YES

Problem:
 merge(x,nil()) -> x
 merge(nil(),y) -> y
 merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
 merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))

Proof:
 DP Processor:
  DPs:
   merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),v()))
   merge#(++(x,y),++(u(),v())) -> merge#(++(x,y),v())
  TRS:
   merge(x,nil()) -> x
   merge(nil(),y) -> y
   merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
   merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [merge#](x0, x1) = x0 + 2x1 + 7,
    
    [v] = 0,
    
    [u] = 0,
    
    [++](x0, x1) = x0 + x1 + 1,
    
    [merge](x0, x1) = x0 + 6x1 + 1,
    
    [nil] = 5
   orientation:
    merge#(++(x,y),++(u(),v())) = x + y + 10 >= y + 9 = merge#(y,++(u(),v()))
    
    merge#(++(x,y),++(u(),v())) = x + y + 10 >= x + y + 8 = merge#(++(x,y),v())
    
    merge(x,nil()) = x + 31 >= x = x
    
    merge(nil(),y) = 6y + 6 >= y = y
    
    merge(++(x,y),++(u(),v())) = x + y + 8 >= x + y + 8 = ++(x,merge(y,++(u(),v())))
    
    merge(++(x,y),++(u(),v())) = x + y + 8 >= x + y + 3 = ++(u(),merge(++(x,y),v()))
   problem:
    DPs:
     
    TRS:
     merge(x,nil()) -> x
     merge(nil(),y) -> y
     merge(++(x,y),++(u(),v())) -> ++(x,merge(y,++(u(),v())))
     merge(++(x,y),++(u(),v())) -> ++(u(),merge(++(x,y),v()))
   Qed