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


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YES

Problem:
 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)))

Proof:
 DP Processor:
  DPs:
   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))
  TRS:
   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)))
  TDG Processor:
   DPs:
    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))
   TRS:
    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)))
   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#(x,y) -> quot#(x,y,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)
   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:
      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)))
    EDG Processor:
     DPs:
      div#(x,y) -> quot#(x,y,y)
      quot#(x,0(),s(z)) -> div#(x,s(z))
     TRS:
      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)))
     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: {9,8}
       transitions:
        div{#,1}(7,10) -> 9*
        s1(7) -> 10*
        quot{#,1}(7,7,7) -> 8*
        div{#,2}(7,11) -> 8*
        s2(7) -> 11*
        quot{#,2}(7,10,10) -> 9*
        quot{#,3}(7,11,11) -> 8*
        div{#,0}(7,7) -> 8*
        quot{#,0}(7,7,7) -> 9*
        00() -> 7*
        s0(7) -> 7*
        div0(7,7) -> 7*
        quot0(7,7,7) -> 7*
      problem:
       DPs:
        
       TRS:
        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)))
      Qed