YES

Problem:
 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

Proof:
 DP Processor:
  DPs:
   merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
   merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
   merge#(.(x,y),.(u,v)) -> if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
   ++#(.(x,y),z) -> ++#(y,z)
  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
  Usable Rule Processor:
   DPs:
    merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
    merge#(.(x,y),.(u,v)) -> if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    ++#(.(x,y),z) -> ++#(y,z)
   TRS:
    merge(x,nil()) -> x
    merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    merge(nil(),y) -> y
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     merge(x,nil()) -> x
     merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
     merge(nil(),y) -> y
    interpretation:
     [++#](x0, x1) = 4x0 + 4,
     
     [if#](x0, x1, x2) = x0 + x1,
     
     [merge#](x0, x1) = 3x0 + 4x1 + 3,
     
     [if](x0, x1, x2) = 4,
     
     [<](x0, x1) = 3x0 + 4,
     
     [.](x0, x1) = 5x0 + x1 + 1,
     
     [merge](x0, x1) = 2x0 + 4x1,
     
     [nil] = 7
    orientation:
     merge#(.(x,y),.(u,v)) = 20u + 4v + 15x + 3y + 10 >= 4v + 15x + 3y + 6 = merge#(.(x,y),v)
     
     merge#(.(x,y),.(u,v)) = 20u + 4v + 15x + 3y + 10 >= 20u + 4v + 3y + 7 = merge#(y,.(u,v))
     
     merge#(.(x,y),.(u,v)) = 20u + 4v + 15x + 3y + 10 >= 20u + 4v + 8x + 2y + 9 = if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
     
     ++#(.(x,y),z) = 20x + 4y + 8 >= 4y + 4 = ++#(y,z)
     
     merge(x,nil()) = 2x + 28 >= x = x
     
     merge(.(x,y),.(u,v)) = 20u + 4v + 10x + 2y + 6 >= 4 = if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
     
     merge(nil(),y) = 4y + 14 >= y = y
    problem:
     DPs:
      
     TRS:
      merge(x,nil()) -> x
      merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
      merge(nil(),y) -> y
    Qed