YES

Problem:
 admit(x,nil()) -> nil()
 admit(x,.(u,.(v,.(w(),z)))) -> cond(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
 cond(true(),y) -> y

Proof:
 DP Processor:
  DPs:
   admit#(x,.(u,.(v,.(w(),z)))) -> admit#(carry(x,u,v),z)
   admit#(x,.(u,.(v,.(w(),z)))) -> cond#(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
  TRS:
   admit(x,nil()) -> nil()
   admit(x,.(u,.(v,.(w(),z)))) -> cond(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
   cond(true(),y) -> y
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [cond#](x0, x1) = 4x0 + x1,
    
    [admit#](x0, x1) = 7x0 + 2x1 + 6,
    
    [true] = 4,
    
    [cond](x0, x1) = 3x0 + x1 + 2,
    
    [carry](x0, x1, x2) = x0 + x1 + 2,
    
    [=](x0, x1) = x0 + x1,
    
    [sum](x0, x1, x2) = x1,
    
    [.](x0, x1) = 4x0 + x1,
    
    [w] = 2,
    
    [admit](x0, x1) = 2x1,
    
    [nil] = 4
   orientation:
    admit#(x,.(u,.(v,.(w(),z)))) = 8u + 8v + 7x + 2z + 22 >= 7u + 7x + 2z + 20 = admit#(carry(x,u,v),z)
    
    admit#(x,.(u,.(v,.(w(),z)))) = 8u + 8v + 7x + 2z + 22 >= 8u + 4v + 2z + 16 = cond#(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
    
    admit(x,nil()) = 8 >= 4 = nil()
    
    admit(x,.(u,.(v,.(w(),z)))) = 8u + 8v + 2z + 16 >= 7u + 4v + 2z + 16 = cond(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
    
    cond(true(),y) = y + 14 >= y = y
   problem:
    DPs:
     
    TRS:
     admit(x,nil()) -> nil()
     admit(x,.(u,.(v,.(w(),z)))) -> cond(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
     cond(true(),y) -> y
   Qed