/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:
 2nd(cons1(X,cons(Y,Z))) -> Y
 2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   2nd#(cons(X,X1)) -> activate#(X1)
   2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
   activate#(n__from(X)) -> activate#(X)
   activate#(n__from(X)) -> from#(activate(X))
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
  TRS:
   2nd(cons1(X,cons(Y,Z))) -> Y
   2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
   from(X) -> cons(X,n__from(n__s(X)))
   from(X) -> n__from(X)
   s(X) -> n__s(X)
   activate(n__from(X)) -> from(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X
  TDG Processor:
   DPs:
    2nd#(cons(X,X1)) -> activate#(X1)
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    activate#(n__from(X)) -> activate#(X)
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> s#(activate(X))
   TRS:
    2nd(cons1(X,cons(Y,Z))) -> Y
    2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
    from(X) -> cons(X,n__from(n__s(X)))
    from(X) -> n__from(X)
    s(X) -> n__s(X)
    activate(n__from(X)) -> from(activate(X))
    activate(n__s(X)) -> s(activate(X))
    activate(X) -> X
   graph:
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__from(X)) -> activate#(X) ->
    activate#(n__from(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> s#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__s(X)) -> activate#(X)
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__from(X)) -> from#(activate(X))
    activate#(n__s(X)) -> activate#(X) ->
    activate#(n__from(X)) -> activate#(X)
    2nd#(cons(X,X1)) -> activate#(X1) ->
    activate#(n__s(X)) -> s#(activate(X))
    2nd#(cons(X,X1)) -> activate#(X1) ->
    activate#(n__s(X)) -> activate#(X)
    2nd#(cons(X,X1)) -> activate#(X1) ->
    activate#(n__from(X)) -> from#(activate(X))
    2nd#(cons(X,X1)) -> activate#(X1) ->
    activate#(n__from(X)) -> activate#(X)
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1))) ->
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1))) -> 2nd#(cons(X,X1)) -> activate#(X1)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 14/36
    DPs:
     2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
    TRS:
     2nd(cons1(X,cons(Y,Z))) -> Y
     2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
     from(X) -> cons(X,n__from(n__s(X)))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
    EDG Processor:
     DPs:
      2nd#(cons(X,X1)) -> 2nd#(cons1(X,activate(X1)))
     TRS:
      2nd(cons1(X,cons(Y,Z))) -> Y
      2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
      from(X) -> cons(X,n__from(n__s(X)))
      from(X) -> n__from(X)
      s(X) -> n__s(X)
      activate(n__from(X)) -> from(activate(X))
      activate(n__s(X)) -> s(activate(X))
      activate(X) -> X
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     activate#(n__from(X)) -> activate#(X)
     activate#(n__s(X)) -> activate#(X)
    TRS:
     2nd(cons1(X,cons(Y,Z))) -> Y
     2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
     from(X) -> cons(X,n__from(n__s(X)))
     from(X) -> n__from(X)
     s(X) -> n__s(X)
     activate(n__from(X)) -> from(activate(X))
     activate(n__s(X)) -> s(activate(X))
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(activate#) = 0
     problem:
      DPs:
       
      TRS:
       2nd(cons1(X,cons(Y,Z))) -> Y
       2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
       from(X) -> cons(X,n__from(n__s(X)))
       from(X) -> n__from(X)
       s(X) -> n__s(X)
       activate(n__from(X)) -> from(activate(X))
       activate(n__s(X)) -> s(activate(X))
       activate(X) -> X
     Qed