YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 quot(0(),s(y)) -> 0()
 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 minus(minus(x,y),z) -> minus(x,plus(y,z))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   plus#(s(x),y) -> plus#(x,y)
   minus#(minus(x,y),z) -> plus#(y,z)
   minus#(minus(x,y),z) -> minus#(x,plus(y,z))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   minus(minus(x,y),z) -> minus(x,plus(y,z))
  TDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    plus#(s(x),y) -> plus#(x,y)
    minus#(minus(x,y),z) -> plus#(y,z)
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    minus(minus(x,y),z) -> minus(x,plus(y,z))
   graph:
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(s(x),y) -> plus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> plus#(y,z)
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    minus#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> plus#(y,z)
    minus#(s(x),s(y)) -> minus#(x,y) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(minus(x,y),z) -> plus#(y,z) ->
    plus#(s(x),y) -> plus#(x,y)
    minus#(minus(x,y),z) -> minus#(x,plus(y,z)) ->
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    minus#(minus(x,y),z) -> minus#(x,plus(y,z)) ->
    minus#(minus(x,y),z) -> plus#(y,z)
    minus#(minus(x,y),z) -> minus#(x,plus(y,z)) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 13/36
    DPs:
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
    Usable Rule Processor:
     DPs:
      quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      minus(minus(x,y),z) -> minus(x,plus(y,z))
      plus(0(),y) -> y
      plus(s(x),y) -> s(plus(x,y))
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       minus(minus(x,y),z) -> minus(x,plus(y,z))
      interpretation:
       [quot#](x0, x1) = x0,
       
       [plus](x0, x1) = -4x0 + 1x1 + -2,
       
       [s](x0) = 1x0 + 0,
       
       [minus](x0, x1) = x0 + -4,
       
       [0] = 4
      orientation:
       quot#(s(x),s(y)) = 1x + 0 >= x + -4 = quot#(minus(x,y),s(y))
       
       minus(x,0()) = x + -4 >= x = x
       
       minus(s(x),s(y)) = 1x + 0 >= x + -4 = minus(x,y)
       
       minus(minus(x,y),z) = x + -4 >= x + -4 = minus(x,plus(y,z))
       
       plus(0(),y) = 1y + 0 >= y = y
       
       plus(s(x),y) = -3x + 1y + -2 >= -3x + 2y + 0 = s(plus(x,y))
      problem:
       DPs:
        
       TRS:
        minus(x,0()) -> x
        minus(s(x),s(y)) -> minus(x,y)
        minus(minus(x,y),z) -> minus(x,plus(y,z))
        plus(0(),y) -> y
        plus(s(x),y) -> s(plus(x,y))
      Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
     minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
     Qed
    
    DPs:
     plus#(s(x),y) -> plus#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
     Qed