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

Proof:
 DP Processor:
  DPs:
   f#(f(f(a(),b()),c()),x) -> f#(b(),x)
   f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x))
   f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
   f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),f(b(),x))))
   f#(x,f(y,z)) -> f#(x,y)
   f#(x,f(y,z)) -> f#(f(x,y),z)
  TRS:
   f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),f(b(),x))))
   f(x,f(y,z)) -> f(f(x,y),z)
  EDG Processor:
   DPs:
    f#(f(f(a(),b()),c()),x) -> f#(b(),x)
    f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x))
    f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
    f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),f(b(),x))))
    f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z)
   TRS:
    f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),f(b(),x))))
    f(x,f(y,z)) -> f(f(x,y),z)
   graph:
    f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x)) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x)) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),f(b(),x)))) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),f(b(),x)))) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(f(a(),b()),c()),x) -> f#(b(),x) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(f(a(),b()),c()),x) -> f#(b(),x) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x))) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x))) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(f(a(),b()),c()),x) -> f#(b(),x)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x))
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),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(f(a(),b()),c()),x) -> f#(b(),x)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x))
    f#(x,f(y,z)) -> f#(x,y) ->
    f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
    f#(x,f(y,z)) -> f#(x,y) ->
    f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),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:
      f50() -> 2*
      f{#,0}(3,2) -> 1*
      b0() -> 3*
      f0(3,2) -> 3*
    problem:
     DPs:
      f#(f(f(a(),b()),c()),x) -> f#(c(),f(b(),x))
      f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
      f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),f(b(),x))))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),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(4,2) -> 4*
       f0(5,3) -> 31*
       f0(31,2) -> 31*
       f0(3,2) -> 4*
       f0(5,4) -> 31*
       f120() -> 2*
       f{#,0}(5,3) -> 1*
       f{#,0}(31,2) -> 1*
       f{#,0}(5,4) -> 1*
       b0() -> 3*
       c0() -> 5*
     problem:
      DPs:
       f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
       f#(f(f(a(),b()),c()),x) -> f#(b(),f(a(),f(c(),f(b(),x))))
       f#(x,f(y,z)) -> f#(x,y)
       f#(x,f(y,z)) -> f#(f(x,y),z)
      TRS:
       f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),f(b(),x))))
       f(x,f(y,z)) -> f(f(x,y),z)
     Semantic Labeling Processor:
      dimension: 1
      usable rules:
       f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),f(b(),x))))
       f(x,f(y,z)) -> f(f(x,y),z)
      interpretation:
       [c] = 0,
       
       [f](x0, x1) = 0,
       
       [b] = 0,
       
       [a] = 0
       labeled:
        a
        b
       usable (for model):
        a
        b
       argument filtering:
        pi(a) = []
        pi(b) = []
        pi(f) = 0
        pi(c) = []
        pi(f#) = [0]
      precedence:
       a > b > f# ~ c ~ f
      problem:
       DPs:
        f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
        f#(x,f(y,z)) -> f#(x,y)
        f#(x,f(y,z)) -> f#(f(x,y),z)
       TRS:
        f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),f(b(),x))))
        f(x,f(y,z)) -> f(f(x,y),z)
      Restore Modifier:
       DPs:
        f#(f(f(a(),b()),c()),x) -> f#(a(),f(c(),f(b(),x)))
        f#(x,f(y,z)) -> f#(x,y)
        f#(x,f(y,z)) -> f#(f(x,y),z)
       TRS:
        f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),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:
          f360() -> 2*
          f{#,0}(20,3) -> 1*
          f{#,0}(7,5) -> 1*
          f{#,0}(7,21) -> 1*
          f{#,0}(25,2) -> 1*
          f{#,0}(20,4) -> 1*
          f{#,0}(7,6) -> 1*
          b0() -> 3*
          c0() -> 5*
          f0(4,2) -> 4*
          f0(20,3) -> 25*
          f0(5,3) -> 21*
          f0(21,2) -> 6*
          f0(6,2) -> 6*
          f0(7,5) -> 20*
          f0(7,21) -> 25*
          f0(3,2) -> 4*
          f0(25,2) -> 25*
          f0(20,4) -> 25*
          f0(5,4) -> 6*
          f0(7,6) -> 25*
          a0() -> 7*
        problem:
         DPs:
          f#(x,f(y,z)) -> f#(x,y)
          f#(x,f(y,z)) -> f#(f(x,y),z)
         TRS:
          f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),f(b(),x))))
          f(x,f(y,z)) -> f(f(x,y),z)
        Size-Change Termination Processor:
         DPs:
          
         TRS:
          f(f(f(a(),b()),c()),x) -> f(b(),f(a(),f(c(),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