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()))
  Subterm Criterion Processor:
   simple projection:
    pi(merge#) = 1
   problem:
    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()))
   Subterm Criterion Processor:
    simple projection:
     pi(merge#) = 0
    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