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_15^0'=x_15^post_1, y_13^0'=y_13^post_1, [ 1+y_13^0<=1 && rt_11^post_1==st_14^0 && st_14^0==st_14^post_1 && x_15^0==x_15^post_1 && y_13^0==y_13^post_1 ], cost: 1
      1: l0 -> l2 : rt_11^0'=rt_11^post_2, st_14^0'=st_14^post_2, x_15^0'=x_15^post_2, y_13^0'=y_13^post_2, [ 1<=y_13^0 && rt_11^0==rt_11^post_2 && st_14^0==st_14^post_2 && x_15^0==x_15^post_2 && y_13^0==y_13^post_2 ], cost: 1
      2: l2 -> l1 : rt_11^0'=rt_11^post_3, st_14^0'=st_14^post_3, x_15^0'=x_15^post_3, y_13^0'=y_13^post_3, [ x_15^0<=0 && rt_11^post_3==st_14^0 && st_14^0==st_14^post_3 && x_15^0==x_15^post_3 && y_13^0==y_13^post_3 ], cost: 1
      3: l2 -> l3 : rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, x_15^0'=x_15^post_4, y_13^0'=y_13^post_4, [ 1<=x_15^0 && x_15^post_4==x_15^0-y_13^0 && y_13^post_4==1+y_13^0 && rt_11^0==rt_11^post_4 && st_14^0==st_14^post_4 ], cost: 1
      4: l3 -> l2 : rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, x_15^0'=x_15^post_5, y_13^0'=y_13^post_5, [ rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && x_15^0==x_15^post_5 && y_13^0==y_13^post_5 ], cost: 1
      5: l4 -> l0 : rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, x_15^0'=x_15^post_6, y_13^0'=y_13^post_6, [ rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 && x_15^0==x_15^post_6 && y_13^0==y_13^post_6 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l0 : rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, x_15^0'=x_15^post_6, y_13^0'=y_13^post_6, [ rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 && x_15^0==x_15^post_6 && y_13^0==y_13^post_6 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      1: l0 -> l2 : rt_11^0'=rt_11^post_2, st_14^0'=st_14^post_2, x_15^0'=x_15^post_2, y_13^0'=y_13^post_2, [ 1<=y_13^0 && rt_11^0==rt_11^post_2 && st_14^0==st_14^post_2 && x_15^0==x_15^post_2 && y_13^0==y_13^post_2 ], cost: 1
      3: l2 -> l3 : rt_11^0'=rt_11^post_4, st_14^0'=st_14^post_4, x_15^0'=x_15^post_4, y_13^0'=y_13^post_4, [ 1<=x_15^0 && x_15^post_4==x_15^0-y_13^0 && y_13^post_4==1+y_13^0 && rt_11^0==rt_11^post_4 && st_14^0==st_14^post_4 ], cost: 1
      4: l3 -> l2 : rt_11^0'=rt_11^post_5, st_14^0'=st_14^post_5, x_15^0'=x_15^post_5, y_13^0'=y_13^post_5, [ rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && x_15^0==x_15^post_5 && y_13^0==y_13^post_5 ], cost: 1
      5: l4 -> l0 : rt_11^0'=rt_11^post_6, st_14^0'=st_14^post_6, x_15^0'=x_15^post_6, y_13^0'=y_13^post_6, [ rt_11^0==rt_11^post_6 && st_14^0==st_14^post_6 && x_15^0==x_15^post_6 && y_13^0==y_13^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      1: l0 -> l2 : [ 1<=y_13^0 ], cost: 1
      3: l2 -> l3 : x_15^0'=x_15^0-y_13^0, y_13^0'=1+y_13^0, [ 1<=x_15^0 ], cost: 1
      4: l3 -> l2 : [], cost: 1
      5: l4 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      7: l2 -> l2 : x_15^0'=x_15^0-y_13^0, y_13^0'=1+y_13^0, [ 1<=x_15^0 ], cost: 2
      6: l4 -> l2 : [ 1<=y_13^0 ], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
      7: l2 -> l2 : x_15^0'=x_15^0-y_13^0, y_13^0'=1+y_13^0, [ 1<=x_15^0 ], cost: 2

[test] deduced invariant 1-y_13^0<=0
   Accelerated rule 7 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 1 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      7: l2 -> l2 : x_15^0'=x_15^0-y_13^0, y_13^0'=1+y_13^0, [ 1<=x_15^0 ], cost: 2
      8: l2 -> l2 : x_15^0'=-1/2*k^2+x_15^0-k*y_13^0+1/2*k, y_13^0'=k+y_13^0, [ 1-y_13^0<=0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2-(-1+k)*y_13^0+x_15^0+1/2*k ], cost: 2*k
      6: l4 -> l2 : [ 1<=y_13^0 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l2 : [ 1<=y_13^0 ], cost: 2
      9: l4 -> l2 : x_15^0'=x_15^0-y_13^0, y_13^0'=1+y_13^0, [ 1<=y_13^0 && 1<=x_15^0 ], cost: 4
     10: l4 -> l2 : x_15^0'=-1/2*k^2+x_15^0-k*y_13^0+1/2*k, y_13^0'=k+y_13^0, [ 1<=y_13^0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2-(-1+k)*y_13^0+x_15^0+1/2*k ], cost: 2+2*k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     10: l4 -> l2 : x_15^0'=-1/2*k^2+x_15^0-k*y_13^0+1/2*k, y_13^0'=k+y_13^0, [ 1<=y_13^0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2-(-1+k)*y_13^0+x_15^0+1/2*k ], cost: 2+2*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     10: l4 -> l2 : x_15^0'=-1/2*k^2+x_15^0-k*y_13^0+1/2*k, y_13^0'=k+y_13^0, [ 1<=y_13^0 && k>=0 && 1<=-1/2-1/2*(-1+k)^2-(-1+k)*y_13^0+x_15^0+1/2*k ], cost: 2+2*k

Computing asymptotic complexity for rule 10
   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_6 && st_14^0==st_14^post_6 && x_15^0==x_15^post_6 && y_13^0==y_13^post_6 ]

WORST_CASE(Omega(1),?)