YES

Problem:
 rev(nil()) -> nil()
 rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
 rev1(x,nil()) -> x
 rev1(x,++(y,z)) -> rev1(y,z)
 rev2(x,nil()) -> nil()
 rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))

Proof:
 DP Processor:
  DPs:
   rev#(++(x,y)) -> rev2#(x,y)
   rev#(++(x,y)) -> rev1#(x,y)
   rev1#(x,++(y,z)) -> rev1#(y,z)
   rev2#(x,++(y,z)) -> rev2#(y,z)
   rev2#(x,++(y,z)) -> rev#(rev2(y,z))
   rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
  TRS:
   rev(nil()) -> nil()
   rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
   rev1(x,nil()) -> x
   rev1(x,++(y,z)) -> rev1(y,z)
   rev2(x,nil()) -> nil()
   rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
  TDG Processor:
   DPs:
    rev#(++(x,y)) -> rev2#(x,y)
    rev#(++(x,y)) -> rev1#(x,y)
    rev1#(x,++(y,z)) -> rev1#(y,z)
    rev2#(x,++(y,z)) -> rev2#(y,z)
    rev2#(x,++(y,z)) -> rev#(rev2(y,z))
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
   TRS:
    rev(nil()) -> nil()
    rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
    rev1(x,nil()) -> x
    rev1(x,++(y,z)) -> rev1(y,z)
    rev2(x,nil()) -> nil()
    rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
   graph:
    rev1#(x,++(y,z)) -> rev1#(y,z) -> rev1#(x,++(y,z)) -> rev1#(y,z)
    rev2#(x,++(y,z)) -> rev2#(y,z) ->
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
    rev2#(x,++(y,z)) -> rev2#(y,z) ->
    rev2#(x,++(y,z)) -> rev#(rev2(y,z))
    rev2#(x,++(y,z)) -> rev2#(y,z) ->
    rev2#(x,++(y,z)) -> rev2#(y,z)
    rev2#(x,++(y,z)) -> rev#(rev2(y,z)) ->
    rev#(++(x,y)) -> rev1#(x,y)
    rev2#(x,++(y,z)) -> rev#(rev2(y,z)) ->
    rev#(++(x,y)) -> rev2#(x,y)
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z)))) ->
    rev#(++(x,y)) -> rev1#(x,y)
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z)))) ->
    rev#(++(x,y)) -> rev2#(x,y)
    rev#(++(x,y)) -> rev1#(x,y) -> rev1#(x,++(y,z)) -> rev1#(y,z)
    rev#(++(x,y)) -> rev2#(x,y) ->
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
    rev#(++(x,y)) -> rev2#(x,y) -> rev2#(x,++(y,z)) -> rev#(rev2(y,z))
    rev#(++(x,y)) -> rev2#(x,y) -> rev2#(x,++(y,z)) -> rev2#(y,z)
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 12/36
    DPs:
     rev2#(x,++(y,z)) -> rev2#(y,z)
     rev2#(x,++(y,z)) -> rev#(rev2(y,z))
     rev#(++(x,y)) -> rev2#(x,y)
     rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
    TRS:
     rev(nil()) -> nil()
     rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
     rev1(x,nil()) -> x
     rev1(x,++(y,z)) -> rev1(y,z)
     rev2(x,nil()) -> nil()
     rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      rev(nil()) -> nil()
      rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
      rev2(x,nil()) -> nil()
      rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
     interpretation:
      [rev2#](x0, x1) = 2x1 + 0,
      
      [rev#](x0) = x0 + 2,
      
      [rev2](x0, x1) = x1,
      
      [rev1](x0, x1) = 3x0 + x1,
      
      [++](x0, x1) = 4x1 + 0,
      
      [rev](x0) = x0,
      
      [nil] = 4
     orientation:
      rev2#(x,++(y,z)) = 6z + 2 >= 2z + 0 = rev2#(y,z)
      
      rev2#(x,++(y,z)) = 6z + 2 >= z + 2 = rev#(rev2(y,z))
      
      rev#(++(x,y)) = 4y + 2 >= 2y + 0 = rev2#(x,y)
      
      rev2#(x,++(y,z)) = 6z + 2 >= 4z + 2 = rev#(++(x,rev(rev2(y,z))))
      
      rev(nil()) = 4 >= 4 = nil()
      
      rev(++(x,y)) = 4y + 0 >= 4y + 0 = ++(rev1(x,y),rev2(x,y))
      
      rev1(x,nil()) = 3x + 4 >= x = x
      
      rev1(x,++(y,z)) = 3x + 4z + 0 >= 3y + z = rev1(y,z)
      
      rev2(x,nil()) = 4 >= 4 = nil()
      
      rev2(x,++(y,z)) = 4z + 0 >= 4z + 0 = rev(++(x,rev(rev2(y,z))))
     problem:
      DPs:
       rev2#(x,++(y,z)) -> rev#(rev2(y,z))
       rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
      TRS:
       rev(nil()) -> nil()
       rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
       rev1(x,nil()) -> x
       rev1(x,++(y,z)) -> rev1(y,z)
       rev2(x,nil()) -> nil()
       rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
     Restore Modifier:
      DPs:
       rev2#(x,++(y,z)) -> rev#(rev2(y,z))
       rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
      TRS:
       rev(nil()) -> nil()
       rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
       rev1(x,nil()) -> x
       rev1(x,++(y,z)) -> rev1(y,z)
       rev2(x,nil()) -> nil()
       rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 8/4
       
    
    DPs:
     rev1#(x,++(y,z)) -> rev1#(y,z)
    TRS:
     rev(nil()) -> nil()
     rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
     rev1(x,nil()) -> x
     rev1(x,++(y,z)) -> rev1(y,z)
     rev2(x,nil()) -> nil()
     rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
    Subterm Criterion Processor:
     simple projection:
      pi(rev1#) = 1
     problem:
      DPs:
       
      TRS:
       rev(nil()) -> nil()
       rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
       rev1(x,nil()) -> x
       rev1(x,++(y,z)) -> rev1(y,z)
       rev2(x,nil()) -> nil()
       rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
     Qed