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

max/plus interpretations on N:

  merge_A(x1,x2) = max{10, 4 + x1, 1 + x2}
  merge#_A(x1,x2) = max{2, 7, 1}
  nil_A = 0
  nil#_A = 0
  ._A(x1,x2) = max{11, 9, 7}
  .#_A(x1,x2) = max{6, 4, 3}
  if_A(x1,x2,x3) = max{14, 11, 3 + x2, 8}
  if#_A(x1,x2,x3) = max{0, 0, 3, 0}
  <_A(x1,x2) = max{1, 1 + x1, 1 + x2}
  <#_A(x1,x2) = max{6, 0, 0}
  ++_A(x1,x2) = max{11, 9, 6 + x2}
  ++#_A(x1,x2) = max{7, 7, 5}
  true_A = 0
  true#_A = 0
  false_A = 0
  false#_A = 0

precedence:

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