/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:
 -(x,0()) -> x
 -(0(),s(y)) -> 0()
 -(s(x),s(y)) -> -(x,y)
 lt(x,0()) -> false()
 lt(0(),s(y)) -> true()
 lt(s(x),s(y)) -> lt(x,y)
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 div(x,0()) -> 0()
 div(0(),y) -> 0()
 div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))

Proof:
 DP Processor:
  DPs:
   -#(s(x),s(y)) -> -#(x,y)
   lt#(s(x),s(y)) -> lt#(x,y)
   div#(s(x),s(y)) -> -#(x,y)
   div#(s(x),s(y)) -> div#(-(x,y),s(y))
   div#(s(x),s(y)) -> lt#(x,y)
   div#(s(x),s(y)) -> if#(lt(x,y),0(),s(div(-(x,y),s(y))))
  TRS:
   -(x,0()) -> x
   -(0(),s(y)) -> 0()
   -(s(x),s(y)) -> -(x,y)
   lt(x,0()) -> false()
   lt(0(),s(y)) -> true()
   lt(s(x),s(y)) -> lt(x,y)
   if(true(),x,y) -> x
   if(false(),x,y) -> y
   div(x,0()) -> 0()
   div(0(),y) -> 0()
   div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
  TDG Processor:
   DPs:
    -#(s(x),s(y)) -> -#(x,y)
    lt#(s(x),s(y)) -> lt#(x,y)
    div#(s(x),s(y)) -> -#(x,y)
    div#(s(x),s(y)) -> div#(-(x,y),s(y))
    div#(s(x),s(y)) -> lt#(x,y)
    div#(s(x),s(y)) -> if#(lt(x,y),0(),s(div(-(x,y),s(y))))
   TRS:
    -(x,0()) -> x
    -(0(),s(y)) -> 0()
    -(s(x),s(y)) -> -(x,y)
    lt(x,0()) -> false()
    lt(0(),s(y)) -> true()
    lt(s(x),s(y)) -> lt(x,y)
    if(true(),x,y) -> x
    if(false(),x,y) -> y
    div(x,0()) -> 0()
    div(0(),y) -> 0()
    div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
   graph:
    div#(s(x),s(y)) -> div#(-(x,y),s(y)) ->
    div#(s(x),s(y)) -> if#(lt(x,y),0(),s(div(-(x,y),s(y))))
    div#(s(x),s(y)) -> div#(-(x,y),s(y)) ->
    div#(s(x),s(y)) -> lt#(x,y)
    div#(s(x),s(y)) -> div#(-(x,y),s(y)) ->
    div#(s(x),s(y)) -> div#(-(x,y),s(y))
    div#(s(x),s(y)) -> div#(-(x,y),s(y)) -> div#(s(x),s(y)) -> -#(x,y)
    div#(s(x),s(y)) -> lt#(x,y) -> lt#(s(x),s(y)) -> lt#(x,y)
    div#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    lt#(s(x),s(y)) -> lt#(x,y) -> lt#(s(x),s(y)) -> lt#(x,y)
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 8/36
    DPs:
     div#(s(x),s(y)) -> div#(-(x,y),s(y))
    TRS:
     -(x,0()) -> x
     -(0(),s(y)) -> 0()
     -(s(x),s(y)) -> -(x,y)
     lt(x,0()) -> false()
     lt(0(),s(y)) -> true()
     lt(s(x),s(y)) -> lt(x,y)
     if(true(),x,y) -> x
     if(false(),x,y) -> y
     div(x,0()) -> 0()
     div(0(),y) -> 0()
     div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
    Subterm Criterion Processor:
     simple projection:
      pi(-) = 0
      pi(div#) = 0
     problem:
      DPs:
       
      TRS:
       -(x,0()) -> x
       -(0(),s(y)) -> 0()
       -(s(x),s(y)) -> -(x,y)
       lt(x,0()) -> false()
       lt(0(),s(y)) -> true()
       lt(s(x),s(y)) -> lt(x,y)
       if(true(),x,y) -> x
       if(false(),x,y) -> y
       div(x,0()) -> 0()
       div(0(),y) -> 0()
       div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
     Qed
    
    DPs:
     lt#(s(x),s(y)) -> lt#(x,y)
    TRS:
     -(x,0()) -> x
     -(0(),s(y)) -> 0()
     -(s(x),s(y)) -> -(x,y)
     lt(x,0()) -> false()
     lt(0(),s(y)) -> true()
     lt(s(x),s(y)) -> lt(x,y)
     if(true(),x,y) -> x
     if(false(),x,y) -> y
     div(x,0()) -> 0()
     div(0(),y) -> 0()
     div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
    Subterm Criterion Processor:
     simple projection:
      pi(lt#) = 0
     problem:
      DPs:
       
      TRS:
       -(x,0()) -> x
       -(0(),s(y)) -> 0()
       -(s(x),s(y)) -> -(x,y)
       lt(x,0()) -> false()
       lt(0(),s(y)) -> true()
       lt(s(x),s(y)) -> lt(x,y)
       if(true(),x,y) -> x
       if(false(),x,y) -> y
       div(x,0()) -> 0()
       div(0(),y) -> 0()
       div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
     Qed
    
    DPs:
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     -(x,0()) -> x
     -(0(),s(y)) -> 0()
     -(s(x),s(y)) -> -(x,y)
     lt(x,0()) -> false()
     lt(0(),s(y)) -> true()
     lt(s(x),s(y)) -> lt(x,y)
     if(true(),x,y) -> x
     if(false(),x,y) -> y
     div(x,0()) -> 0()
     div(0(),y) -> 0()
     div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
    Subterm Criterion Processor:
     simple projection:
      pi(-#) = 0
     problem:
      DPs:
       
      TRS:
       -(x,0()) -> x
       -(0(),s(y)) -> 0()
       -(s(x),s(y)) -> -(x,y)
       lt(x,0()) -> false()
       lt(0(),s(y)) -> true()
       lt(s(x),s(y)) -> lt(x,y)
       if(true(),x,y) -> x
       if(false(),x,y) -> y
       div(x,0()) -> 0()
       div(0(),y) -> 0()
       div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
     Qed