/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 bsort(nil()) -> nil()
 bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
 bubble(nil()) -> nil()
 bubble(.(x,nil())) -> .(x,nil())
 bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
 last(nil()) -> 0()
 last(.(x,nil())) -> x
 last(.(x,.(y,z))) -> last(.(y,z))
 butlast(nil()) -> nil()
 butlast(.(x,nil())) -> nil()
 butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))

Proof:
 DP Processor:
  DPs:
   bsort#(.(x,y)) -> butlast#(bubble(.(x,y)))
   bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y))))
   bsort#(.(x,y)) -> bubble#(.(x,y))
   bsort#(.(x,y)) -> last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
   bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
   bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
   last#(.(x,.(y,z))) -> last#(.(y,z))
   butlast#(.(x,.(y,z))) -> butlast#(.(y,z))
  TRS:
   bsort(nil()) -> nil()
   bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
   bubble(nil()) -> nil()
   bubble(.(x,nil())) -> .(x,nil())
   bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
   last(nil()) -> 0()
   last(.(x,nil())) -> x
   last(.(x,.(y,z))) -> last(.(y,z))
   butlast(nil()) -> nil()
   butlast(.(x,nil())) -> nil()
   butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
  TDG Processor:
   DPs:
    bsort#(.(x,y)) -> butlast#(bubble(.(x,y)))
    bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y))))
    bsort#(.(x,y)) -> bubble#(.(x,y))
    bsort#(.(x,y)) -> last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
    bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
    bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
    last#(.(x,.(y,z))) -> last#(.(y,z))
    butlast#(.(x,.(y,z))) -> butlast#(.(y,z))
   TRS:
    bsort(nil()) -> nil()
    bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
    bubble(nil()) -> nil()
    bubble(.(x,nil())) -> .(x,nil())
    bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
    last(nil()) -> 0()
    last(.(x,nil())) -> x
    last(.(x,.(y,z))) -> last(.(y,z))
    butlast(nil()) -> nil()
    butlast(.(x,nil())) -> nil()
    butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
   graph:
    last#(.(x,.(y,z))) -> last#(.(y,z)) ->
    last#(.(x,.(y,z))) -> last#(.(y,z))
    bubble#(.(x,.(y,z))) -> bubble#(.(y,z)) ->
    bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
    bubble#(.(x,.(y,z))) -> bubble#(.(y,z)) ->
    bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
    bubble#(.(x,.(y,z))) -> bubble#(.(x,z)) ->
    bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
    bubble#(.(x,.(y,z))) -> bubble#(.(x,z)) ->
    bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
    butlast#(.(x,.(y,z))) -> butlast#(.(y,z)) ->
    butlast#(.(x,.(y,z))) -> butlast#(.(y,z))
    bsort#(.(x,y)) -> last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y)))))) ->
    last#(.(x,.(y,z))) -> last#(.(y,z))
    bsort#(.(x,y)) -> bubble#(.(x,y)) ->
    bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
    bsort#(.(x,y)) -> bubble#(.(x,y)) ->
    bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
    bsort#(.(x,y)) -> butlast#(bubble(.(x,y))) ->
    butlast#(.(x,.(y,z))) -> butlast#(.(y,z))
    bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y)))) ->
    bsort#(.(x,y)) -> last#(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
    bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y)))) ->
    bsort#(.(x,y)) -> bubble#(.(x,y))
    bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y)))) ->
    bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y))))
    bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y)))) -> bsort#(.(x,y)) -> butlast#(bubble(.(x,y)))
   SCC Processor:
    #sccs: 4
    #rules: 5
    #arcs: 14/64
    DPs:
     bsort#(.(x,y)) -> bsort#(butlast(bubble(.(x,y))))
    TRS:
     bsort(nil()) -> nil()
     bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
     bubble(nil()) -> nil()
     bubble(.(x,nil())) -> .(x,nil())
     bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
     last(nil()) -> 0()
     last(.(x,nil())) -> x
     last(.(x,.(y,z))) -> last(.(y,z))
     butlast(nil()) -> nil()
     butlast(.(x,nil())) -> nil()
     butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
    Bounds Processor:
     bound: 1
     enrichment: top-dp
     automaton:
      final states: {4}
      transitions:
       if0(3,3,3) -> 3*
       nil1() -> 10,11
       bsort{#,0}(3) -> 4*
       .1(3,9) -> 17,16
       .1(3,11) -> 9*
       .1(3,3) -> 8*
       if1(18,17,16) -> 9*
       butlast0(3) -> 3*
       .0(3,3) -> 3*
       <=0(3,3) -> 3*
       butlast1(9) -> 10*
       bubble0(3) -> 3*
       bsort{#,1}(10) -> 4*
       bubble1(8) -> 9*
       <=1(3,3) -> 18*
       bsort0(3) -> 3*
       last0(3) -> 3*
       nil0() -> 3*
       00() -> 3*
     problem:
      DPs:
       
      TRS:
       bsort(nil()) -> nil()
       bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
       bubble(nil()) -> nil()
       bubble(.(x,nil())) -> .(x,nil())
       bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
       last(nil()) -> 0()
       last(.(x,nil())) -> x
       last(.(x,.(y,z))) -> last(.(y,z))
       butlast(nil()) -> nil()
       butlast(.(x,nil())) -> nil()
       butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
     Qed
    
    DPs:
     butlast#(.(x,.(y,z))) -> butlast#(.(y,z))
    TRS:
     bsort(nil()) -> nil()
     bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
     bubble(nil()) -> nil()
     bubble(.(x,nil())) -> .(x,nil())
     bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
     last(nil()) -> 0()
     last(.(x,nil())) -> x
     last(.(x,.(y,z))) -> last(.(y,z))
     butlast(nil()) -> nil()
     butlast(.(x,nil())) -> nil()
     butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
    Subterm Criterion Processor:
     simple projection:
      pi(butlast#) = 0
     problem:
      DPs:
       
      TRS:
       bsort(nil()) -> nil()
       bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
       bubble(nil()) -> nil()
       bubble(.(x,nil())) -> .(x,nil())
       bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
       last(nil()) -> 0()
       last(.(x,nil())) -> x
       last(.(x,.(y,z))) -> last(.(y,z))
       butlast(nil()) -> nil()
       butlast(.(x,nil())) -> nil()
       butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
     Qed
    
    DPs:
     bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
     bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
    TRS:
     bsort(nil()) -> nil()
     bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
     bubble(nil()) -> nil()
     bubble(.(x,nil())) -> .(x,nil())
     bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
     last(nil()) -> 0()
     last(.(x,nil())) -> x
     last(.(x,.(y,z))) -> last(.(y,z))
     butlast(nil()) -> nil()
     butlast(.(x,nil())) -> nil()
     butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
    Usable Rule Processor:
     DPs:
      bubble#(.(x,.(y,z))) -> bubble#(.(y,z))
      bubble#(.(x,.(y,z))) -> bubble#(.(x,z))
     TRS:
      
     Semantic Labeling Processor:
      dimension: 1
      usable rules:
       
      interpretation:
       [.](x0, x1) = x0 + x1 + 1
       labeled:
        bubble#
       usable (for model):
        bubble#
        .
       argument filtering:
        pi(.) = 0
        pi(bubble#) = []
      precedence:
       bubble# ~ .
      problem:
       DPs:
        
       TRS:
        
      Qed
    
    DPs:
     last#(.(x,.(y,z))) -> last#(.(y,z))
    TRS:
     bsort(nil()) -> nil()
     bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
     bubble(nil()) -> nil()
     bubble(.(x,nil())) -> .(x,nil())
     bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
     last(nil()) -> 0()
     last(.(x,nil())) -> x
     last(.(x,.(y,z))) -> last(.(y,z))
     butlast(nil()) -> nil()
     butlast(.(x,nil())) -> nil()
     butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
    Subterm Criterion Processor:
     simple projection:
      pi(last#) = 0
     problem:
      DPs:
       
      TRS:
       bsort(nil()) -> nil()
       bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
       bubble(nil()) -> nil()
       bubble(.(x,nil())) -> .(x,nil())
       bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
       last(nil()) -> 0()
       last(.(x,nil())) -> x
       last(.(x,.(y,z))) -> last(.(y,z))
       butlast(nil()) -> nil()
       butlast(.(x,nil())) -> nil()
       butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))
     Qed