y_15^0

Computing asymptotic complexity for rule 10
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 11
   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:  [ rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && x_13^0==x_13^post_5 && y_15^0==y_15^post_5 ]

WORST_CASE(Omega(1),?)