/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:
 from(X) -> cons(X,n__from(s(X)))
 sel(0(),cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
 minus(X,0()) -> 0()
 minus(s(X),s(Y)) -> minus(X,Y)
 quot(0(),s(Y)) -> 0()
 quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
 zWquot(XS,nil()) -> nil()
 zWquot(nil(),XS) -> nil()
 zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
 from(X) -> n__from(X)
 zWquot(X1,X2) -> n__zWquot(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   sel#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
   minus#(s(X),s(Y)) -> minus#(X,Y)
   quot#(s(X),s(Y)) -> minus#(X,Y)
   quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
   zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
   zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
   activate#(n__from(X)) -> from#(X)
   activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
  TRS:
   from(X) -> cons(X,n__from(s(X)))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
   minus(X,0()) -> 0()
   minus(s(X),s(Y)) -> minus(X,Y)
   quot(0(),s(Y)) -> 0()
   quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
   zWquot(XS,nil()) -> nil()
   zWquot(nil(),XS) -> nil()
   zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
   from(X) -> n__from(X)
   zWquot(X1,X2) -> n__zWquot(X1,X2)
   activate(n__from(X)) -> from(X)
   activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
   activate(X) -> X
  TDG Processor:
   DPs:
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    minus#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
    activate#(n__from(X)) -> from#(X)
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
   TRS:
    from(X) -> cons(X,n__from(s(X)))
    sel(0(),cons(X,XS)) -> X
    sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
    minus(X,0()) -> 0()
    minus(s(X),s(Y)) -> minus(X,Y)
    quot(0(),s(Y)) -> 0()
    quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
    zWquot(XS,nil()) -> nil()
    zWquot(nil(),XS) -> nil()
    zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
    from(X) -> n__from(X)
    zWquot(X1,X2) -> n__zWquot(X1,X2)
    activate(n__from(X)) -> from(X)
    activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
    activate(X) -> X
   graph:
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y) ->
    quot#(s(X),s(Y)) -> minus#(X,Y)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) ->
    activate#(n__from(X)) -> from#(X)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(X)
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) ->
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) ->
    quot#(s(X),s(Y)) -> minus#(X,Y)
    quot#(s(X),s(Y)) -> minus#(X,Y) ->
    minus#(s(X),s(Y)) -> minus#(X,Y)
    minus#(s(X),s(Y)) -> minus#(X,Y) ->
    minus#(s(X),s(Y)) -> minus#(X,Y)
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) ->
    zWquot#(cons(X,XS),cons(Y,YS)) -> quot#(X,Y)
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) ->
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) ->
    zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__from(X)) -> from#(X)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) ->
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) -> sel#(s(N),cons(X,XS)) -> activate#(XS)
   SCC Processor:
    #sccs: 4
    #rules: 6
    #arcs: 17/100
    DPs:
     sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    TRS:
     from(X) -> cons(X,n__from(s(X)))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     minus(X,0()) -> 0()
     minus(s(X),s(Y)) -> minus(X,Y)
     quot(0(),s(Y)) -> 0()
     quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
     zWquot(XS,nil()) -> nil()
     zWquot(nil(),XS) -> nil()
     zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
     from(X) -> n__from(X)
     zWquot(X1,X2) -> n__zWquot(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(sel#) = 0
     problem:
      DPs:
       
      TRS:
       from(X) -> cons(X,n__from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       minus(X,0()) -> 0()
       minus(s(X),s(Y)) -> minus(X,Y)
       quot(0(),s(Y)) -> 0()
       quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
       zWquot(XS,nil()) -> nil()
       zWquot(nil(),XS) -> nil()
       zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
       from(X) -> n__from(X)
       zWquot(X1,X2) -> n__zWquot(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
       activate(X) -> X
     Qed
    
    DPs:
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS)
     activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2)
     zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS)
    TRS:
     from(X) -> cons(X,n__from(s(X)))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     minus(X,0()) -> 0()
     minus(s(X),s(Y)) -> minus(X,Y)
     quot(0(),s(Y)) -> 0()
     quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
     zWquot(XS,nil()) -> nil()
     zWquot(nil(),XS) -> nil()
     zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
     from(X) -> n__from(X)
     zWquot(X1,X2) -> n__zWquot(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
     activate(X) -> X
    Size-Change Termination Processor:
     DPs:
      
     TRS:
      from(X) -> cons(X,n__from(s(X)))
      sel(0(),cons(X,XS)) -> X
      sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
      minus(X,0()) -> 0()
      minus(s(X),s(Y)) -> minus(X,Y)
      quot(0(),s(Y)) -> 0()
      quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
      zWquot(XS,nil()) -> nil()
      zWquot(nil(),XS) -> nil()
      zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
      from(X) -> n__from(X)
      zWquot(X1,X2) -> n__zWquot(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
      activate(X) -> X
     The DP: zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(YS) has the edges:
       1 >   0
     The DP: activate#(n__zWquot(X1,X2)) -> zWquot#(X1,X2) has the edges:
       0 >   1
       0 >   0
     The DP: zWquot#(cons(X,XS),cons(Y,YS)) -> activate#(XS) has the edges:
       0 >   0
     Qed
    
    DPs:
     quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
    TRS:
     from(X) -> cons(X,n__from(s(X)))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     minus(X,0()) -> 0()
     minus(s(X),s(Y)) -> minus(X,Y)
     quot(0(),s(Y)) -> 0()
     quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
     zWquot(XS,nil()) -> nil()
     zWquot(nil(),XS) -> nil()
     zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
     from(X) -> n__from(X)
     zWquot(X1,X2) -> n__zWquot(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
     activate(X) -> X
    EDG Processor:
     DPs:
      quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y))
     TRS:
      from(X) -> cons(X,n__from(s(X)))
      sel(0(),cons(X,XS)) -> X
      sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
      minus(X,0()) -> 0()
      minus(s(X),s(Y)) -> minus(X,Y)
      quot(0(),s(Y)) -> 0()
      quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
      zWquot(XS,nil()) -> nil()
      zWquot(nil(),XS) -> nil()
      zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
      from(X) -> n__from(X)
      zWquot(X1,X2) -> n__zWquot(X1,X2)
      activate(n__from(X)) -> from(X)
      activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
      activate(X) -> X
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     minus#(s(X),s(Y)) -> minus#(X,Y)
    TRS:
     from(X) -> cons(X,n__from(s(X)))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     minus(X,0()) -> 0()
     minus(s(X),s(Y)) -> minus(X,Y)
     quot(0(),s(Y)) -> 0()
     quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
     zWquot(XS,nil()) -> nil()
     zWquot(nil(),XS) -> nil()
     zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
     from(X) -> n__from(X)
     zWquot(X1,X2) -> n__zWquot(X1,X2)
     activate(n__from(X)) -> from(X)
     activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       from(X) -> cons(X,n__from(s(X)))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       minus(X,0()) -> 0()
       minus(s(X),s(Y)) -> minus(X,Y)
       quot(0(),s(Y)) -> 0()
       quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
       zWquot(XS,nil()) -> nil()
       zWquot(nil(),XS) -> nil()
       zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
       from(X) -> n__from(X)
       zWquot(X1,X2) -> n__zWquot(X1,X2)
       activate(n__from(X)) -> from(X)
       activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
       activate(X) -> X
     Qed