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()))
  Usable Rule Processor:
   DPs:
    merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),v()))
    merge#(++(x,y),++(u(),v())) -> merge#(++(x,y),v())
   TRS:
    
   ADG Processor:
    DPs:
     merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),v()))
     merge#(++(x,y),++(u(),v())) -> merge#(++(x,y),v())
    TRS:
     
    graph:
     merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),v())) ->
     merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),v()))
     merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),v())) ->
     merge#(++(x,y),++(u(),v())) -> merge#(++(x,y),v())
    Restore Modifier:
     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()))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/4
      DPs:
       merge#(++(x,y),++(u(),v())) -> merge#(y,++(u(),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:
       dimension: 1
       interpretation:
        [merge#](x0, x1) = x0 + x1,
        
        [v] = 1,
        
        [u] = 0,
        
        [++](x0, x1) = x1 + 1,
        
        [merge](x0, x1) = x0 + x1,
        
        [nil] = 0
       orientation:
        merge#(++(x,y),++(u(),v())) = y + 3 >= y + 2 = merge#(y,++(u(),v()))
        
        merge(x,nil()) = x >= x = x
        
        merge(nil(),y) = y >= y = y
        
        merge(++(x,y),++(u(),v())) = y + 3 >= y + 3 = ++(x,merge(y,++(u(),v())))
        
        merge(++(x,y),++(u(),v())) = y + 3 >= 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