/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(a(),a()),a()),f(a(),x))

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),a())) -> f#(a(),x)
   f#(x,f(a(),a())) -> f#(f(a(),a()),a())
   f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
  TRS:
   f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
  EDG Processor:
   DPs:
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   TRS:
    f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
   graph:
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x)) ->
    f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(a(),x)
    f#(x,f(a(),a())) -> f#(a(),x) ->
    f#(x,f(a(),a())) -> f#(f(a(),a()),a())
    f#(x,f(a(),a())) -> f#(a(),x) -> f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     f#(x,f(a(),a())) -> f#(f(f(a(),a()),a()),f(a(),x))
     f#(x,f(a(),a())) -> f#(a(),x)
    TRS:
     f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {8,7,1}
      transitions:
       f0(6,5) -> 4*
       f0(6,4) -> 4,8
       f0(3,6) -> 4*
       f0(5,3) -> 6*
       f0(3,2) -> 4*
       f0(3,3) -> 5*
       f1(11,9) -> 12*
       f1(9,9) -> 11*
       f1(9,6) -> 10*
       f1(12,10) -> 4*
       a0() -> 3*
       f{#,0}(3,3) -> 7*
       f{#,0}(3,2) -> 7*
       f{#,0}(6,4) -> 7,1
       f{#,0}(3,6) -> 7*
       f{#,0}(6,5) -> 7*
       f30() -> 2*
       a1() -> 9*
       f{#,1}(9,6) -> 7,1
       f{#,1}(12,10) -> 7,1
       7 -> 1*
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),a())) -> f(f(f(a(),a()),a()),f(a(),x))
     Qed