/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 purge(nil()) -> nil()
 purge(.(x,y)) -> .(x,purge(remove(x,y)))
 remove(x,nil()) -> nil()
 remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))

Proof:
 DP Processor:
  DPs:
   purge#(.(x,y)) -> remove#(x,y)
   purge#(.(x,y)) -> purge#(remove(x,y))
   remove#(x,.(y,z)) -> remove#(x,z)
  TRS:
   purge(nil()) -> nil()
   purge(.(x,y)) -> .(x,purge(remove(x,y)))
   remove(x,nil()) -> nil()
   remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
  TDG Processor:
   DPs:
    purge#(.(x,y)) -> remove#(x,y)
    purge#(.(x,y)) -> purge#(remove(x,y))
    remove#(x,.(y,z)) -> remove#(x,z)
   TRS:
    purge(nil()) -> nil()
    purge(.(x,y)) -> .(x,purge(remove(x,y)))
    remove(x,nil()) -> nil()
    remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
   graph:
    remove#(x,.(y,z)) -> remove#(x,z) ->
    remove#(x,.(y,z)) -> remove#(x,z)
    purge#(.(x,y)) -> remove#(x,y) ->
    remove#(x,.(y,z)) -> remove#(x,z)
    purge#(.(x,y)) -> purge#(remove(x,y)) ->
    purge#(.(x,y)) -> purge#(remove(x,y))
    purge#(.(x,y)) -> purge#(remove(x,y)) -> purge#(.(x,y)) -> remove#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 4/9
    DPs:
     purge#(.(x,y)) -> purge#(remove(x,y))
    TRS:
     purge(nil()) -> nil()
     purge(.(x,y)) -> .(x,purge(remove(x,y)))
     remove(x,nil()) -> nil()
     remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
    EDG Processor:
     DPs:
      purge#(.(x,y)) -> purge#(remove(x,y))
     TRS:
      purge(nil()) -> nil()
      purge(.(x,y)) -> .(x,purge(remove(x,y)))
      remove(x,nil()) -> nil()
      remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     remove#(x,.(y,z)) -> remove#(x,z)
    TRS:
     purge(nil()) -> nil()
     purge(.(x,y)) -> .(x,purge(remove(x,y)))
     remove(x,nil()) -> nil()
     remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
    Subterm Criterion Processor:
     simple projection:
      pi(remove#) = 1
     problem:
      DPs:
       
      TRS:
       purge(nil()) -> nil()
       purge(.(x,y)) -> .(x,purge(remove(x,y)))
       remove(x,nil()) -> nil()
       remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
     Qed