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

Proof:
 DP Processor:
  DPs:
   f#(f(x,a()),y) -> f#(a(),x)
   f#(f(x,a()),y) -> f#(a(),y)
   f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
  TRS:
   f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
  EDG Processor:
   DPs:
    f#(f(x,a()),y) -> f#(a(),x)
    f#(f(x,a()),y) -> f#(a(),y)
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
   TRS:
    f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
   graph:
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x)) ->
    f#(f(x,a()),y) -> f#(a(),x)
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x)) ->
    f#(f(x,a()),y) -> f#(a(),y)
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x)) -> f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
    TRS:
     f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f0(3,2) -> 5,4
       f0(3,3) -> 6*
       f0(3,4) -> 7*
       a0() -> 3*
       f{#,0}(7,6) -> 1*
       f{#,0}(5,4) -> 1*
       f30() -> 2*
     problem:
      DPs:
       
      TRS:
       f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
     Qed