/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:
 f(f(a(),b()),x) -> f(a(),f(a(),x))
 f(f(b(),a()),x) -> f(b(),f(b(),x))
 f(x,f(y,z)) -> f(f(x,y),z)

Proof:
 DP Processor:
  DPs:
   f#(f(a(),b()),x) -> f#(a(),x)
   f#(f(a(),b()),x) -> f#(a(),f(a(),x))
   f#(f(b(),a()),x) -> f#(b(),x)
   f#(f(b(),a()),x) -> f#(b(),f(b(),x))
   f#(x,f(y,z)) -> f#(x,y)
   f#(x,f(y,z)) -> f#(f(x,y),z)
  TRS:
   f(f(a(),b()),x) -> f(a(),f(a(),x))
   f(f(b(),a()),x) -> f(b(),f(b(),x))
   f(x,f(y,z)) -> f(f(x,y),z)
  EDG Processor:
   DPs:
    f#(f(a(),b()),x) -> f#(a(),x)
    f#(f(a(),b()),x) -> f#(a(),f(a(),x))
    f#(f(b(),a()),x) -> f#(b(),x)
    f#(f(b(),a()),x) -> f#(b(),f(b(),x))
    f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z)
   TRS:
    f(f(a(),b()),x) -> f(a(),f(a(),x))
    f(f(b(),a()),x) -> f(b(),f(b(),x))
    f(x,f(y,z)) -> f(f(x,y),z)
   graph:
    f#(f(b(),a()),x) -> f#(b(),f(b(),x)) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(b(),a()),x) -> f#(b(),f(b(),x)) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(b(),a()),x) -> f#(b(),x) -> f#(x,f(y,z)) -> f#(x,y)
    f#(f(b(),a()),x) -> f#(b(),x) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),b()),x) -> f#(a(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),b()),x) -> f#(a(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),b()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),b()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(f(a(),b()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),b()),x) -> f#(a(),f(a(),x))
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(f(b(),a()),x) -> f#(b(),x)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(b(),a()),x) -> f#(b(),f(b(),x))
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),b()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),b()),x) -> f#(a(),f(a(),x))
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(b(),a()),x) -> f#(b(),x)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(b(),a()),x) -> f#(b(),f(b(),x))
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(f(x,y),z)
   Bounds Processor:
    bound: 0
    enrichment: match-dp
    automaton:
     final states: {1}
     transitions:
      f{#,0}(3,3) -> 1*
      f{#,0}(3,2) -> 1*
      a0() -> 3*
      f0(3,3) -> 3*
      f0(3,2) -> 3*
      f40() -> 2*
    problem:
     DPs:
      f#(f(a(),b()),x) -> f#(a(),f(a(),x))
      f#(f(b(),a()),x) -> f#(b(),x)
      f#(f(b(),a()),x) -> f#(b(),f(b(),x))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(a(),b()),x) -> f(a(),f(a(),x))
      f(f(b(),a()),x) -> f(b(),f(b(),x))
      f(x,f(y,z)) -> f(f(x,y),z)
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {5}
      transitions:
       f{#,0}(7,7) -> 5*
       f{#,0}(7,6) -> 5*
       f120() -> 6*
       f0(7,7) -> 7*
       f0(7,6) -> 7*
       b0() -> 7*
     problem:
      DPs:
       f#(f(a(),b()),x) -> f#(a(),f(a(),x))
       f#(f(b(),a()),x) -> f#(b(),f(b(),x))
       f#(x,f(y,z)) -> f#(x,y)
       f#(x,f(y,z)) -> f#(f(x,y),z)
      TRS:
       f(f(a(),b()),x) -> f(a(),f(a(),x))
       f(f(b(),a()),x) -> f(b(),f(b(),x))
       f(x,f(y,z)) -> f(f(x,y),z)
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {5}
       transitions:
        f0(17,7) -> 17,8
        f0(7,7) -> 17*
        f0(8,6) -> 8*
        f0(17,6) -> 17*
        f0(17,8) -> 17,8
        f0(7,6) -> 8*
        f0(7,8) -> 17*
        b0() -> 7*
        f{#,0}(17,7) -> 5*
        f{#,0}(7,7) -> 5*
        f{#,0}(17,6) -> 5*
        f{#,0}(17,8) -> 5*
        f{#,0}(7,8) -> 5*
        f140() -> 6*
        17 -> 8*
      problem:
       DPs:
        f#(f(a(),b()),x) -> f#(a(),f(a(),x))
        f#(x,f(y,z)) -> f#(x,y)
        f#(x,f(y,z)) -> f#(f(x,y),z)
       TRS:
        f(f(a(),b()),x) -> f(a(),f(a(),x))
        f(f(b(),a()),x) -> f(b(),f(b(),x))
        f(x,f(y,z)) -> f(f(x,y),z)
      Bounds Processor:
       bound: 0
       enrichment: match-dp
       automaton:
        final states: {1}
        transitions:
         f0(13,3) -> 13,4
         f0(3,3) -> 13*
         f0(4,2) -> 4*
         f0(13,2) -> 13*
         f0(13,4) -> 13,4
         f0(3,2) -> 4*
         f0(3,4) -> 13*
         f200() -> 2*
         f{#,0}(13,3) -> 1*
         f{#,0}(3,3) -> 1*
         f{#,0}(13,2) -> 1*
         f{#,0}(13,4) -> 1*
         f{#,0}(3,4) -> 1*
         a0() -> 3*
         13 -> 4*
       problem:
        DPs:
         f#(x,f(y,z)) -> f#(x,y)
         f#(x,f(y,z)) -> f#(f(x,y),z)
        TRS:
         f(f(a(),b()),x) -> f(a(),f(a(),x))
         f(f(b(),a()),x) -> f(b(),f(b(),x))
         f(x,f(y,z)) -> f(f(x,y),z)
       Size-Change Termination Processor:
        DPs:
         
        TRS:
         f(f(a(),b()),x) -> f(a(),f(a(),x))
         f(f(b(),a()),x) -> f(b(),f(b(),x))
         f(x,f(y,z)) -> f(f(x,y),z)
        The DP: f#(x,f(y,z)) -> f#(x,y) has the edges:
          0 >=  0
          1 >   1
        The DP: f#(x,f(y,z)) -> f#(f(x,y),z) has the edges:
          1 >   1
        Qed