YES

Problem:
 a(lambda(x),y) -> lambda(a(x,1()))
 a(lambda(x),y) -> lambda(a(x,a(y,t())))
 a(a(x,y),z) -> a(x,a(y,z))
 lambda(x) -> x
 a(x,y) -> x
 a(x,y) -> y

Proof:
 DP Processor:
  DPs:
   a#(lambda(x),y) -> a#(x,1())
   a#(lambda(x),y) -> lambda#(a(x,1()))
   a#(lambda(x),y) -> a#(y,t())
   a#(lambda(x),y) -> a#(x,a(y,t()))
   a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
   a#(a(x,y),z) -> a#(y,z)
   a#(a(x,y),z) -> a#(x,a(y,z))
  TRS:
   a(lambda(x),y) -> lambda(a(x,1()))
   a(lambda(x),y) -> lambda(a(x,a(y,t())))
   a(a(x,y),z) -> a(x,a(y,z))
   lambda(x) -> x
   a(x,y) -> x
   a(x,y) -> y
  TDG Processor:
   DPs:
    a#(lambda(x),y) -> a#(x,1())
    a#(lambda(x),y) -> lambda#(a(x,1()))
    a#(lambda(x),y) -> a#(y,t())
    a#(lambda(x),y) -> a#(x,a(y,t()))
    a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
    a#(a(x,y),z) -> a#(y,z)
    a#(a(x,y),z) -> a#(x,a(y,z))
   TRS:
    a(lambda(x),y) -> lambda(a(x,1()))
    a(lambda(x),y) -> lambda(a(x,a(y,t())))
    a(a(x,y),z) -> a(x,a(y,z))
    lambda(x) -> x
    a(x,y) -> x
    a(x,y) -> y
   graph:
    a#(a(x,y),z) -> a#(y,z) -> a#(a(x,y),z) -> a#(x,a(y,z))
    a#(a(x,y),z) -> a#(y,z) -> a#(a(x,y),z) -> a#(y,z)
    a#(a(x,y),z) -> a#(y,z) -> a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
    a#(a(x,y),z) -> a#(y,z) -> a#(lambda(x),y) -> a#(x,a(y,t()))
    a#(a(x,y),z) -> a#(y,z) -> a#(lambda(x),y) -> a#(y,t())
    a#(a(x,y),z) -> a#(y,z) -> a#(lambda(x),y) -> lambda#(a(x,1()))
    a#(a(x,y),z) -> a#(y,z) -> a#(lambda(x),y) -> a#(x,1())
    a#(a(x,y),z) -> a#(x,a(y,z)) -> a#(a(x,y),z) -> a#(x,a(y,z))
    a#(a(x,y),z) -> a#(x,a(y,z)) -> a#(a(x,y),z) -> a#(y,z)
    a#(a(x,y),z) -> a#(x,a(y,z)) ->
    a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
    a#(a(x,y),z) -> a#(x,a(y,z)) -> a#(lambda(x),y) -> a#(x,a(y,t()))
    a#(a(x,y),z) -> a#(x,a(y,z)) -> a#(lambda(x),y) -> a#(y,t())
    a#(a(x,y),z) -> a#(x,a(y,z)) ->
    a#(lambda(x),y) -> lambda#(a(x,1()))
    a#(a(x,y),z) -> a#(x,a(y,z)) -> a#(lambda(x),y) -> a#(x,1())
    a#(lambda(x),y) -> a#(y,t()) -> a#(a(x,y),z) -> a#(x,a(y,z))
    a#(lambda(x),y) -> a#(y,t()) -> a#(a(x,y),z) -> a#(y,z)
    a#(lambda(x),y) -> a#(y,t()) ->
    a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
    a#(lambda(x),y) -> a#(y,t()) -> a#(lambda(x),y) -> a#(x,a(y,t()))
    a#(lambda(x),y) -> a#(y,t()) -> a#(lambda(x),y) -> a#(y,t())
    a#(lambda(x),y) -> a#(y,t()) ->
    a#(lambda(x),y) -> lambda#(a(x,1()))
    a#(lambda(x),y) -> a#(y,t()) -> a#(lambda(x),y) -> a#(x,1())
    a#(lambda(x),y) -> a#(x,1()) -> a#(a(x,y),z) -> a#(x,a(y,z))
    a#(lambda(x),y) -> a#(x,1()) -> a#(a(x,y),z) -> a#(y,z)
    a#(lambda(x),y) -> a#(x,1()) ->
    a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
    a#(lambda(x),y) -> a#(x,1()) -> a#(lambda(x),y) -> a#(x,a(y,t()))
    a#(lambda(x),y) -> a#(x,1()) -> a#(lambda(x),y) -> a#(y,t())
    a#(lambda(x),y) -> a#(x,1()) ->
    a#(lambda(x),y) -> lambda#(a(x,1()))
    a#(lambda(x),y) -> a#(x,1()) -> a#(lambda(x),y) -> a#(x,1())
    a#(lambda(x),y) -> a#(x,a(y,t())) ->
    a#(a(x,y),z) -> a#(x,a(y,z))
    a#(lambda(x),y) -> a#(x,a(y,t())) -> a#(a(x,y),z) -> a#(y,z)
    a#(lambda(x),y) -> a#(x,a(y,t())) ->
    a#(lambda(x),y) -> lambda#(a(x,a(y,t())))
    a#(lambda(x),y) -> a#(x,a(y,t())) ->
    a#(lambda(x),y) -> a#(x,a(y,t()))
    a#(lambda(x),y) -> a#(x,a(y,t())) ->
    a#(lambda(x),y) -> a#(y,t())
    a#(lambda(x),y) -> a#(x,a(y,t())) ->
    a#(lambda(x),y) -> lambda#(a(x,1()))
    a#(lambda(x),y) -> a#(x,a(y,t())) -> a#(lambda(x),y) -> a#(x,1())
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 35/49
    DPs:
     a#(a(x,y),z) -> a#(y,z)
     a#(lambda(x),y) -> a#(x,1())
     a#(lambda(x),y) -> a#(y,t())
     a#(lambda(x),y) -> a#(x,a(y,t()))
     a#(a(x,y),z) -> a#(x,a(y,z))
    TRS:
     a(lambda(x),y) -> lambda(a(x,1()))
     a(lambda(x),y) -> lambda(a(x,a(y,t())))
     a(a(x,y),z) -> a(x,a(y,z))
     lambda(x) -> x
     a(x,y) -> x
     a(x,y) -> y
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [a#](x0, x1) = 2x0 + 2x1,
      
      [t] = 0,
      
      [1] = 0,
      
      [a](x0, x1) = x0 + x1,
      
      [lambda](x0) = x0 + 1
     orientation:
      a#(a(x,y),z) = 2x + 2y + 2z >= 2y + 2z = a#(y,z)
      
      a#(lambda(x),y) = 2x + 2y + 2 >= 2x = a#(x,1())
      
      a#(lambda(x),y) = 2x + 2y + 2 >= 2y = a#(y,t())
      
      a#(lambda(x),y) = 2x + 2y + 2 >= 2x + 2y = a#(x,a(y,t()))
      
      a#(a(x,y),z) = 2x + 2y + 2z >= 2x + 2y + 2z = a#(x,a(y,z))
      
      a(lambda(x),y) = x + y + 1 >= x + 1 = lambda(a(x,1()))
      
      a(lambda(x),y) = x + y + 1 >= x + y + 1 = lambda(a(x,a(y,t())))
      
      a(a(x,y),z) = x + y + z >= x + y + z = a(x,a(y,z))
      
      lambda(x) = x + 1 >= x = x
      
      a(x,y) = x + y >= x = x
      
      a(x,y) = x + y >= y = y
     problem:
      DPs:
       a#(a(x,y),z) -> a#(y,z)
       a#(a(x,y),z) -> a#(x,a(y,z))
      TRS:
       a(lambda(x),y) -> lambda(a(x,1()))
       a(lambda(x),y) -> lambda(a(x,a(y,t())))
       a(a(x,y),z) -> a(x,a(y,z))
       lambda(x) -> x
       a(x,y) -> x
       a(x,y) -> y
     Subterm Criterion Processor:
      simple projection:
       pi(a#) = 0
      problem:
       DPs:
        
       TRS:
        a(lambda(x),y) -> lambda(a(x,1()))
        a(lambda(x),y) -> lambda(a(x,a(y,t())))
        a(a(x,y),z) -> a(x,a(y,z))
        lambda(x) -> x
        a(x,y) -> x
        a(x,y) -> y
      Qed