YES

Problem:
 rev(nil()) -> nil()
 rev(.(x,y)) -> ++(rev(y),.(x,nil()))
 car(.(x,y)) -> x
 cdr(.(x,y)) -> y
 null(nil()) -> true()
 null(.(x,y)) -> false()
 ++(nil(),y) -> y
 ++(.(x,y),z) -> .(x,++(y,z))

Proof:
 DP Processor:
  DPs:
   rev#(.(x,y)) -> rev#(y)
   rev#(.(x,y)) -> ++#(rev(y),.(x,nil()))
   ++#(.(x,y),z) -> ++#(y,z)
  TRS:
   rev(nil()) -> nil()
   rev(.(x,y)) -> ++(rev(y),.(x,nil()))
   car(.(x,y)) -> x
   cdr(.(x,y)) -> y
   null(nil()) -> true()
   null(.(x,y)) -> false()
   ++(nil(),y) -> y
   ++(.(x,y),z) -> .(x,++(y,z))
  Usable Rule Processor:
   DPs:
    rev#(.(x,y)) -> rev#(y)
    rev#(.(x,y)) -> ++#(rev(y),.(x,nil()))
    ++#(.(x,y),z) -> ++#(y,z)
   TRS:
    rev(nil()) -> nil()
    rev(.(x,y)) -> ++(rev(y),.(x,nil()))
    ++(nil(),y) -> y
    ++(.(x,y),z) -> .(x,++(y,z))
   ADG Processor:
    DPs:
     rev#(.(x,y)) -> rev#(y)
     rev#(.(x,y)) -> ++#(rev(y),.(x,nil()))
     ++#(.(x,y),z) -> ++#(y,z)
    TRS:
     rev(nil()) -> nil()
     rev(.(x,y)) -> ++(rev(y),.(x,nil()))
     ++(nil(),y) -> y
     ++(.(x,y),z) -> .(x,++(y,z))
    graph:
     ++#(.(x,y),z) -> ++#(y,z) -> ++#(.(x,y),z) -> ++#(y,z)
     rev#(.(x,y)) -> ++#(rev(y),.(x,nil())) -> ++#(.(x,y),z) -> ++#(y,z)
     rev#(.(x,y)) -> rev#(y) -> rev#(.(x,y)) -> rev#(y)
     rev#(.(x,y)) -> rev#(y) -> rev#(.(x,y)) -> ++#(rev(y),.(x,nil()))
    Restore Modifier:
     DPs:
      rev#(.(x,y)) -> rev#(y)
      rev#(.(x,y)) -> ++#(rev(y),.(x,nil()))
      ++#(.(x,y),z) -> ++#(y,z)
     TRS:
      rev(nil()) -> nil()
      rev(.(x,y)) -> ++(rev(y),.(x,nil()))
      car(.(x,y)) -> x
      cdr(.(x,y)) -> y
      null(nil()) -> true()
      null(.(x,y)) -> false()
      ++(nil(),y) -> y
      ++(.(x,y),z) -> .(x,++(y,z))
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       rev#(.(x,y)) -> rev#(y)
      TRS:
       rev(nil()) -> nil()
       rev(.(x,y)) -> ++(rev(y),.(x,nil()))
       car(.(x,y)) -> x
       cdr(.(x,y)) -> y
       null(nil()) -> true()
       null(.(x,y)) -> false()
       ++(nil(),y) -> y
       ++(.(x,y),z) -> .(x,++(y,z))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [rev#](x0) = x0 + 1,
        
        [false] = 1,
        
        [true] = 0,
        
        [null](x0) = 1,
        
        [cdr](x0) = x0,
        
        [car](x0) = x0,
        
        [++](x0, x1) = x0 + x1,
        
        [.](x0, x1) = x0 + x1 + 1,
        
        [rev](x0) = x0,
        
        [nil] = 0
       orientation:
        rev#(.(x,y)) = x + y + 2 >= y + 1 = rev#(y)
        
        rev(nil()) = 0 >= 0 = nil()
        
        rev(.(x,y)) = x + y + 1 >= x + y + 1 = ++(rev(y),.(x,nil()))
        
        car(.(x,y)) = x + y + 1 >= x = x
        
        cdr(.(x,y)) = x + y + 1 >= y = y
        
        null(nil()) = 1 >= 0 = true()
        
        null(.(x,y)) = 1 >= 1 = false()
        
        ++(nil(),y) = y >= y = y
        
        ++(.(x,y),z) = x + y + z + 1 >= x + y + z + 1 = .(x,++(y,z))
       problem:
        DPs:
         
        TRS:
         rev(nil()) -> nil()
         rev(.(x,y)) -> ++(rev(y),.(x,nil()))
         car(.(x,y)) -> x
         cdr(.(x,y)) -> y
         null(nil()) -> true()
         null(.(x,y)) -> false()
         ++(nil(),y) -> y
         ++(.(x,y),z) -> .(x,++(y,z))
       Qed
      
      DPs:
       ++#(.(x,y),z) -> ++#(y,z)
      TRS:
       rev(nil()) -> nil()
       rev(.(x,y)) -> ++(rev(y),.(x,nil()))
       car(.(x,y)) -> x
       cdr(.(x,y)) -> y
       null(nil()) -> true()
       null(.(x,y)) -> false()
       ++(nil(),y) -> y
       ++(.(x,y),z) -> .(x,++(y,z))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [++#](x0, x1) = x0 + 1,
        
        [false] = 0,
        
        [true] = 0,
        
        [null](x0) = 0,
        
        [cdr](x0) = x0,
        
        [car](x0) = x0,
        
        [++](x0, x1) = x0 + x1,
        
        [.](x0, x1) = x0 + x1 + 1,
        
        [rev](x0) = x0 + 1,
        
        [nil] = 0
       orientation:
        ++#(.(x,y),z) = x + y + 2 >= y + 1 = ++#(y,z)
        
        rev(nil()) = 1 >= 0 = nil()
        
        rev(.(x,y)) = x + y + 2 >= x + y + 2 = ++(rev(y),.(x,nil()))
        
        car(.(x,y)) = x + y + 1 >= x = x
        
        cdr(.(x,y)) = x + y + 1 >= y = y
        
        null(nil()) = 0 >= 0 = true()
        
        null(.(x,y)) = 0 >= 0 = false()
        
        ++(nil(),y) = y >= y = y
        
        ++(.(x,y),z) = x + y + z + 1 >= x + y + z + 1 = .(x,++(y,z))
       problem:
        DPs:
         
        TRS:
         rev(nil()) -> nil()
         rev(.(x,y)) -> ++(rev(y),.(x,nil()))
         car(.(x,y)) -> x
         cdr(.(x,y)) -> y
         null(nil()) -> true()
         null(.(x,y)) -> false()
         ++(nil(),y) -> y
         ++(.(x,y),z) -> .(x,++(y,z))
       Qed