/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:
 or(true(),y) -> true()
 or(x,true()) -> true()
 or(false(),false()) -> false()
 mem(x,nil()) -> false()
 mem(x,set(y)) -> =(x,y)
 mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))

Proof:
 DP Processor:
  DPs:
   mem#(x,union(y,z)) -> mem#(x,z)
   mem#(x,union(y,z)) -> mem#(x,y)
   mem#(x,union(y,z)) -> or#(mem(x,y),mem(x,z))
  TRS:
   or(true(),y) -> true()
   or(x,true()) -> true()
   or(false(),false()) -> false()
   mem(x,nil()) -> false()
   mem(x,set(y)) -> =(x,y)
   mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
  TDG Processor:
   DPs:
    mem#(x,union(y,z)) -> mem#(x,z)
    mem#(x,union(y,z)) -> mem#(x,y)
    mem#(x,union(y,z)) -> or#(mem(x,y),mem(x,z))
   TRS:
    or(true(),y) -> true()
    or(x,true()) -> true()
    or(false(),false()) -> false()
    mem(x,nil()) -> false()
    mem(x,set(y)) -> =(x,y)
    mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
   graph:
    mem#(x,union(y,z)) -> mem#(x,z) ->
    mem#(x,union(y,z)) -> or#(mem(x,y),mem(x,z))
    mem#(x,union(y,z)) -> mem#(x,z) ->
    mem#(x,union(y,z)) -> mem#(x,y)
    mem#(x,union(y,z)) -> mem#(x,z) ->
    mem#(x,union(y,z)) -> mem#(x,z)
    mem#(x,union(y,z)) -> mem#(x,y) ->
    mem#(x,union(y,z)) -> or#(mem(x,y),mem(x,z))
    mem#(x,union(y,z)) -> mem#(x,y) ->
    mem#(x,union(y,z)) -> mem#(x,y)
    mem#(x,union(y,z)) -> mem#(x,y) -> mem#(x,union(y,z)) -> mem#(x,z)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     mem#(x,union(y,z)) -> mem#(x,z)
     mem#(x,union(y,z)) -> mem#(x,y)
    TRS:
     or(true(),y) -> true()
     or(x,true()) -> true()
     or(false(),false()) -> false()
     mem(x,nil()) -> false()
     mem(x,set(y)) -> =(x,y)
     mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
    Subterm Criterion Processor:
     simple projection:
      pi(mem#) = 1
     problem:
      DPs:
       
      TRS:
       or(true(),y) -> true()
       or(x,true()) -> true()
       or(false(),false()) -> false()
       mem(x,nil()) -> false()
       mem(x,set(y)) -> =(x,y)
       mem(x,union(y,z)) -> or(mem(x,y),mem(x,z))
     Qed