/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:
 rev(nil()) -> nil()
 rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
 rev1(0(),nil()) -> 0()
 rev1(s(x),nil()) -> s(x)
 rev1(x,cons(y,l)) -> rev1(y,l)
 rev2(x,nil()) -> nil()
 rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))

Proof:
 DP Processor:
  DPs:
   rev#(cons(x,l)) -> rev2#(x,l)
   rev#(cons(x,l)) -> rev1#(x,l)
   rev1#(x,cons(y,l)) -> rev1#(y,l)
   rev2#(x,cons(y,l)) -> rev2#(y,l)
   rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l)))
  TRS:
   rev(nil()) -> nil()
   rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
   rev1(0(),nil()) -> 0()
   rev1(s(x),nil()) -> s(x)
   rev1(x,cons(y,l)) -> rev1(y,l)
   rev2(x,nil()) -> nil()
   rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))
  TDG Processor:
   DPs:
    rev#(cons(x,l)) -> rev2#(x,l)
    rev#(cons(x,l)) -> rev1#(x,l)
    rev1#(x,cons(y,l)) -> rev1#(y,l)
    rev2#(x,cons(y,l)) -> rev2#(y,l)
    rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l)))
   TRS:
    rev(nil()) -> nil()
    rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
    rev1(0(),nil()) -> 0()
    rev1(s(x),nil()) -> s(x)
    rev1(x,cons(y,l)) -> rev1(y,l)
    rev2(x,nil()) -> nil()
    rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))
   graph:
    rev1#(x,cons(y,l)) -> rev1#(y,l) ->
    rev1#(x,cons(y,l)) -> rev1#(y,l)
    rev2#(x,cons(y,l)) -> rev2#(y,l) ->
    rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l)))
    rev2#(x,cons(y,l)) -> rev2#(y,l) ->
    rev2#(x,cons(y,l)) -> rev2#(y,l)
    rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l))) ->
    rev#(cons(x,l)) -> rev1#(x,l)
    rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l))) ->
    rev#(cons(x,l)) -> rev2#(x,l)
    rev#(cons(x,l)) -> rev1#(x,l) -> rev1#(x,cons(y,l)) -> rev1#(y,l)
    rev#(cons(x,l)) -> rev2#(x,l) ->
    rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l)))
    rev#(cons(x,l)) -> rev2#(x,l) -> rev2#(x,cons(y,l)) -> rev2#(y,l)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 8/25
    DPs:
     rev2#(x,cons(y,l)) -> rev2#(y,l)
     rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l)))
     rev#(cons(x,l)) -> rev2#(x,l)
    TRS:
     rev(nil()) -> nil()
     rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
     rev1(0(),nil()) -> 0()
     rev1(s(x),nil()) -> s(x)
     rev1(x,cons(y,l)) -> rev1(y,l)
     rev2(x,nil()) -> nil()
     rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))
    Subterm Criterion Processor:
     simple projection:
      pi(rev) = 0
      pi(cons) = [1,1]
      pi(rev2) = 1
      pi(rev#) = 0
      pi(rev2#) = 1
     problem:
      DPs:
       rev2#(x,cons(y,l)) -> rev#(cons(x,rev2(y,l)))
      TRS:
       rev(nil()) -> nil()
       rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
       rev1(0(),nil()) -> 0()
       rev1(s(x),nil()) -> s(x)
       rev1(x,cons(y,l)) -> rev1(y,l)
       rev2(x,nil()) -> nil()
       rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 5/1
      
    
    DPs:
     rev1#(x,cons(y,l)) -> rev1#(y,l)
    TRS:
     rev(nil()) -> nil()
     rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
     rev1(0(),nil()) -> 0()
     rev1(s(x),nil()) -> s(x)
     rev1(x,cons(y,l)) -> rev1(y,l)
     rev2(x,nil()) -> nil()
     rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))
    Subterm Criterion Processor:
     simple projection:
      pi(rev1#) = 1
     problem:
      DPs:
       
      TRS:
       rev(nil()) -> nil()
       rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l))
       rev1(0(),nil()) -> 0()
       rev1(s(x),nil()) -> s(x)
       rev1(x,cons(y,l)) -> rev1(y,l)
       rev2(x,nil()) -> nil()
       rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l)))
     Qed