/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:
 f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())

Proof:
 DP Processor:
  DPs:
   f#(f(x,a()),a()) -> f#(a(),a())
   f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
   f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),x)
   f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
  TRS:
   f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
  EDG Processor:
   DPs:
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
    f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),x)
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
   TRS:
    f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
   graph:
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(a(),a())
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(a(),f(a(),a()))
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(f(a(),f(a(),a())),x)
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a()) ->
    f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(f(x,a()),a()) -> f#(f(f(a(),f(a(),a())),x),a())
    TRS:
     f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(5,5) -> 6*
       f0(5,3) -> 6*
       f0(2,2) -> 4*
       f0(2,4) -> 5*
       a0() -> 2*
       f{#,0}(6,2) -> 1*
       f30() -> 3*
     problem:
      DPs:
       
      TRS:
       f(f(x,a()),a()) -> f(f(f(a(),f(a(),a())),x),a())
     Qed