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
  Usable Rule 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)))))
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [cond#](x0, x1) = x0 + 1,
     
     [admit#](x0, x1) = 4x0 + 4x1 + 0,
     
     [cond](x0, x1) = x1 + 0,
     
     [carry](x0, x1, x2) = x1,
     
     [=](x0, x1) = x0 + x1 + 1,
     
     [sum](x0, x1, x2) = x0 + x2 + 1,
     
     [.](x0, x1) = 1x0 + 1x1 + 0,
     
     [w] = 0,
     
     [admit](x0, x1) = 4x0 + x1 + 1,
     
     [nil] = 4
    orientation:
     admit#(x,.(u,.(v,.(w(),z)))) = 5u + 6v + 4x + 7z + 7 >= 4u + 4z + 0 = admit#(carry(x,u,v),z)
     
     admit#(x,.(u,.(v,.(w(),z)))) = 5u + 6v + 4x + 7z + 7 >= v + x + 1 = cond#(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
     
     admit(x,nil()) = 4x + 4 >= 4 = nil()
     
     admit(x,.(u,.(v,.(w(),z)))) = 1u + 2v + 4x + 3z + 3 >= 7u + 2v + 3z + 4 = cond(=(sum(x,u,v),w()),.(u,.(v,.(w(),admit(carry(x,u,v),z)))))
    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)))))
    Qed