YES

Problem:
 plus(x,0()) -> x
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 times(0(),y) -> 0()
 times(s(0()),y) -> y
 times(s(x),y) -> plus(y,times(x,y))
 div(0(),y) -> 0()
 div(x,y) -> quot(x,y,y)
 quot(0(),s(y),z) -> 0()
 quot(s(x),s(y),z) -> quot(x,y,z)
 quot(x,0(),s(z)) -> s(div(x,s(z)))
 div(div(x,y),z) -> div(x,times(y,z))
 eq(0(),0()) -> true()
 eq(s(x),0()) -> false()
 eq(0(),s(y)) -> false()
 eq(s(x),s(y)) -> eq(x,y)
 divides(y,x) -> eq(x,times(div(x,y),y))
 prime(s(s(x))) -> pr(s(s(x)),s(x))
 pr(x,s(0())) -> true()
 pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
 if(true(),x,y) -> false()
 if(false(),x,y) -> pr(x,y)

Proof:
 DP Processor:
  DPs:
   plus#(s(x),y) -> plus#(x,y)
   times#(s(x),y) -> times#(x,y)
   times#(s(x),y) -> plus#(y,times(x,y))
   div#(x,y) -> quot#(x,y,y)
   quot#(s(x),s(y),z) -> quot#(x,y,z)
   quot#(x,0(),s(z)) -> div#(x,s(z))
   div#(div(x,y),z) -> times#(y,z)
   div#(div(x,y),z) -> div#(x,times(y,z))
   eq#(s(x),s(y)) -> eq#(x,y)
   divides#(y,x) -> div#(x,y)
   divides#(y,x) -> times#(div(x,y),y)
   divides#(y,x) -> eq#(x,times(div(x,y),y))
   prime#(s(s(x))) -> pr#(s(s(x)),s(x))
   pr#(x,s(s(y))) -> divides#(s(s(y)),x)
   pr#(x,s(s(y))) -> if#(divides(s(s(y)),x),x,s(y))
   if#(false(),x,y) -> pr#(x,y)
  TRS:
   plus(x,0()) -> x
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   times(0(),y) -> 0()
   times(s(0()),y) -> y
   times(s(x),y) -> plus(y,times(x,y))
   div(0(),y) -> 0()
   div(x,y) -> quot(x,y,y)
   quot(0(),s(y),z) -> 0()
   quot(s(x),s(y),z) -> quot(x,y,z)
   quot(x,0(),s(z)) -> s(div(x,s(z)))
   div(div(x,y),z) -> div(x,times(y,z))
   eq(0(),0()) -> true()
   eq(s(x),0()) -> false()
   eq(0(),s(y)) -> false()
   eq(s(x),s(y)) -> eq(x,y)
   divides(y,x) -> eq(x,times(div(x,y),y))
   prime(s(s(x))) -> pr(s(s(x)),s(x))
   pr(x,s(0())) -> true()
   pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
   if(true(),x,y) -> false()
   if(false(),x,y) -> pr(x,y)
  EDG Processor:
   DPs:
    plus#(s(x),y) -> plus#(x,y)
    times#(s(x),y) -> times#(x,y)
    times#(s(x),y) -> plus#(y,times(x,y))
    div#(x,y) -> quot#(x,y,y)
    quot#(s(x),s(y),z) -> quot#(x,y,z)
    quot#(x,0(),s(z)) -> div#(x,s(z))
    div#(div(x,y),z) -> times#(y,z)
    div#(div(x,y),z) -> div#(x,times(y,z))
    eq#(s(x),s(y)) -> eq#(x,y)
    divides#(y,x) -> div#(x,y)
    divides#(y,x) -> times#(div(x,y),y)
    divides#(y,x) -> eq#(x,times(div(x,y),y))
    prime#(s(s(x))) -> pr#(s(s(x)),s(x))
    pr#(x,s(s(y))) -> divides#(s(s(y)),x)
    pr#(x,s(s(y))) -> if#(divides(s(s(y)),x),x,s(y))
    if#(false(),x,y) -> pr#(x,y)
   TRS:
    plus(x,0()) -> x
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    times(0(),y) -> 0()
    times(s(0()),y) -> y
    times(s(x),y) -> plus(y,times(x,y))
    div(0(),y) -> 0()
    div(x,y) -> quot(x,y,y)
    quot(0(),s(y),z) -> 0()
    quot(s(x),s(y),z) -> quot(x,y,z)
    quot(x,0(),s(z)) -> s(div(x,s(z)))
    div(div(x,y),z) -> div(x,times(y,z))
    eq(0(),0()) -> true()
    eq(s(x),0()) -> false()
    eq(0(),s(y)) -> false()
    eq(s(x),s(y)) -> eq(x,y)
    divides(y,x) -> eq(x,times(div(x,y),y))
    prime(s(s(x))) -> pr(s(s(x)),s(x))
    pr(x,s(0())) -> true()
    pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
    if(true(),x,y) -> false()
    if(false(),x,y) -> pr(x,y)
   graph:
    if#(false(),x,y) -> pr#(x,y) ->
    pr#(x,s(s(y))) -> divides#(s(s(y)),x)
    if#(false(),x,y) -> pr#(x,y) ->
    pr#(x,s(s(y))) -> if#(divides(s(s(y)),x),x,s(y))
    pr#(x,s(s(y))) -> if#(divides(s(s(y)),x),x,s(y)) ->
    if#(false(),x,y) -> pr#(x,y)
    pr#(x,s(s(y))) -> divides#(s(s(y)),x) ->
    divides#(y,x) -> div#(x,y)
    pr#(x,s(s(y))) -> divides#(s(s(y)),x) ->
    divides#(y,x) -> times#(div(x,y),y)
    pr#(x,s(s(y))) -> divides#(s(s(y)),x) ->
    divides#(y,x) -> eq#(x,times(div(x,y),y))
    prime#(s(s(x))) -> pr#(s(s(x)),s(x)) ->
    pr#(x,s(s(y))) -> divides#(s(s(y)),x)
    prime#(s(s(x))) -> pr#(s(s(x)),s(x)) ->
    pr#(x,s(s(y))) -> if#(divides(s(s(y)),x),x,s(y))
    divides#(y,x) -> eq#(x,times(div(x,y),y)) ->
    eq#(s(x),s(y)) -> eq#(x,y)
    divides#(y,x) -> div#(x,y) -> div#(x,y) -> quot#(x,y,y)
    divides#(y,x) -> div#(x,y) -> div#(div(x,y),z) -> times#(y,z)
    divides#(y,x) -> div#(x,y) ->
    div#(div(x,y),z) -> div#(x,times(y,z))
    divides#(y,x) -> times#(div(x,y),y) ->
    times#(s(x),y) -> times#(x,y)
    divides#(y,x) -> times#(div(x,y),y) ->
    times#(s(x),y) -> plus#(y,times(x,y))
    eq#(s(x),s(y)) -> eq#(x,y) -> eq#(s(x),s(y)) -> eq#(x,y)
    quot#(s(x),s(y),z) -> quot#(x,y,z) ->
    quot#(s(x),s(y),z) -> quot#(x,y,z)
    quot#(s(x),s(y),z) -> quot#(x,y,z) ->
    quot#(x,0(),s(z)) -> div#(x,s(z))
    quot#(x,0(),s(z)) -> div#(x,s(z)) -> div#(x,y) -> quot#(x,y,y)
    quot#(x,0(),s(z)) -> div#(x,s(z)) ->
    div#(div(x,y),z) -> times#(y,z)
    quot#(x,0(),s(z)) -> div#(x,s(z)) ->
    div#(div(x,y),z) -> div#(x,times(y,z))
    div#(div(x,y),z) -> div#(x,times(y,z)) ->
    div#(x,y) -> quot#(x,y,y)
    div#(div(x,y),z) -> div#(x,times(y,z)) ->
    div#(div(x,y),z) -> times#(y,z)
    div#(div(x,y),z) -> div#(x,times(y,z)) ->
    div#(div(x,y),z) -> div#(x,times(y,z))
    div#(div(x,y),z) -> times#(y,z) -> times#(s(x),y) -> times#(x,y)
    div#(div(x,y),z) -> times#(y,z) ->
    times#(s(x),y) -> plus#(y,times(x,y))
    div#(x,y) -> quot#(x,y,y) -> quot#(s(x),s(y),z) -> quot#(x,y,z)
    div#(x,y) -> quot#(x,y,y) -> quot#(x,0(),s(z)) -> div#(x,s(z))
    times#(s(x),y) -> times#(x,y) -> times#(s(x),y) -> times#(x,y)
    times#(s(x),y) -> times#(x,y) ->
    times#(s(x),y) -> plus#(y,times(x,y))
    times#(s(x),y) -> plus#(y,times(x,y)) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 9
    #arcs: 31/256
    DPs:
     if#(false(),x,y) -> pr#(x,y)
     pr#(x,s(s(y))) -> if#(divides(s(s(y)),x),x,s(y))
    TRS:
     plus(x,0()) -> x
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(0()),y) -> y
     times(s(x),y) -> plus(y,times(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,times(y,z))
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(y)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     divides(y,x) -> eq(x,times(div(x,y),y))
     prime(s(s(x))) -> pr(s(s(x)),s(x))
     pr(x,s(0())) -> true()
     pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
     if(true(),x,y) -> false()
     if(false(),x,y) -> pr(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(pr#) = 1
      pi(if#) = 2
     problem:
      DPs:
       if#(false(),x,y) -> pr#(x,y)
      TRS:
       plus(x,0()) -> x
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(0()),y) -> y
       times(s(x),y) -> plus(y,times(x,y))
       div(0(),y) -> 0()
       div(x,y) -> quot(x,y,y)
       quot(0(),s(y),z) -> 0()
       quot(s(x),s(y),z) -> quot(x,y,z)
       quot(x,0(),s(z)) -> s(div(x,s(z)))
       div(div(x,y),z) -> div(x,times(y,z))
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(y)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       divides(y,x) -> eq(x,times(div(x,y),y))
       prime(s(s(x))) -> pr(s(s(x)),s(x))
       pr(x,s(0())) -> true()
       pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
       if(true(),x,y) -> false()
       if(false(),x,y) -> pr(x,y)
     Bounds Processor:
      bound: 0
      enrichment: top-dp
      automaton:
       final states: {7}
       transitions:
        false0() -> 5*
        pr{#,0}(5,5) -> 7*
        pr{#,0}(5,7) -> 7*
        pr{#,0}(6,6) -> 7*
        pr{#,0}(7,5) -> 7*
        pr{#,0}(7,7) -> 7*
        pr{#,0}(5,6) -> 7*
        pr{#,0}(6,5) -> 7*
        pr{#,0}(6,7) -> 7*
        pr{#,0}(7,6) -> 7*
        plus0(5,5) -> 6*
        plus0(5,7) -> 6*
        plus0(6,6) -> 6*
        plus0(7,5) -> 6*
        plus0(7,7) -> 6*
        plus0(5,6) -> 6*
        plus0(6,5) -> 6*
        plus0(6,7) -> 6*
        plus0(7,6) -> 6*
        00() -> 6*
        s0(5) -> 6*
        s0(7) -> 6*
        s0(6) -> 6*
        times0(5,5) -> 6*
        times0(5,7) -> 6*
        times0(6,6) -> 6*
        times0(7,5) -> 6*
        times0(7,7) -> 6*
        times0(5,6) -> 6*
        times0(6,5) -> 6*
        times0(6,7) -> 6*
        times0(7,6) -> 6*
        div0(5,5) -> 6*
        div0(5,7) -> 6*
        div0(6,6) -> 6*
        div0(7,5) -> 6*
        div0(7,7) -> 6*
        div0(5,6) -> 6*
        div0(6,5) -> 6*
        div0(6,7) -> 6*
        div0(7,6) -> 6*
        quot0(6,5,7) -> 6*
        quot0(6,7,7) -> 6*
        quot0(7,5,5) -> 6*
        quot0(5,5,6) -> 6*
        quot0(7,7,5) -> 6*
        quot0(5,7,6) -> 6*
        quot0(7,6,7) -> 6*
        quot0(6,6,6) -> 6*
        quot0(7,5,6) -> 6*
        quot0(7,7,6) -> 6*
        quot0(5,6,5) -> 6*
        quot0(5,5,7) -> 6*
        quot0(5,7,7) -> 6*
        quot0(6,5,5) -> 6*
        quot0(6,7,5) -> 6*
        quot0(6,6,7) -> 6*
        quot0(7,6,5) -> 6*
        quot0(5,6,6) -> 6*
        quot0(7,5,7) -> 6*
        quot0(7,7,7) -> 6*
        quot0(6,5,6) -> 6*
        quot0(6,7,6) -> 6*
        quot0(7,6,6) -> 6*
        quot0(5,5,5) -> 6*
        quot0(5,7,5) -> 6*
        quot0(5,6,7) -> 6*
        quot0(6,6,5) -> 6*
        eq0(5,5) -> 6*
        eq0(5,7) -> 6*
        eq0(6,6) -> 6*
        eq0(7,5) -> 6*
        eq0(7,7) -> 6*
        eq0(5,6) -> 6*
        eq0(6,5) -> 6*
        eq0(6,7) -> 6*
        eq0(7,6) -> 6*
        true0() -> 6*
        divides0(5,5) -> 6*
        divides0(5,7) -> 6*
        divides0(6,6) -> 6*
        divides0(7,5) -> 6*
        divides0(7,7) -> 6*
        divides0(5,6) -> 6*
        divides0(6,5) -> 6*
        divides0(6,7) -> 6*
        divides0(7,6) -> 6*
        prime0(5) -> 6*
        prime0(7) -> 6*
        prime0(6) -> 6*
        pr0(5,5) -> 6*
        pr0(5,7) -> 6*
        pr0(6,6) -> 6*
        pr0(7,5) -> 6*
        pr0(7,7) -> 6*
        pr0(5,6) -> 6*
        pr0(6,5) -> 6*
        pr0(6,7) -> 6*
        pr0(7,6) -> 6*
        if0(6,5,7) -> 6*
        if0(6,7,7) -> 6*
        if0(7,5,5) -> 6*
        if0(5,5,6) -> 6*
        if0(7,7,5) -> 6*
        if0(5,7,6) -> 6*
        if0(7,6,7) -> 6*
        if0(6,6,6) -> 6*
        if0(7,5,6) -> 6*
        if0(7,7,6) -> 6*
        if0(5,6,5) -> 6*
        if0(5,5,7) -> 6*
        if0(5,7,7) -> 6*
        if0(6,5,5) -> 6*
        if0(6,7,5) -> 6*
        if0(6,6,7) -> 6*
        if0(7,6,5) -> 6*
        if0(5,6,6) -> 6*
        if0(7,5,7) -> 6*
        if0(7,7,7) -> 6*
        if0(6,5,6) -> 6*
        if0(6,7,6) -> 6*
        if0(7,6,6) -> 6*
        if0(5,5,5) -> 6*
        if0(5,7,5) -> 6*
        if0(5,6,7) -> 6*
        if0(6,6,5) -> 6*
        5 -> 6*
        7 -> 6*
      problem:
       DPs:
        
       TRS:
        plus(x,0()) -> x
        plus(0(),y) -> y
        plus(s(x),y) -> s(plus(x,y))
        times(0(),y) -> 0()
        times(s(0()),y) -> y
        times(s(x),y) -> plus(y,times(x,y))
        div(0(),y) -> 0()
        div(x,y) -> quot(x,y,y)
        quot(0(),s(y),z) -> 0()
        quot(s(x),s(y),z) -> quot(x,y,z)
        quot(x,0(),s(z)) -> s(div(x,s(z)))
        div(div(x,y),z) -> div(x,times(y,z))
        eq(0(),0()) -> true()
        eq(s(x),0()) -> false()
        eq(0(),s(y)) -> false()
        eq(s(x),s(y)) -> eq(x,y)
        divides(y,x) -> eq(x,times(div(x,y),y))
        prime(s(s(x))) -> pr(s(s(x)),s(x))
        pr(x,s(0())) -> true()
        pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
        if(true(),x,y) -> false()
        if(false(),x,y) -> pr(x,y)
      Qed
    
    DPs:
     div#(div(x,y),z) -> div#(x,times(y,z))
     div#(x,y) -> quot#(x,y,y)
     quot#(x,0(),s(z)) -> div#(x,s(z))
     quot#(s(x),s(y),z) -> quot#(x,y,z)
    TRS:
     plus(x,0()) -> x
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(0()),y) -> y
     times(s(x),y) -> plus(y,times(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,times(y,z))
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(y)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     divides(y,x) -> eq(x,times(div(x,y),y))
     prime(s(s(x))) -> pr(s(s(x)),s(x))
     pr(x,s(0())) -> true()
     pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
     if(true(),x,y) -> false()
     if(false(),x,y) -> pr(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(div#) = 0
      pi(quot#) = 0
     problem:
      DPs:
       div#(x,y) -> quot#(x,y,y)
       quot#(x,0(),s(z)) -> div#(x,s(z))
      TRS:
       plus(x,0()) -> x
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(0()),y) -> y
       times(s(x),y) -> plus(y,times(x,y))
       div(0(),y) -> 0()
       div(x,y) -> quot(x,y,y)
       quot(0(),s(y),z) -> 0()
       quot(s(x),s(y),z) -> quot(x,y,z)
       quot(x,0(),s(z)) -> s(div(x,s(z)))
       div(div(x,y),z) -> div(x,times(y,z))
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(y)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       divides(y,x) -> eq(x,times(div(x,y),y))
       prime(s(s(x))) -> pr(s(s(x)),s(x))
       pr(x,s(0())) -> true()
       pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
       if(true(),x,y) -> false()
       if(false(),x,y) -> pr(x,y)
     Bounds Processor:
      bound: 1
      enrichment: top-dp
      automaton:
       final states: {12}
       transitions:
        quot0(11,11,10) -> 9*
        quot0(10,9,9) -> 9*
        quot0(10,11,9) -> 9*
        quot0(9,10,12) -> 9*
        quot0(9,12,12) -> 9*
        quot0(12,10,10) -> 9*
        quot0(12,12,10) -> 9*
        quot0(11,10,9) -> 9*
        quot0(11,12,9) -> 9*
        quot0(10,9,12) -> 9*
        quot0(10,11,12) -> 9*
        quot0(9,9,11) -> 9*
        quot0(9,11,11) -> 9*
        quot0(12,9,9) -> 9*
        quot0(12,11,9) -> 9*
        quot0(11,10,12) -> 9*
        quot0(11,12,12) -> 9*
        quot0(10,10,11) -> 9*
        quot0(10,12,11) -> 9*
        quot0(9,10,10) -> 9*
        quot0(9,12,10) -> 9*
        quot0(12,9,12) -> 9*
        quot0(12,11,12) -> 9*
        quot0(11,9,11) -> 9*
        quot0(11,11,11) -> 9*
        quot0(10,9,10) -> 9*
        quot0(10,11,10) -> 9*
        quot0(9,9,9) -> 9*
        quot0(9,11,9) -> 9*
        quot0(12,10,11) -> 9*
        quot0(12,12,11) -> 9*
        quot0(11,10,10) -> 9*
        quot0(11,12,10) -> 9*
        quot0(10,10,9) -> 9*
        quot0(10,12,9) -> 9*
        quot0(9,9,12) -> 9*
        quot0(9,11,12) -> 9*
        quot0(12,9,10) -> 9*
        quot0(12,11,10) -> 9*
        quot0(11,9,9) -> 9*
        quot0(11,11,9) -> 9*
        quot0(10,10,12) -> 9*
        quot0(10,12,12) -> 9*
        quot0(9,10,11) -> 9*
        quot0(9,12,11) -> 9*
        quot0(12,10,9) -> 9*
        quot0(12,12,9) -> 9*
        quot0(11,9,12) -> 9*
        quot0(11,11,12) -> 9*
        quot0(10,9,11) -> 9*
        quot0(10,11,11) -> 9*
        quot0(9,9,10) -> 9*
        quot0(9,11,10) -> 9*
        quot0(12,10,12) -> 9*
        quot0(12,12,12) -> 9*
        quot0(11,10,11) -> 9*
        quot0(11,12,11) -> 9*
        quot0(10,10,10) -> 9*
        quot0(10,12,10) -> 9*
        quot0(9,10,9) -> 9*
        quot0(9,12,9) -> 9*
        quot0(12,9,11) -> 9*
        quot0(12,11,11) -> 9*
        quot0(11,9,10) -> 9*
        eq0(12,10) -> 9*
        eq0(12,12) -> 9*
        eq0(9,10) -> 9*
        eq0(9,12) -> 9*
        eq0(10,9) -> 9*
        eq0(10,11) -> 9*
        eq0(11,10) -> 9*
        eq0(11,12) -> 9*
        eq0(12,9) -> 9*
        eq0(12,11) -> 9*
        eq0(9,9) -> 9*
        eq0(9,11) -> 9*
        eq0(10,10) -> 9*
        eq0(10,12) -> 9*
        eq0(11,9) -> 9*
        eq0(11,11) -> 9*
        true0() -> 9*
        divides0(12,10) -> 9*
        divides0(12,12) -> 9*
        divides0(9,10) -> 9*
        divides0(9,12) -> 9*
        divides0(10,9) -> 9*
        divides0(10,11) -> 9*
        divides0(11,10) -> 9*
        divides0(11,12) -> 9*
        divides0(12,9) -> 9*
        divides0(12,11) -> 9*
        divides0(9,9) -> 9*
        divides0(9,11) -> 9*
        divides0(10,10) -> 9*
        divides0(10,12) -> 9*
        divides0(11,9) -> 9*
        divides0(11,11) -> 9*
        prime0(10) -> 9*
        prime0(12) -> 9*
        prime0(9) -> 9*
        prime0(11) -> 9*
        pr0(12,10) -> 9*
        pr0(12,12) -> 9*
        pr0(9,10) -> 9*
        pr0(9,12) -> 9*
        pr0(10,9) -> 9*
        pr0(10,11) -> 9*
        pr0(11,10) -> 9*
        pr0(11,12) -> 9*
        pr0(12,9) -> 9*
        pr0(12,11) -> 9*
        pr0(9,9) -> 9*
        pr0(9,11) -> 9*
        pr0(10,10) -> 9*
        pr0(10,12) -> 9*
        pr0(11,9) -> 9*
        pr0(11,11) -> 9*
        if0(11,11,10) -> 9*
        if0(10,9,9) -> 9*
        if0(10,11,9) -> 9*
        if0(9,10,12) -> 9*
        if0(9,12,12) -> 9*
        if0(12,10,10) -> 9*
        if0(12,12,10) -> 9*
        if0(11,10,9) -> 9*
        if0(11,12,9) -> 9*
        if0(10,9,12) -> 9*
        if0(10,11,12) -> 9*
        if0(9,9,11) -> 9*
        if0(9,11,11) -> 9*
        if0(12,9,9) -> 9*
        if0(12,11,9) -> 9*
        if0(11,10,12) -> 9*
        if0(11,12,12) -> 9*
        if0(10,10,11) -> 9*
        if0(10,12,11) -> 9*
        if0(9,10,10) -> 9*
        if0(9,12,10) -> 9*
        if0(12,9,12) -> 9*
        if0(12,11,12) -> 9*
        if0(11,9,11) -> 9*
        if0(11,11,11) -> 9*
        if0(10,9,10) -> 9*
        if0(10,11,10) -> 9*
        if0(9,9,9) -> 9*
        if0(9,11,9) -> 9*
        if0(12,10,11) -> 9*
        if0(12,12,11) -> 9*
        if0(11,10,10) -> 9*
        if0(11,12,10) -> 9*
        if0(10,10,9) -> 9*
        if0(10,12,9) -> 9*
        if0(9,9,12) -> 9*
        if0(9,11,12) -> 9*
        if0(12,9,10) -> 9*
        if0(12,11,10) -> 9*
        if0(11,9,9) -> 9*
        if0(11,11,9) -> 9*
        if0(10,10,12) -> 9*
        if0(10,12,12) -> 9*
        if0(9,10,11) -> 9*
        if0(9,12,11) -> 9*
        if0(12,10,9) -> 9*
        if0(12,12,9) -> 9*
        if0(11,9,12) -> 9*
        if0(11,11,12) -> 9*
        if0(10,9,11) -> 9*
        if0(10,11,11) -> 9*
        if0(9,9,10) -> 9*
        if0(9,11,10) -> 9*
        if0(12,10,12) -> 9*
        if0(12,12,12) -> 9*
        if0(11,10,11) -> 9*
        if0(11,12,11) -> 9*
        if0(10,10,10) -> 9*
        if0(10,12,10) -> 9*
        if0(9,10,9) -> 9*
        if0(9,12,9) -> 9*
        if0(12,9,11) -> 9*
        if0(12,11,11) -> 9*
        if0(11,9,10) -> 9*
        div{#,0}(12,10) -> 9*
        div{#,0}(12,12) -> 9*
        div{#,0}(9,10) -> 9*
        div{#,0}(9,12) -> 9*
        div{#,0}(10,9) -> 9*
        div{#,0}(10,11) -> 12*
        div{#,0}(11,10) -> 9*
        div{#,0}(11,12) -> 9*
        div{#,0}(12,9) -> 9*
        div{#,0}(12,11) -> 12*
        div{#,0}(9,9) -> 9*
        div{#,0}(9,11) -> 12*
        div{#,0}(10,10) -> 9*
        div{#,0}(10,12) -> 9*
        div{#,0}(11,9) -> 9*
        div{#,0}(11,11) -> 12*
        quot{#,0}(11,11,10) -> 9*
        quot{#,0}(10,9,9) -> 9*
        quot{#,0}(10,11,9) -> 9*
        quot{#,0}(9,10,12) -> 9*
        quot{#,0}(9,12,12) -> 9*
        quot{#,0}(12,10,10) -> 9*
        quot{#,0}(12,12,10) -> 9*
        quot{#,0}(11,10,9) -> 9*
        quot{#,0}(11,12,9) -> 9*
        quot{#,0}(10,9,12) -> 9*
        quot{#,0}(10,11,12) -> 9*
        quot{#,0}(9,9,11) -> 9*
        quot{#,0}(9,11,11) -> 12,9
        quot{#,0}(12,9,9) -> 9*
        quot{#,0}(12,11,9) -> 9*
        quot{#,0}(11,10,12) -> 9*
        quot{#,0}(11,12,12) -> 9*
        quot{#,0}(10,10,11) -> 9*
        quot{#,0}(10,12,11) -> 9*
        quot{#,0}(9,10,10) -> 9*
        quot{#,0}(9,12,10) -> 9*
        quot{#,0}(12,9,12) -> 9*
        quot{#,0}(12,11,12) -> 9*
        quot{#,0}(11,9,11) -> 9*
        quot{#,0}(11,11,11) -> 12,9
        quot{#,0}(10,9,10) -> 9*
        quot{#,0}(10,11,10) -> 9*
        quot{#,0}(9,9,9) -> 9*
        quot{#,0}(9,11,9) -> 9*
        quot{#,0}(12,10,11) -> 9*
        quot{#,0}(12,12,11) -> 9*
        quot{#,0}(11,10,10) -> 9*
        quot{#,0}(11,12,10) -> 9*
        quot{#,0}(10,10,9) -> 9*
        quot{#,0}(10,12,9) -> 9*
        quot{#,0}(9,9,12) -> 9*
        quot{#,0}(9,11,12) -> 9*
        quot{#,0}(12,9,10) -> 9*
        quot{#,0}(12,11,10) -> 9*
        quot{#,0}(11,9,9) -> 9*
        quot{#,0}(11,11,9) -> 9*
        quot{#,0}(10,10,12) -> 9*
        quot{#,0}(10,12,12) -> 9*
        quot{#,0}(9,10,11) -> 9*
        quot{#,0}(9,12,11) -> 9*
        quot{#,0}(12,10,9) -> 9*
        quot{#,0}(12,12,9) -> 9*
        quot{#,0}(11,9,12) -> 9*
        quot{#,0}(11,11,12) -> 9*
        quot{#,0}(10,9,11) -> 9*
        quot{#,0}(10,11,11) -> 12,9
        quot{#,0}(9,9,10) -> 9*
        quot{#,0}(9,11,10) -> 9*
        quot{#,0}(12,10,12) -> 9*
        quot{#,0}(12,12,12) -> 9*
        quot{#,0}(11,10,11) -> 9*
        quot{#,0}(11,12,11) -> 9*
        quot{#,0}(10,10,10) -> 9*
        quot{#,0}(10,12,10) -> 9*
        quot{#,0}(9,10,9) -> 9*
        quot{#,0}(9,12,9) -> 9*
        quot{#,0}(12,9,11) -> 9*
        quot{#,0}(12,11,11) -> 12,9
        quot{#,0}(11,9,10) -> 9*
        quot{#,1}(10,13,13) -> 9*
        quot{#,1}(12,13,13) -> 9*
        quot{#,1}(9,13,13) -> 9*
        quot{#,1}(11,13,13) -> 9*
        div{#,1}(10,13) -> 9*
        div{#,1}(12,13) -> 9*
        div{#,1}(9,13) -> 9*
        div{#,1}(11,13) -> 9*
        s1(10) -> 13*
        s1(12) -> 13*
        s1(9) -> 13*
        s1(11) -> 13*
        false0() -> 9*
        plus0(12,10) -> 9*
        plus0(12,12) -> 9*
        plus0(9,10) -> 9*
        plus0(9,12) -> 9*
        plus0(10,9) -> 9*
        plus0(10,11) -> 9*
        plus0(11,10) -> 9*
        plus0(11,12) -> 9*
        plus0(12,9) -> 9*
        plus0(12,11) -> 9*
        plus0(9,9) -> 9*
        plus0(9,11) -> 9*
        plus0(10,10) -> 9*
        plus0(10,12) -> 9*
        plus0(11,9) -> 9*
        plus0(11,11) -> 9*
        00() -> 10*
        s0(10) -> 11*
        s0(12) -> 11*
        s0(9) -> 11*
        s0(11) -> 11*
        times0(12,10) -> 9*
        times0(12,12) -> 9*
        times0(9,10) -> 9*
        times0(9,12) -> 9*
        times0(10,9) -> 9*
        times0(10,11) -> 9*
        times0(11,10) -> 9*
        times0(11,12) -> 9*
        times0(12,9) -> 9*
        times0(12,11) -> 9*
        times0(9,9) -> 9*
        times0(9,11) -> 9*
        times0(10,10) -> 9*
        times0(10,12) -> 9*
        times0(11,9) -> 9*
        times0(11,11) -> 9*
        div0(12,10) -> 9*
        div0(12,12) -> 9*
        div0(9,10) -> 9*
        div0(9,12) -> 9*
        div0(10,9) -> 9*
        div0(10,11) -> 9*
        div0(11,10) -> 9*
        div0(11,12) -> 9*
        div0(12,9) -> 9*
        div0(12,11) -> 9*
        div0(9,9) -> 9*
        div0(9,11) -> 9*
        div0(10,10) -> 9*
        div0(10,12) -> 9*
        div0(11,9) -> 9*
        div0(11,11) -> 9*
        10 -> 9*
        11 -> 9*
        12 -> 9*
      problem:
       DPs:
        div#(x,y) -> quot#(x,y,y)
       TRS:
        plus(x,0()) -> x
        plus(0(),y) -> y
        plus(s(x),y) -> s(plus(x,y))
        times(0(),y) -> 0()
        times(s(0()),y) -> y
        times(s(x),y) -> plus(y,times(x,y))
        div(0(),y) -> 0()
        div(x,y) -> quot(x,y,y)
        quot(0(),s(y),z) -> 0()
        quot(s(x),s(y),z) -> quot(x,y,z)
        quot(x,0(),s(z)) -> s(div(x,s(z)))
        div(div(x,y),z) -> div(x,times(y,z))
        eq(0(),0()) -> true()
        eq(s(x),0()) -> false()
        eq(0(),s(y)) -> false()
        eq(s(x),s(y)) -> eq(x,y)
        divides(y,x) -> eq(x,times(div(x,y),y))
        prime(s(s(x))) -> pr(s(s(x)),s(x))
        pr(x,s(0())) -> true()
        pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
        if(true(),x,y) -> false()
        if(false(),x,y) -> pr(x,y)
      Bounds Processor:
       bound: 0
       enrichment: top-dp
       automaton:
        final states: {3}
        transitions:
         times0(3,1) -> 1*
         times0(3,3) -> 1*
         times0(1,1) -> 1*
         times0(1,3) -> 1*
         div0(3,1) -> 1*
         div0(3,3) -> 1*
         div0(1,1) -> 1*
         div0(1,3) -> 1*
         quot0(1,1,1) -> 1*
         quot0(1,3,1) -> 1*
         quot0(3,1,1) -> 1*
         quot0(3,3,1) -> 1*
         quot0(1,1,3) -> 1*
         quot0(1,3,3) -> 1*
         quot0(3,1,3) -> 1*
         quot0(3,3,3) -> 1*
         eq0(3,1) -> 1*
         eq0(3,3) -> 1*
         eq0(1,1) -> 1*
         eq0(1,3) -> 1*
         true0() -> 1*
         divides0(3,1) -> 1*
         divides0(3,3) -> 1*
         divides0(1,1) -> 1*
         divides0(1,3) -> 1*
         prime0(1) -> 1*
         prime0(3) -> 1*
         pr0(3,1) -> 1*
         pr0(3,3) -> 1*
         pr0(1,1) -> 1*
         pr0(1,3) -> 1*
         if0(1,1,1) -> 1*
         if0(1,3,1) -> 1*
         if0(3,1,1) -> 1*
         if0(3,3,1) -> 1*
         if0(1,1,3) -> 1*
         if0(1,3,3) -> 1*
         if0(3,1,3) -> 1*
         if0(3,3,3) -> 1*
         quot{#,0}(1,1,1) -> 3*
         quot{#,0}(1,3,1) -> 3*
         quot{#,0}(3,1,1) -> 3*
         quot{#,0}(3,3,1) -> 3*
         quot{#,0}(1,1,3) -> 3*
         quot{#,0}(1,3,3) -> 3*
         quot{#,0}(3,1,3) -> 3*
         quot{#,0}(3,3,3) -> 3*
         false0() -> 1*
         plus0(3,1) -> 1*
         plus0(3,3) -> 1*
         plus0(1,1) -> 1*
         plus0(1,3) -> 1*
         00() -> 1*
         s0(1) -> 1*
         s0(3) -> 1*
         3 -> 1*
       problem:
        DPs:
         
        TRS:
         plus(x,0()) -> x
         plus(0(),y) -> y
         plus(s(x),y) -> s(plus(x,y))
         times(0(),y) -> 0()
         times(s(0()),y) -> y
         times(s(x),y) -> plus(y,times(x,y))
         div(0(),y) -> 0()
         div(x,y) -> quot(x,y,y)
         quot(0(),s(y),z) -> 0()
         quot(s(x),s(y),z) -> quot(x,y,z)
         quot(x,0(),s(z)) -> s(div(x,s(z)))
         div(div(x,y),z) -> div(x,times(y,z))
         eq(0(),0()) -> true()
         eq(s(x),0()) -> false()
         eq(0(),s(y)) -> false()
         eq(s(x),s(y)) -> eq(x,y)
         divides(y,x) -> eq(x,times(div(x,y),y))
         prime(s(s(x))) -> pr(s(s(x)),s(x))
         pr(x,s(0())) -> true()
         pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
         if(true(),x,y) -> false()
         if(false(),x,y) -> pr(x,y)
       Qed
    
    DPs:
     times#(s(x),y) -> times#(x,y)
    TRS:
     plus(x,0()) -> x
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(0()),y) -> y
     times(s(x),y) -> plus(y,times(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,times(y,z))
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(y)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     divides(y,x) -> eq(x,times(div(x,y),y))
     prime(s(s(x))) -> pr(s(s(x)),s(x))
     pr(x,s(0())) -> true()
     pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
     if(true(),x,y) -> false()
     if(false(),x,y) -> pr(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(times#) = 0
     problem:
      DPs:
       
      TRS:
       plus(x,0()) -> x
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(0()),y) -> y
       times(s(x),y) -> plus(y,times(x,y))
       div(0(),y) -> 0()
       div(x,y) -> quot(x,y,y)
       quot(0(),s(y),z) -> 0()
       quot(s(x),s(y),z) -> quot(x,y,z)
       quot(x,0(),s(z)) -> s(div(x,s(z)))
       div(div(x,y),z) -> div(x,times(y,z))
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(y)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       divides(y,x) -> eq(x,times(div(x,y),y))
       prime(s(s(x))) -> pr(s(s(x)),s(x))
       pr(x,s(0())) -> true()
       pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
       if(true(),x,y) -> false()
       if(false(),x,y) -> pr(x,y)
     Qed
    
    DPs:
     plus#(s(x),y) -> plus#(x,y)
    TRS:
     plus(x,0()) -> x
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(0()),y) -> y
     times(s(x),y) -> plus(y,times(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,times(y,z))
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(y)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     divides(y,x) -> eq(x,times(div(x,y),y))
     prime(s(s(x))) -> pr(s(s(x)),s(x))
     pr(x,s(0())) -> true()
     pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
     if(true(),x,y) -> false()
     if(false(),x,y) -> pr(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       plus(x,0()) -> x
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(0()),y) -> y
       times(s(x),y) -> plus(y,times(x,y))
       div(0(),y) -> 0()
       div(x,y) -> quot(x,y,y)
       quot(0(),s(y),z) -> 0()
       quot(s(x),s(y),z) -> quot(x,y,z)
       quot(x,0(),s(z)) -> s(div(x,s(z)))
       div(div(x,y),z) -> div(x,times(y,z))
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(y)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       divides(y,x) -> eq(x,times(div(x,y),y))
       prime(s(s(x))) -> pr(s(s(x)),s(x))
       pr(x,s(0())) -> true()
       pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
       if(true(),x,y) -> false()
       if(false(),x,y) -> pr(x,y)
     Qed
    
    DPs:
     eq#(s(x),s(y)) -> eq#(x,y)
    TRS:
     plus(x,0()) -> x
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(0()),y) -> y
     times(s(x),y) -> plus(y,times(x,y))
     div(0(),y) -> 0()
     div(x,y) -> quot(x,y,y)
     quot(0(),s(y),z) -> 0()
     quot(s(x),s(y),z) -> quot(x,y,z)
     quot(x,0(),s(z)) -> s(div(x,s(z)))
     div(div(x,y),z) -> div(x,times(y,z))
     eq(0(),0()) -> true()
     eq(s(x),0()) -> false()
     eq(0(),s(y)) -> false()
     eq(s(x),s(y)) -> eq(x,y)
     divides(y,x) -> eq(x,times(div(x,y),y))
     prime(s(s(x))) -> pr(s(s(x)),s(x))
     pr(x,s(0())) -> true()
     pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
     if(true(),x,y) -> false()
     if(false(),x,y) -> pr(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(eq#) = 1
     problem:
      DPs:
       
      TRS:
       plus(x,0()) -> x
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(0()),y) -> y
       times(s(x),y) -> plus(y,times(x,y))
       div(0(),y) -> 0()
       div(x,y) -> quot(x,y,y)
       quot(0(),s(y),z) -> 0()
       quot(s(x),s(y),z) -> quot(x,y,z)
       quot(x,0(),s(z)) -> s(div(x,s(z)))
       div(div(x,y),z) -> div(x,times(y,z))
       eq(0(),0()) -> true()
       eq(s(x),0()) -> false()
       eq(0(),s(y)) -> false()
       eq(s(x),s(y)) -> eq(x,y)
       divides(y,x) -> eq(x,times(div(x,y),y))
       prime(s(s(x))) -> pr(s(s(x)),s(x))
       pr(x,s(0())) -> true()
       pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y))
       if(true(),x,y) -> false()
       if(false(),x,y) -> pr(x,y)
     Qed