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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),a())) -> f#(f(a(),a()),a())
   f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x)
   f#(x,f(a(),a())) -> f#(f(f(f(a(),a()),a()),x),a())
  TRS:
   f(x,f(a(),a())) -> f(f(f(f(a(),a()),a()),x),a())
  EDG Processor:
   DPs:
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x)
    f#(x,f(a(),a())) -> f#(f(f(f(a(),a()),a()),x),a())
   TRS:
    f(x,f(a(),a())) -> f(f(f(f(a(),a()),a()),x),a())
   graph:
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x) ->
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x)
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x) ->
    f#(x,f(a(),a())) -> f#(f(f(f(a(),a()),a()),x),a())
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),x)
    TRS:
     f(x,f(a(),a())) -> f(f(f(f(a(),a()),a()),x),a())
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(4,3) -> 5*
       f0(3,3) -> 4*
       a0() -> 3*
       f{#,0}(5,5) -> 1*
       f{#,0}(5,2) -> 1*
       f30() -> 2*
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),a())) -> f(f(f(f(a(),a()),a()),x),a())
     Qed