WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l7
      0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_1, nd_12^0'=nd_12^post_1, rt_11^0'=rt_11^post_1, rv_15^0'=rv_15^post_1, st_14^0'=st_14^post_1, st_16^0'=st_16^post_1, x_13^0'=x_13^post_1, y_17^0'=y_17^post_1, [ __disjvr_0^0==__disjvr_0^post_1 && nd_12^0==nd_12^post_1 && rt_11^0==rt_11^post_1 && rv_15^0==rv_15^post_1 && st_14^0==st_14^post_1 && st_16^0==st_16^post_1 && x_13^0==x_13^post_1 && y_17^0==y_17^post_1 ], cost: 1
      1: l1 -> l2 : __disjvr_0^0'=__disjvr_0^post_2, nd_12^0'=nd_12^post_2, rt_11^0'=rt_11^post_2, rv_15^0'=rv_15^post_2, st_14^0'=st_14^post_2, st_16^0'=st_16^post_2, x_13^0'=x_13^post_2, y_17^0'=y_17^post_2, [ x_13^0<=0 && rt_11^post_2==st_14^0 && __disjvr_0^0==__disjvr_0^post_2 && nd_12^0==nd_12^post_2 && rv_15^0==rv_15^post_2 && st_14^0==st_14^post_2 && st_16^0==st_16^post_2 && x_13^0==x_13^post_2 && y_17^0==y_17^post_2 ], cost: 1
      2: l1 -> l3 : __disjvr_0^0'=__disjvr_0^post_3, nd_12^0'=nd_12^post_3, rt_11^0'=rt_11^post_3, rv_15^0'=rv_15^post_3, st_14^0'=st_14^post_3, st_16^0'=st_16^post_3, x_13^0'=x_13^post_3, y_17^0'=y_17^post_3, [ 1<=x_13^0 && nd_12^1_1==nd_12^1_1 && rv_15^post_3==nd_12^1_1 && nd_12^post_3==nd_12^post_3 && 0<=rv_15^post_3 && rv_15^post_3<=0 && y_17^post_3==-1+y_17^0 && st_16^post_3==st_16^post_3 && 2<=y_17^post_3 && __disjvr_0^0==__disjvr_0^post_3 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 && x_13^0==x_13^post_3 ], cost: 1
      4: l1 -> l5 : __disjvr_0^0'=__disjvr_0^post_5, nd_12^0'=nd_12^post_5, rt_11^0'=rt_11^post_5, rv_15^0'=rv_15^post_5, st_14^0'=st_14^post_5, st_16^0'=st_16^post_5, x_13^0'=x_13^post_5, y_17^0'=y_17^post_5, [ 1<=x_13^0 && nd_12^1_2==nd_12^1_2 && rv_15^post_5==nd_12^1_2 && nd_12^post_5==nd_12^post_5 && __disjvr_0^0==__disjvr_0^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && st_16^0==st_16^post_5 && x_13^0==x_13^post_5 && y_17^0==y_17^post_5 ], cost: 1
      3: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post_4, nd_12^0'=nd_12^post_4, rt_11^0'=rt_11^post_4, rv_15^0'=rv_15^post_4, st_14^0'=st_14^post_4, st_16^0'=st_16^post_4, x_13^0'=x_13^post_4, y_17^0'=y_17^post_4, [ __disjvr_0^0==__disjvr_0^post_4 && nd_12^0==nd_12^post_4 && rt_11^0==rt_11^post_4 && rv_15^0==rv_15^post_4 && st_14^0==st_14^post_4 && st_16^0==st_16^post_4 && x_13^0==x_13^post_4 && y_17^0==y_17^post_4 ], cost: 1
      5: l5 -> l6 : __disjvr_0^0'=__disjvr_0^post_6, nd_12^0'=nd_12^post_6, rt_11^0'=rt_11^post_6, rv_15^0'=rv_15^post_6, st_14^0'=st_14^post_6, st_16^0'=st_16^post_6, x_13^0'=x_13^post_6, y_17^0'=y_17^post_6, [ __disjvr_0^post_6==__disjvr_0^0 && __disjvr_0^0==__disjvr_0^post_6 && nd_12^0==nd_12^post_6 && rt_11^0==rt_11^post_6 && rv_15^0==rv_15^post_6 && st_14^0==st_14^post_6 && st_16^0==st_16^post_6 && x_13^0==x_13^post_6 && y_17^0==y_17^post_6 ], cost: 1
      6: l6 -> l4 : __disjvr_0^0'=__disjvr_0^post_7, nd_12^0'=nd_12^post_7, rt_11^0'=rt_11^post_7, rv_15^0'=rv_15^post_7, st_14^0'=st_14^post_7, st_16^0'=st_16^post_7, x_13^0'=x_13^post_7, y_17^0'=y_17^post_7, [ x_13^post_7==-1+x_13^0 && nd_12^1_3==nd_12^1_3 && y_17^post_7==nd_12^1_3 && nd_12^post_7==nd_12^post_7 && __disjvr_0^0==__disjvr_0^post_7 && rt_11^0==rt_11^post_7 && rv_15^0==rv_15^post_7 && st_14^0==st_14^post_7 && st_16^0==st_16^post_7 ], cost: 1
      7: l4 -> l1 : __disjvr_0^0'=__disjvr_0^post_8, nd_12^0'=nd_12^post_8, rt_11^0'=rt_11^post_8, rv_15^0'=rv_15^post_8, st_14^0'=st_14^post_8, st_16^0'=st_16^post_8, x_13^0'=x_13^post_8, y_17^0'=y_17^post_8, [ __disjvr_0^0==__disjvr_0^post_8 && nd_12^0==nd_12^post_8 && rt_11^0==rt_11^post_8 && rv_15^0==rv_15^post_8 && st_14^0==st_14^post_8 && st_16^0==st_16^post_8 && x_13^0==x_13^post_8 && y_17^0==y_17^post_8 ], cost: 1
      8: l7 -> l0 : __disjvr_0^0'=__disjvr_0^post_9, nd_12^0'=nd_12^post_9, rt_11^0'=rt_11^post_9, rv_15^0'=rv_15^post_9, st_14^0'=st_14^post_9, st_16^0'=st_16^post_9, x_13^0'=x_13^post_9, y_17^0'=y_17^post_9, [ __disjvr_0^0==__disjvr_0^post_9 && nd_12^0==nd_12^post_9 && rt_11^0==rt_11^post_9 && rv_15^0==rv_15^post_9 && st_14^0==st_14^post_9 && st_16^0==st_16^post_9 && x_13^0==x_13^post_9 && y_17^0==y_17^post_9 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      8: l7 -> l0 : __disjvr_0^0'=__disjvr_0^post_9, nd_12^0'=nd_12^post_9, rt_11^0'=rt_11^post_9, rv_15^0'=rv_15^post_9, st_14^0'=st_14^post_9, st_16^0'=st_16^post_9, x_13^0'=x_13^post_9, y_17^0'=y_17^post_9, [ __disjvr_0^0==__disjvr_0^post_9 && nd_12^0==nd_12^post_9 && rt_11^0==rt_11^post_9 && rv_15^0==rv_15^post_9 && st_14^0==st_14^post_9 && st_16^0==st_16^post_9 && x_13^0==x_13^post_9 && y_17^0==y_17^post_9 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l7
      0: l0 -> l1 : __disjvr_0^0'=__disjvr_0^post_1, nd_12^0'=nd_12^post_1, rt_11^0'=rt_11^post_1, rv_15^0'=rv_15^post_1, st_14^0'=st_14^post_1, st_16^0'=st_16^post_1, x_13^0'=x_13^post_1, y_17^0'=y_17^post_1, [ __disjvr_0^0==__disjvr_0^post_1 && nd_12^0==nd_12^post_1 && rt_11^0==rt_11^post_1 && rv_15^0==rv_15^post_1 && st_14^0==st_14^post_1 && st_16^0==st_16^post_1 && x_13^0==x_13^post_1 && y_17^0==y_17^post_1 ], cost: 1
      2: l1 -> l3 : __disjvr_0^0'=__disjvr_0^post_3, nd_12^0'=nd_12^post_3, rt_11^0'=rt_11^post_3, rv_15^0'=rv_15^post_3, st_14^0'=st_14^post_3, st_16^0'=st_16^post_3, x_13^0'=x_13^post_3, y_17^0'=y_17^post_3, [ 1<=x_13^0 && nd_12^1_1==nd_12^1_1 && rv_15^post_3==nd_12^1_1 && nd_12^post_3==nd_12^post_3 && 0<=rv_15^post_3 && rv_15^post_3<=0 && y_17^post_3==-1+y_17^0 && st_16^post_3==st_16^post_3 && 2<=y_17^post_3 && __disjvr_0^0==__disjvr_0^post_3 && rt_11^0==rt_11^post_3 && st_14^0==st_14^post_3 && x_13^0==x_13^post_3 ], cost: 1
      4: l1 -> l5 : __disjvr_0^0'=__disjvr_0^post_5, nd_12^0'=nd_12^post_5, rt_11^0'=rt_11^post_5, rv_15^0'=rv_15^post_5, st_14^0'=st_14^post_5, st_16^0'=st_16^post_5, x_13^0'=x_13^post_5, y_17^0'=y_17^post_5, [ 1<=x_13^0 && nd_12^1_2==nd_12^1_2 && rv_15^post_5==nd_12^1_2 && nd_12^post_5==nd_12^post_5 && __disjvr_0^0==__disjvr_0^post_5 && rt_11^0==rt_11^post_5 && st_14^0==st_14^post_5 && st_16^0==st_16^post_5 && x_13^0==x_13^post_5 && y_17^0==y_17^post_5 ], cost: 1
      3: l3 -> l1 : __disjvr_0^0'=__disjvr_0^post_4, nd_12^0'=nd_12^post_4, rt_11^0'=rt_11^post_4, rv_15^0'=rv_15^post_4, st_14^0'=st_14^post_4, st_16^0'=st_16^post_4, x_13^0'=x_13^post_4, y_17^0'=y_17^post_4, [ __disjvr_0^0==__disjvr_0^post_4 && nd_12^0==nd_12^post_4 && rt_11^0==rt_11^post_4 && rv_15^0==rv_15^post_4 && st_14^0==st_14^post_4 && st_16^0==st_16^post_4 && x_13^0==x_13^post_4 && y_17^0==y_17^post_4 ], cost: 1
      5: l5 -> l6 : __disjvr_0^0'=__disjvr_0^post_6, nd_12^0'=nd_12^post_6, rt_11^0'=rt_11^post_6, rv_15^0'=rv_15^post_6, st_14^0'=st_14^post_6, st_16^0'=st_16^post_6, x_13^0'=x_13^post_6, y_17^0'=y_17^post_6, [ __disjvr_0^post_6==__disjvr_0^0 && __disjvr_0^0==__disjvr_0^post_6 && nd_12^0==nd_12^post_6 && rt_11^0==rt_11^post_6 && rv_15^0==rv_15^post_6 && st_14^0==st_14^post_6 && st_16^0==st_16^post_6 && x_13^0==x_13^post_6 && y_17^0==y_17^post_6 ], cost: 1
      6: l6 -> l4 : __disjvr_0^0'=__disjvr_0^post_7, nd_12^0'=nd_12^post_7, rt_11^0'=rt_11^post_7, rv_15^0'=rv_15^post_7, st_14^0'=st_14^post_7, st_16^0'=st_16^post_7, x_13^0'=x_13^post_7, y_17^0'=y_17^post_7, [ x_13^post_7==-1+x_13^0 && nd_12^1_3==nd_12^1_3 && y_17^post_7==nd_12^1_3 && nd_12^post_7==nd_12^post_7 && __disjvr_0^0==__disjvr_0^post_7 && rt_11^0==rt_11^post_7 && rv_15^0==rv_15^post_7 && st_14^0==st_14^post_7 && st_16^0==st_16^post_7 ], cost: 1
      7: l4 -> l1 : __disjvr_0^0'=__disjvr_0^post_8, nd_12^0'=nd_12^post_8, rt_11^0'=rt_11^post_8, rv_15^0'=rv_15^post_8, st_14^0'=st_14^post_8, st_16^0'=st_16^post_8, x_13^0'=x_13^post_8, y_17^0'=y_17^post_8, [ __disjvr_0^0==__disjvr_0^post_8 && nd_12^0==nd_12^post_8 && rt_11^0==rt_11^post_8 && rv_15^0==rv_15^post_8 && st_14^0==st_14^post_8 && st_16^0==st_16^post_8 && x_13^0==x_13^post_8 && y_17^0==y_17^post_8 ], cost: 1
      8: l7 -> l0 : __disjvr_0^0'=__disjvr_0^post_9, nd_12^0'=nd_12^post_9, rt_11^0'=rt_11^post_9, rv_15^0'=rv_15^post_9, st_14^0'=st_14^post_9, st_16^0'=st_16^post_9, x_13^0'=x_13^post_9, y_17^0'=y_17^post_9, [ __disjvr_0^0==__disjvr_0^post_9 && nd_12^0==nd_12^post_9 && rt_11^0==rt_11^post_9 && rv_15^0==rv_15^post_9 && st_14^0==st_14^post_9 && st_16^0==st_16^post_9 && x_13^0==x_13^post_9 && y_17^0==y_17^post_9 ], cost: 1

Simplified all rules, resulting in:
   Start location: l7
      0: l0 -> l1 : [], cost: 1
      2: l1 -> l3 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=-1+y_17^0, [ 1<=x_13^0 && 2<=-1+y_17^0 ], cost: 1
      4: l1 -> l5 : nd_12^0'=nd_12^post_5, rv_15^0'=nd_12^1_2, [ 1<=x_13^0 ], cost: 1
      3: l3 -> l1 : [], cost: 1
      5: l5 -> l6 : [], cost: 1
      6: l6 -> l4 : nd_12^0'=nd_12^post_7, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [], cost: 1
      7: l4 -> l1 : [], cost: 1
      8: l7 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l7
     10: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=-1+y_17^0, [ 1<=x_13^0 && 2<=-1+y_17^0 ], cost: 2
     13: l1 -> l1 : nd_12^0'=nd_12^post_7, rv_15^0'=nd_12^1_2, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 ], cost: 4
      9: l7 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     10: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=-1+y_17^0, [ 1<=x_13^0 && 2<=-1+y_17^0 ], cost: 2
     13: l1 -> l1 : nd_12^0'=nd_12^post_7, rv_15^0'=nd_12^1_2, x_13^0'=-1+x_13^0, y_17^0'=nd_12^1_3, [ 1<=x_13^0 ], cost: 4

   Accelerated rule 10 with backward acceleration, yielding the new rule 14.
   Accelerated rule 13 with backward acceleration, yielding the new rule 15.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Nested simple loops 13 (outer loop) and 14 (inner loop) with Rule(1 | -2+nd_12^1_3>=1, -1+x_13^0>=1, 1<=1, | 2*nd_12^1_3*(-1+x_13^0) || 1 | 1=nd_12^post_3, 3=0, 5=st_16^post_3, 6=1, 7=2, ), resulting in the new rules: 16, 17.
   Removing the simple loops: 10 13.

Accelerated all simple loops using metering functions (where possible):
   Start location: l7
     14: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -4+2*y_17^0
     15: l1 -> l1 : nd_12^0'=nd_12^post_7, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ x_13^0>=1 ], cost: 4*x_13^0
     16: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2*nd_12^1_3*(-1+x_13^0)
     17: l1 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -4+2*y_17^0+2*nd_12^1_3*(-1+x_13^0)
      9: l7 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l7
      9: l7 -> l1 : [], cost: 2
     18: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0
     19: l7 -> l1 : nd_12^0'=nd_12^post_7, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ x_13^0>=1 ], cost: 2+4*x_13^0
     20: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2+2*nd_12^1_3*(-1+x_13^0)
     21: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -2+2*y_17^0+2*nd_12^1_3*(-1+x_13^0)

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l7
     18: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0
     19: l7 -> l1 : nd_12^0'=nd_12^post_7, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ x_13^0>=1 ], cost: 2+4*x_13^0
     20: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2+2*nd_12^1_3*(-1+x_13^0)
     21: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -2+2*y_17^0+2*nd_12^1_3*(-1+x_13^0)

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l7
     18: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, y_17^0'=2, [ 1<=x_13^0 && -2+y_17^0>=1 ], cost: -2+2*y_17^0
     19: l7 -> l1 : nd_12^0'=nd_12^post_7, rv_15^0'=nd_12^1_2, x_13^0'=0, y_17^0'=nd_12^1_3, [ x_13^0>=1 ], cost: 2+4*x_13^0
     20: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: 2+2*nd_12^1_3*(-1+x_13^0)
     21: l7 -> l1 : nd_12^0'=nd_12^post_3, rv_15^0'=0, st_16^0'=st_16^post_3, x_13^0'=1, y_17^0'=2, [ -2+y_17^0>=1 && -2+nd_12^1_3>=1 && -1+x_13^0>=1 ], cost: -2+2*y_17^0+2*nd_12^1_3*(-1+x_13^0)

Computing asymptotic complexity for rule 20
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 21
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 19
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 18
   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:  [ __disjvr_0^0==__disjvr_0^post_9 && nd_12^0==nd_12^post_9 && rt_11^0==rt_11^post_9 && rv_15^0==rv_15^post_9 && st_14^0==st_14^post_9 && st_16^0==st_16^post_9 && x_13^0==x_13^post_9 && y_17^0==y_17^post_9 ]

WORST_CASE(Omega(1),?)