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

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)
   plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
   plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
  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))
   plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
   plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
  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)
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
   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))
    plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
    plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
   graph:
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0()))) ->
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0()))) ->
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0()))) ->
    plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(s(x),y) -> plus#(x,y)
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
    plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
    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#(s(x),s(y)) -> minus#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #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))
     plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
     plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
    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)
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
      interpretation:
       [quot#](x0, x1) = 3x0 + -16,
       
       [s](x0) = 1x0 + -3,
       
       [minus](x0, x1) = x0 + -11,
       
       [0] = 8
      orientation:
       quot#(s(x),s(y)) = 4x + 0 >= 3x + -8 = quot#(minus(x,y),s(y))
       
       minus(x,0()) = x + -11 >= x = x
       
       minus(s(x),s(y)) = 1x + -3 >= x + -11 = minus(x,y)
      problem:
       DPs:
        
       TRS:
        minus(x,0()) -> x
        minus(s(x),s(y)) -> minus(x,y)
      Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(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))
     plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
     plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 1
     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))
       plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
       plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
     Qed
    
    DPs:
     plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
     plus#(s(x),y) -> plus#(x,y)
     plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
    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))
     plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
     plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
    CDG Processor:
     DPs:
      plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
      plus#(s(x),y) -> plus#(x,y)
      plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
     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))
      plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
      plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
     graph:
      plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0()))) ->
      plus#(s(x),y) -> plus#(x,y)
      plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
      plus#(s(x),y) -> plus#(x,y) ->
      plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
      plus#(s(x),y) -> plus#(x,y) ->
      plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
      plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
      plus#(s(x),y) -> plus#(x,y)
      plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
      plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
      plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0()))) ->
      plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
     Usable Rule Processor:
      DPs:
       plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
       plus#(s(x),y) -> plus#(x,y)
       plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
      TRS:
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
       plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
       minus(s(x),s(y)) -> minus(x,y)
       minus(x,0()) -> x
      Semantic Labeling Processor:
       dimension: 1
       usable rules:
        
       interpretation:
        [plus](x0, x1) = x0 + x1,
        
        [s](x0) = x0 + 1,
        
        [minus](x0, x1) = 2x0,
        
        [0] = 0
        labeled:
         plus#
        usable (for model):
         plus#
         plus
         s
         0
         minus
        argument filtering:
         pi(0) = []
         pi(minus) = 0
         pi(s) = 0
         pi(plus) = 0
         pi(plus#) = []
       precedence:
        plus# ~ plus ~ s ~ minus ~ 0
       problem:
        DPs:
         plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
         plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
        TRS:
         plus(0(),y) -> y
         plus(s(x),y) -> s(plus(x,y))
         plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
         plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
         minus(s(x),s(y)) -> minus(x,y)
         minus(x,0()) -> x
       Restore Modifier:
        DPs:
         plus#(plus(x,s(0())),plus(y,s(s(z)))) -> plus#(plus(y,s(s(z))),plus(x,s(0())))
         plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
        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))
         plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
         plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 7/4
         DPs:
          plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
         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))
          plus(minus(x,s(0())),minus(y,s(s(z)))) -> plus(minus(y,s(s(z))),minus(x,s(0())))
          plus(plus(x,s(0())),plus(y,s(s(z)))) -> plus(plus(y,s(s(z))),plus(x,s(0())))
         Usable Rule Processor:
          DPs:
           plus#(minus(x,s(0())),minus(y,s(s(z)))) -> plus#(minus(y,s(s(z))),minus(x,s(0())))
          TRS:
           minus(s(x),s(y)) -> minus(x,y)
           minus(x,0()) -> x
          Semantic Labeling Processor:
           dimension: 2
           usable rules:
            
           interpretation:
                      [1 1]     [0]
            [s](x0) = [0 0]x0 + [1],
            
                              [1 1]     [1 0]  
            [minus](x0, x1) = [1 1]x0 + [0 0]x1,
            
                  [0]
            [0] = [0]
            labeled:
             plus#
             s
            usable (for model):
             plus#
             minus
             s
             0
            argument filtering:
             pi(0) = []
             pi(minus) = 1
             pi(s) = []
             pi(plus#) = []
           precedence:
            plus# ~ s ~ minus ~ 0
           problem:
            DPs:
             
            TRS:
             minus(s(x),s(y)) -> minus(x,y)
             minus(x,0()) -> x
           Qed