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
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [++#](x0, x1) = x0 + 4,
    
    [if#](x0, x1, x2) = 6,
    
    [merge#](x0, x1) = x0 + x1 + 5,
    
    [false] = 0,
    
    [true] = 2,
    
    [++](x0, x1) = x0 + 2x1,
    
    [if](x0, x1, x2) = 2x0 + x1,
    
    [<](x0, x1) = 0,
    
    [.](x0, x1) = 4x0 + x1 + 1,
    
    [merge](x0, x1) = x0 + x1,
    
    [nil] = 2
   orientation:
    merge#(.(x,y),.(u,v)) = 4u + v + 4x + y + 7 >= v + 4x + y + 6 = merge#(.(x,y),v)
    
    merge#(.(x,y),.(u,v)) = 4u + v + 4x + y + 7 >= 4u + v + y + 6 = merge#(y,.(u,v))
    
    merge#(.(x,y),.(u,v)) = 4u + v + 4x + y + 7 >= 6 = if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    
    ++#(.(x,y),z) = 4x + y + 5 >= y + 4 = ++#(y,z)
    
    merge(nil(),y) = y + 2 >= y = y
    
    merge(x,nil()) = x + 2 >= x = x
    
    merge(.(x,y),.(u,v)) = 4u + v + 4x + y + 2 >= 4u + v + 4x + y + 2 = if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    
    ++(nil(),y) = 2y + 2 >= y = y
    
    ++(.(x,y),z) = 4x + y + 2z + 1 >= 4x + y + 2z + 1 = .(x,++(y,z))
    
    if(true(),x,y) = x + 4 >= x = x
    
    if(false(),x,y) = x >= x = x
   problem:
    DPs:
     
    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
   Qed