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())))
  EDG 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#(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#(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#(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())))
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> minus#(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)) -> 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())))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [quot#](x0, x1) = x0,
      
      [plus](x0, x1) = x0 + x1,
      
      [quot](x0, x1) = x0,
      
      [s](x0) = x0 + 1,
      
      [minus](x0, x1) = x0,
      
      [0] = 0
     orientation:
      quot#(s(x),s(y)) = x + 1 >= x = quot#(minus(x,y),s(y))
      
      minus(x,0()) = x >= x = x
      
      minus(s(x),s(y)) = x + 1 >= x = minus(x,y)
      
      quot(0(),s(y)) = 0 >= 0 = 0()
      
      quot(s(x),s(y)) = x + 1 >= x + 1 = s(quot(minus(x,y),s(y)))
      
      plus(0(),y) = y >= y = y
      
      plus(s(x),y) = x + y + 1 >= x + y + 1 = s(plus(x,y))
      
      plus(minus(x,s(0())),minus(y,s(s(z)))) = x + y >= x + y = plus(minus(y,s(s(z))),minus(x,s(0())))
      
      plus(plus(x,s(0())),plus(y,s(s(z)))) = x + y + z + 3 >= x + y + z + 3 = plus(plus(y,s(s(z))),plus(x,s(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))
       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:
     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#(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)
    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())))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [plus#](x0, x1) = x0 + x1,
      
      [plus](x0, x1) = x0 + x1,
      
      [quot](x0, x1) = x0 + x1,
      
      [s](x0) = x0 + 1,
      
      [minus](x0, x1) = x0,
      
      [0] = 0
     orientation:
      plus#(plus(x,s(0())),plus(y,s(s(z)))) = x + y + z + 3 >= x + y + z + 3 = plus#(plus(y,s(s(z))),plus(x,s(0())))
      
      plus#(minus(x,s(0())),minus(y,s(s(z)))) = x + y >= x + y = plus#(minus(y,s(s(z))),minus(x,s(0())))
      
      plus#(s(x),y) = x + y + 1 >= x + y = plus#(x,y)
      
      minus(x,0()) = x >= x = x
      
      minus(s(x),s(y)) = x + 1 >= x = minus(x,y)
      
      quot(0(),s(y)) = y + 1 >= 0 = 0()
      
      quot(s(x),s(y)) = x + y + 2 >= x + y + 2 = s(quot(minus(x,y),s(y)))
      
      plus(0(),y) = y >= y = y
      
      plus(s(x),y) = x + y + 1 >= x + y + 1 = s(plus(x,y))
      
      plus(minus(x,s(0())),minus(y,s(s(z)))) = x + y >= x + y = plus(minus(y,s(s(z))),minus(x,s(0())))
      
      plus(plus(x,s(0())),plus(y,s(s(z)))) = x + y + z + 3 >= x + y + z + 3 = plus(plus(y,s(s(z))),plus(x,s(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:
       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#(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
      Bounds Processor:
       bound: 1
       enrichment: match-dp
       automaton:
        final states: {7}
        transitions:
         s0(10) -> 11*
         s0(5) -> 2*
         s0(12) -> 12*
         s0(2) -> 2*
         s0(9) -> 9*
         s0(4) -> 2*
         s0(6) -> 10*
         s0(1) -> 8,2
         s0(3) -> 2*
         00() -> 1*
         minus0(3,1) -> 5*
         minus0(3,3) -> 5*
         minus0(3,5) -> 5*
         minus0(4,2) -> 5*
         minus0(4,4) -> 5*
         minus0(5,1) -> 5*
         minus0(5,3) -> 5*
         minus0(5,5) -> 5*
         minus0(1,2) -> 5*
         minus0(1,4) -> 5*
         minus0(2,1) -> 5*
         minus0(2,3) -> 5*
         minus0(2,5) -> 5*
         minus0(3,2) -> 5*
         minus0(3,4) -> 5*
         minus0(4,1) -> 5*
         minus0(4,3) -> 5*
         minus0(4,5) -> 5*
         minus0(5,2) -> 5*
         minus0(5,4) -> 5*
         minus0(1,1) -> 5*
         minus0(1,3) -> 5*
         minus0(1,5) -> 5*
         minus0(2,2) -> 5*
         minus0(2,4) -> 5*
         plus{#,1}(30,27) -> 4,6
         plus1(2,26) -> 27*
         plus1(3,29) -> 30*
         plus1(4,26) -> 27*
         plus1(5,29) -> 30*
         plus1(1,26) -> 27*
         plus1(2,29) -> 30*
         plus1(3,26) -> 27*
         plus1(4,29) -> 30*
         plus1(5,26) -> 27*
         plus1(1,29) -> 30*
         s1(30) -> 30*
         s1(25) -> 26*
         s1(5) -> 28*
         s1(27) -> 27*
         s1(2) -> 28*
         s1(4) -> 28*
         s1(1) -> 28*
         s1(28) -> 29*
         s1(3) -> 28*
         01() -> 25*
         plus{#,0}(3,1) -> 4*
         plus{#,0}(3,3) -> 4*
         plus{#,0}(3,5) -> 4*
         plus{#,0}(4,2) -> 4*
         plus{#,0}(4,4) -> 4*
         plus{#,0}(5,1) -> 4*
         plus{#,0}(5,3) -> 4*
         plus{#,0}(5,5) -> 4*
         plus{#,0}(1,2) -> 4*
         plus{#,0}(1,4) -> 4*
         plus{#,0}(2,1) -> 4*
         plus{#,0}(2,3) -> 4*
         plus{#,0}(2,5) -> 4*
         plus{#,0}(12,9) -> 7*
         plus{#,0}(3,2) -> 4*
         plus{#,0}(3,4) -> 4*
         plus{#,0}(4,1) -> 4*
         plus{#,0}(4,3) -> 4*
         plus{#,0}(4,5) -> 4*
         plus{#,0}(5,2) -> 4*
         plus{#,0}(5,4) -> 4*
         plus{#,0}(1,1) -> 4*
         plus{#,0}(1,3) -> 4*
         plus{#,0}(1,5) -> 4*
         plus{#,0}(2,2) -> 4*
         plus{#,0}(2,4) -> 4*
         plus0(3,1) -> 3*
         plus0(3,3) -> 3*
         plus0(3,5) -> 3*
         plus0(4,2) -> 3*
         plus0(4,4) -> 3*
         plus0(5,1) -> 3*
         plus0(5,3) -> 3*
         plus0(5,5) -> 3*
         plus0(1,2) -> 3*
         plus0(1,4) -> 3*
         plus0(6,8) -> 9*
         plus0(2,1) -> 3*
         plus0(2,3) -> 3*
         plus0(2,5) -> 3*
         plus0(3,2) -> 3*
         plus0(3,4) -> 3*
         plus0(4,1) -> 3*
         plus0(4,3) -> 3*
         plus0(4,5) -> 3*
         plus0(5,2) -> 3*
         plus0(5,4) -> 3*
         plus0(1,1) -> 3*
         plus0(1,3) -> 3*
         plus0(1,5) -> 3*
         plus0(6,11) -> 12*
         plus0(2,2) -> 3*
         plus0(2,4) -> 3*
         1 -> 5,3,6
         2 -> 5,3,6
         3 -> 5,6
         4 -> 5,3,6
         5 -> 3,6
         8 -> 9*
         11 -> 12*
         26 -> 27*
         29 -> 30*
       problem:
        DPs:
         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#(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
         Bounds Processor:
          bound: 1
          enrichment: match-dp
          automaton:
           final states: {5}
           transitions:
            plus{#,0}(10,7) -> 5*
            s0(2) -> 2*
            s0(4) -> 8*
            s0(1) -> 6,2
            s0(8) -> 9*
            s0(3) -> 2*
            00() -> 1*
            minus0(3,1) -> 7,3
            minus0(3,3) -> 3*
            minus0(4,6) -> 7*
            minus0(1,2) -> 3*
            minus0(1,8) -> 10*
            minus0(2,1) -> 7,3
            minus0(2,3) -> 3*
            minus0(3,2) -> 3*
            minus0(3,4) -> 10*
            minus0(3,8) -> 10*
            minus0(4,9) -> 10*
            minus0(1,1) -> 7,3
            minus0(1,3) -> 3*
            minus0(2,2) -> 3*
            minus0(2,8) -> 10*
            plus{#,1}(22,19) -> 5*
            s1(20) -> 21*
            s1(17) -> 18*
            s1(2) -> 20*
            s1(1) -> 20*
            s1(3) -> 20*
            01() -> 17*
            minus1(2,20) -> 22*
            minus1(3,3) -> 22*
            minus1(3,17) -> 19*
            minus1(3,21) -> 22*
            minus1(1,18) -> 19*
            minus1(1,20) -> 22*
            minus1(2,17) -> 19*
            minus1(3,18) -> 19*
            minus1(3,20) -> 22*
            minus1(1,17) -> 19*
            1 -> 19,7,3,4
            2 -> 19,7,3,4
            3 -> 22,19,10,7,4
          problem:
           DPs:
            
           TRS:
            minus(s(x),s(y)) -> minus(x,y)
            minus(x,0()) -> x
          Qed