YES

TRS:

  merge(nil(),y) -> y
  merge(x,nil()) -> x
  merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
  ++(nil(),y) -> y
  ++(.(x,y),z) -> .(x,++(y,z))
  if(true(),x,y) -> x
  if(false(),x,y) -> x

linear polynomial interpretations on N:

  merge_A(x1,x2) = x1 + x2
  merge#_A(x1,x2) = 1
  nil_A = 1
  nil#_A = 0
  ._A(x1,x2) = 1
  .#_A(x1,x2) = 0
  if_A(x1,x2,x3) = x2
  if#_A(x1,x2,x3) = 0
  <_A(x1,x2) = x1 + 1
  <#_A(x1,x2) = 0
  ++_A(x1,x2) = x2 + 1
  ++#_A(x1,x2) = x2 + 1
  true_A = 1
  true#_A = 0
  false_A = 1
  false#_A = 0

precedence:

  merge = if = ++ > nil = . = < = true = false