/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:
 sort(nil()) -> nil()
 sort(cons(x,y)) -> insert(x,sort(y))
 insert(x,nil()) -> cons(x,nil())
 insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
 choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
 choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
 choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)

Proof:
 DP Processor:
  DPs:
   sort#(cons(x,y)) -> sort#(y)
   sort#(cons(x,y)) -> insert#(x,sort(y))
   insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
   choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w)
   choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
  TRS:
   sort(nil()) -> nil()
   sort(cons(x,y)) -> insert(x,sort(y))
   insert(x,nil()) -> cons(x,nil())
   insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
   choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
   choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
   choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
  TDG Processor:
   DPs:
    sort#(cons(x,y)) -> sort#(y)
    sort#(cons(x,y)) -> insert#(x,sort(y))
    insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
    choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w)
    choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
   TRS:
    sort(nil()) -> nil()
    sort(cons(x,y)) -> insert(x,sort(y))
    insert(x,nil()) -> cons(x,nil())
    insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
    choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
    choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
    choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
   graph:
    choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z) ->
    choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
    choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z) ->
    choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w)
    choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w) ->
    insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
    insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v) ->
    choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
    insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v) ->
    choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w)
    sort#(cons(x,y)) -> insert#(x,sort(y)) ->
    insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
    sort#(cons(x,y)) -> sort#(y) ->
    sort#(cons(x,y)) -> insert#(x,sort(y))
    sort#(cons(x,y)) -> sort#(y) -> sort#(cons(x,y)) -> sort#(y)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 8/25
    DPs:
     sort#(cons(x,y)) -> sort#(y)
    TRS:
     sort(nil()) -> nil()
     sort(cons(x,y)) -> insert(x,sort(y))
     insert(x,nil()) -> cons(x,nil())
     insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
     choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
     choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
     choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
    Subterm Criterion Processor:
     simple projection:
      pi(sort#) = 0
     problem:
      DPs:
       
      TRS:
       sort(nil()) -> nil()
       sort(cons(x,y)) -> insert(x,sort(y))
       insert(x,nil()) -> cons(x,nil())
       insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
       choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
       choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
       choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
     Qed
    
    DPs:
     choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
     choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w)
     insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
    TRS:
     sort(nil()) -> nil()
     sort(cons(x,y)) -> insert(x,sort(y))
     insert(x,nil()) -> cons(x,nil())
     insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
     choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
     choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
     choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
    Subterm Criterion Processor:
     simple projection:
      pi(insert#) = 1
      pi(choose#) = 1
     problem:
      DPs:
       choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
       insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
      TRS:
       sort(nil()) -> nil()
       sort(cons(x,y)) -> insert(x,sort(y))
       insert(x,nil()) -> cons(x,nil())
       insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
       choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
       choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
       choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 5/4
      DPs:
       choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
      TRS:
       sort(nil()) -> nil()
       sort(cons(x,y)) -> insert(x,sort(y))
       insert(x,nil()) -> cons(x,nil())
       insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
       choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
       choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
       choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
      Subterm Criterion Processor:
       simple projection:
        pi(choose#) = 2
       problem:
        DPs:
         
        TRS:
         sort(nil()) -> nil()
         sort(cons(x,y)) -> insert(x,sort(y))
         insert(x,nil()) -> cons(x,nil())
         insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
         choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
         choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
         choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
       Qed