/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:
 msort(nil()) -> nil()
 msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
 min(x,nil()) -> x
 min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
 del(x,nil()) -> nil()
 del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))

Proof:
 DP Processor:
  DPs:
   msort#(.(x,y)) -> del#(min(x,y),.(x,y))
   msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
   msort#(.(x,y)) -> min#(x,y)
   min#(x,.(y,z)) -> min#(y,z)
   min#(x,.(y,z)) -> min#(x,z)
   del#(x,.(y,z)) -> del#(x,z)
  TRS:
   msort(nil()) -> nil()
   msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
   min(x,nil()) -> x
   min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
   del(x,nil()) -> nil()
   del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
  TDG Processor:
   DPs:
    msort#(.(x,y)) -> del#(min(x,y),.(x,y))
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
    msort#(.(x,y)) -> min#(x,y)
    min#(x,.(y,z)) -> min#(y,z)
    min#(x,.(y,z)) -> min#(x,z)
    del#(x,.(y,z)) -> del#(x,z)
   TRS:
    msort(nil()) -> nil()
    msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
    min(x,nil()) -> x
    min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
    del(x,nil()) -> nil()
    del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
   graph:
    min#(x,.(y,z)) -> min#(y,z) -> min#(x,.(y,z)) -> min#(x,z)
    min#(x,.(y,z)) -> min#(y,z) -> min#(x,.(y,z)) -> min#(y,z)
    min#(x,.(y,z)) -> min#(x,z) -> min#(x,.(y,z)) -> min#(x,z)
    min#(x,.(y,z)) -> min#(x,z) -> min#(x,.(y,z)) -> min#(y,z)
    del#(x,.(y,z)) -> del#(x,z) -> del#(x,.(y,z)) -> del#(x,z)
    msort#(.(x,y)) -> min#(x,y) -> min#(x,.(y,z)) -> min#(x,z)
    msort#(.(x,y)) -> min#(x,y) ->
    min#(x,.(y,z)) -> min#(y,z)
    msort#(.(x,y)) -> del#(min(x,y),.(x,y)) ->
    del#(x,.(y,z)) -> del#(x,z)
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y))) ->
    msort#(.(x,y)) -> min#(x,y)
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y))) ->
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
    msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y))) -> msort#(.(x,y)) -> del#(min(x,y),.(x,y))
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 11/36
    DPs:
     msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
    TRS:
     msort(nil()) -> nil()
     msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
     min(x,nil()) -> x
     min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
     del(x,nil()) -> nil()
     del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
    EDG Processor:
     DPs:
      msort#(.(x,y)) -> msort#(del(min(x,y),.(x,y)))
     TRS:
      msort(nil()) -> nil()
      msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
      min(x,nil()) -> x
      min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
      del(x,nil()) -> nil()
      del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     del#(x,.(y,z)) -> del#(x,z)
    TRS:
     msort(nil()) -> nil()
     msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
     min(x,nil()) -> x
     min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
     del(x,nil()) -> nil()
     del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
    Subterm Criterion Processor:
     simple projection:
      pi(del#) = 1
     problem:
      DPs:
       
      TRS:
       msort(nil()) -> nil()
       msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
       min(x,nil()) -> x
       min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
       del(x,nil()) -> nil()
       del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
     Qed
    
    DPs:
     min#(x,.(y,z)) -> min#(y,z)
     min#(x,.(y,z)) -> min#(x,z)
    TRS:
     msort(nil()) -> nil()
     msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
     min(x,nil()) -> x
     min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
     del(x,nil()) -> nil()
     del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
    Subterm Criterion Processor:
     simple projection:
      pi(min#) = 1
     problem:
      DPs:
       
      TRS:
       msort(nil()) -> nil()
       msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
       min(x,nil()) -> x
       min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
       del(x,nil()) -> nil()
       del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
     Qed