YES(?,O(n^1))

Problem:
 merge(x,nil()) -> x
 merge(nil(),y) -> y
 merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
 merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5}
   transitions:
    ++1(3,1) -> 18*
    ++1(3,3) -> 18*
    ++1(3,13) -> 15,5
    ++1(3,15) -> 15,5
    ++1(4,2) -> 18*
    ++1(4,4) -> 18*
    ++1(1,2) -> 18*
    ++1(1,4) -> 18*
    ++1(11,10) -> 12*
    ++1(2,1) -> 18*
    ++1(2,3) -> 18*
    ++1(2,13) -> 15,5
    ++1(2,15) -> 15,5
    ++1(3,2) -> 18*
    ++1(3,4) -> 18*
    ++1(4,1) -> 18*
    ++1(4,3) -> 18*
    ++1(4,13) -> 15,5
    ++1(4,15) -> 15,5
    ++1(1,1) -> 18*
    ++1(1,3) -> 18*
    ++1(1,13) -> 15,5
    ++1(1,15) -> 15,5
    ++1(11,19) -> 15,5
    ++1(2,2) -> 18*
    ++1(2,4) -> 18*
    u1() -> 11*
    merge1(2,12) -> 15*
    merge1(4,12) -> 15*
    merge1(1,12) -> 13*
    merge1(18,10) -> 19*
    merge1(3,12) -> 13*
    v1() -> 10*
    merge0(3,1) -> 5*
    merge0(3,3) -> 5*
    merge0(4,2) -> 5*
    merge0(4,4) -> 5*
    merge0(1,2) -> 5*
    merge0(1,4) -> 5*
    merge0(2,1) -> 5*
    merge0(2,3) -> 5*
    merge0(3,2) -> 5*
    merge0(3,4) -> 5*
    merge0(4,1) -> 5*
    merge0(4,3) -> 5*
    merge0(1,1) -> 5*
    merge0(1,3) -> 5*
    merge0(2,2) -> 5*
    merge0(2,4) -> 5*
    nil0() -> 1*
    ++0(3,1) -> 2*
    ++0(3,3) -> 2*
    ++0(4,2) -> 2*
    ++0(4,4) -> 2*
    ++0(1,2) -> 2*
    ++0(1,4) -> 2*
    ++0(2,1) -> 2*
    ++0(2,3) -> 2*
    ++0(3,2) -> 2*
    ++0(3,4) -> 2*
    ++0(4,1) -> 2*
    ++0(4,3) -> 2*
    ++0(1,1) -> 2*
    ++0(1,3) -> 2*
    ++0(2,2) -> 2*
    ++0(2,4) -> 2*
    u0() -> 3*
    v0() -> 4*
    1 -> 5*
    2 -> 5*
    3 -> 5*
    4 -> 5*
    12 -> 13*
  problem:
   
  Qed