/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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))

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))
  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))
  TDG 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))
   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))
   graph:
    quot#(s(x),s(y),z) -> quot#(x,y,z) ->
    quot#(x,0(),s(z)) -> div#(x,s(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)) ->
    div#(div(x,y),z) -> div#(x,times(y,z))
    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#(x,y) -> quot#(x,y,y)
    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) -> div#(x,times(y,z)) ->
    div#(div(x,y),z) -> 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) -> times#(y,z) ->
    times#(s(x),y) -> plus#(y,times(x,y))
    div#(div(x,y),z) -> times#(y,z) -> times#(s(x),y) -> times#(x,y)
    div#(x,y) -> quot#(x,y,y) -> quot#(x,0(),s(z)) -> div#(x,s(z))
    div#(x,y) -> quot#(x,y,y) -> quot#(s(x),s(y),z) -> quot#(x,y,z)
    times#(s(x),y) -> times#(x,y) ->
    times#(s(x),y) -> plus#(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)) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 6
    #arcs: 16/64
    DPs:
     quot#(s(x),s(y),z) -> quot#(x,y,z)
     quot#(x,0(),s(z)) -> div#(x,s(z))
     div#(x,y) -> quot#(x,y,y)
     div#(div(x,y),z) -> div#(x,times(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))
    Subterm Criterion Processor:
     simple projection:
      pi(div#) = 0
      pi(quot#) = 0
     problem:
      DPs:
       quot#(x,0(),s(z)) -> div#(x,s(z))
       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))
     EDG Processor:
      DPs:
       quot#(x,0(),s(z)) -> div#(x,s(z))
       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))
      graph:
       quot#(x,0(),s(z)) -> div#(x,s(z)) -> div#(x,y) -> quot#(x,y,y)
       div#(x,y) -> quot#(x,y,y) -> quot#(x,0(),s(z)) -> div#(x,s(z))
      Bounds Processor:
       bound: 3
       enrichment: top-dp
       automaton:
        final states: {11,10}
        transitions:
         div0(9,9) -> 9*
         quot0(9,9,9) -> 9*
         quot{#,1}(9,9,9) -> 11*
         div{#,1}(9,13) -> 10*
         s1(9) -> 13*
         quot{#,2}(9,13,13) -> 10*
         div{#,2}(9,14) -> 11*
         s2(9) -> 14*
         quot{#,3}(9,14,14) -> 11*
         quot{#,0}(9,9,9) -> 10*
         00() -> 9*
         s0(9) -> 9*
         div{#,0}(9,9) -> 11*
         plus0(9,9) -> 9*
         times0(9,9) -> 9*
       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))
       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))
    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))
     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))
    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))
     Qed