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


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(),f(x,a())) -> f#(a(),x)
   f#(a(),f(x,a())) -> f#(a(),a())
   f#(a(),f(x,a())) -> f#(f(a(),a()),f(a(),x))
   f#(a(),f(x,a())) -> f#(a(),f(f(a(),a()),f(a(),x)))
  TRS:
   f(a(),f(x,a())) -> f(a(),f(f(a(),a()),f(a(),x)))
  EDG Processor:
   DPs:
    f#(a(),f(x,a())) -> f#(a(),x)
    f#(a(),f(x,a())) -> f#(a(),a())
    f#(a(),f(x,a())) -> f#(f(a(),a()),f(a(),x))
    f#(a(),f(x,a())) -> f#(a(),f(f(a(),a()),f(a(),x)))
   TRS:
    f(a(),f(x,a())) -> f(a(),f(f(a(),a()),f(a(),x)))
   graph:
    f#(a(),f(x,a())) -> f#(a(),x) -> f#(a(),f(x,a())) -> f#(a(),x)
    f#(a(),f(x,a())) -> f#(a(),x) -> f#(a(),f(x,a())) -> f#(a(),a())
    f#(a(),f(x,a())) -> f#(a(),x) ->
    f#(a(),f(x,a())) -> f#(f(a(),a()),f(a(),x))
    f#(a(),f(x,a())) -> f#(a(),x) -> f#(a(),f(x,a())) -> f#(a(),f(f(a(),a()),f(a(),x)))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(a(),f(x,a())) -> f#(a(),x)
    TRS:
     f(a(),f(x,a())) -> f(a(),f(f(a(),a()),f(a(),x)))
    Bounds Processor:
     bound: 0
     enrichment: match
     automaton:
      final states: {4,1}
      transitions:
       a0() -> 3*
       f0(6,5) -> 7*
       f0(3,3) -> 6*
       f0(3,7) -> 4*
       f0(3,2) -> 5*
       f30() -> 2*
       f{#,0}(3,2) -> 1*
       4 -> 5*
     problem:
      DPs:
       
      TRS:
       f(a(),f(x,a())) -> f(a(),f(f(a(),a()),f(a(),x)))
     Qed