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()))
  EDG 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()))
   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())
   CDG 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()))
    graph:
     
    Qed