/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:
 rev(nil()) -> nil()
 rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
 rev1(x,nil()) -> x
 rev1(x,++(y,z)) -> rev1(y,z)
 rev2(x,nil()) -> nil()
 rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))

Proof:
 DP Processor:
  DPs:
   rev#(++(x,y)) -> rev2#(x,y)
   rev#(++(x,y)) -> rev1#(x,y)
   rev1#(x,++(y,z)) -> rev1#(y,z)
   rev2#(x,++(y,z)) -> rev2#(y,z)
   rev2#(x,++(y,z)) -> rev#(rev2(y,z))
   rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
  TRS:
   rev(nil()) -> nil()
   rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
   rev1(x,nil()) -> x
   rev1(x,++(y,z)) -> rev1(y,z)
   rev2(x,nil()) -> nil()
   rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
  TDG Processor:
   DPs:
    rev#(++(x,y)) -> rev2#(x,y)
    rev#(++(x,y)) -> rev1#(x,y)
    rev1#(x,++(y,z)) -> rev1#(y,z)
    rev2#(x,++(y,z)) -> rev2#(y,z)
    rev2#(x,++(y,z)) -> rev#(rev2(y,z))
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
   TRS:
    rev(nil()) -> nil()
    rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
    rev1(x,nil()) -> x
    rev1(x,++(y,z)) -> rev1(y,z)
    rev2(x,nil()) -> nil()
    rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
   graph:
    rev1#(x,++(y,z)) -> rev1#(y,z) -> rev1#(x,++(y,z)) -> rev1#(y,z)
    rev2#(x,++(y,z)) -> rev2#(y,z) ->
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
    rev2#(x,++(y,z)) -> rev2#(y,z) ->
    rev2#(x,++(y,z)) -> rev#(rev2(y,z))
    rev2#(x,++(y,z)) -> rev2#(y,z) ->
    rev2#(x,++(y,z)) -> rev2#(y,z)
    rev2#(x,++(y,z)) -> rev#(rev2(y,z)) ->
    rev#(++(x,y)) -> rev1#(x,y)
    rev2#(x,++(y,z)) -> rev#(rev2(y,z)) ->
    rev#(++(x,y)) -> rev2#(x,y)
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z)))) ->
    rev#(++(x,y)) -> rev1#(x,y)
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z)))) ->
    rev#(++(x,y)) -> rev2#(x,y)
    rev#(++(x,y)) -> rev1#(x,y) -> rev1#(x,++(y,z)) -> rev1#(y,z)
    rev#(++(x,y)) -> rev2#(x,y) ->
    rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
    rev#(++(x,y)) -> rev2#(x,y) -> rev2#(x,++(y,z)) -> rev#(rev2(y,z))
    rev#(++(x,y)) -> rev2#(x,y) -> rev2#(x,++(y,z)) -> rev2#(y,z)
   SCC Processor:
    #sccs: 2
    #rules: 5
    #arcs: 12/36
    DPs:
     rev2#(x,++(y,z)) -> rev2#(y,z)
     rev2#(x,++(y,z)) -> rev#(rev2(y,z))
     rev#(++(x,y)) -> rev2#(x,y)
     rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
    TRS:
     rev(nil()) -> nil()
     rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
     rev1(x,nil()) -> x
     rev1(x,++(y,z)) -> rev1(y,z)
     rev2(x,nil()) -> nil()
     rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
    Subterm Criterion Processor:
     simple projection:
      pi(rev) = 0
      pi(++) = [1,1]
      pi(rev2) = 1
      pi(rev#) = 0
      pi(rev2#) = 1
     problem:
      DPs:
       rev2#(x,++(y,z)) -> rev#(++(x,rev(rev2(y,z))))
      TRS:
       rev(nil()) -> nil()
       rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
       rev1(x,nil()) -> x
       rev1(x,++(y,z)) -> rev1(y,z)
       rev2(x,nil()) -> nil()
       rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 8/1
      
    
    DPs:
     rev1#(x,++(y,z)) -> rev1#(y,z)
    TRS:
     rev(nil()) -> nil()
     rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
     rev1(x,nil()) -> x
     rev1(x,++(y,z)) -> rev1(y,z)
     rev2(x,nil()) -> nil()
     rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
    Subterm Criterion Processor:
     simple projection:
      pi(rev1#) = 1
     problem:
      DPs:
       
      TRS:
       rev(nil()) -> nil()
       rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
       rev1(x,nil()) -> x
       rev1(x,++(y,z)) -> rev1(y,z)
       rev2(x,nil()) -> nil()
       rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
     Qed