YES

TRS:

  or(true(),y) -> true()
  or(x,true()) -> true()
  or(false(),false()) -> false()
  mem(x,nil()) -> false()
  mem(x,set(y)) -> =(x,y)
  mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))

linear polynomial interpretations on N:

  or_A(x1,x2) = 1
  or#_A(x1,x2) = 1
  true_A = 1
  true#_A = 2
  false_A = 1
  false#_A = 0
  mem_A(x1,x2) = x1 + x2 + 1
  mem#_A(x1,x2) = x1 + x2 + 1
  nil_A = 1
  nil#_A = 1
  set_A(x1) = x1 + 1
  set#_A(x1) = 0
  =_A(x1,x2) = x1 + x2
  =#_A(x1,x2) = 0
  union_A(x1,x2) = x1 + x2 + 1
  union#_A(x1,x2) = 0

precedence:

  true = mem > or = nil = set = = = union > false