/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(f(f(a(),a()),a()),a())) -> f#(x,a())
   f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
  TRS:
   f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
  EDG Processor:
   DPs:
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(x,a())
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
   TRS:
    f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
   graph:
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x) ->
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(x,a())
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x) ->
    f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 2/4
    DPs:
     f#(x,f(f(f(a(),a()),a()),a())) -> f#(f(x,a()),x)
    TRS:
     f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
    Bounds Processor:
     bound: 4
     enrichment: top-dp
     automaton:
      final states: {3}
      transitions:
       f3(14,19) -> 20*
       a3() -> 19*
       f{#,4}(22,20) -> 3*
       f4(20,21) -> 22*
       f{#,0}(1,2) -> 3*
       f{#,0}(2,1) -> 3*
       f{#,0}(1,1) -> 3*
       f{#,0}(2,2) -> 3*
       a4() -> 21*
       f0(1,2) -> 1*
       f0(2,1) -> 1*
       f0(1,1) -> 1*
       f0(2,2) -> 1*
       a0() -> 2*
       f{#,1}(7,1) -> 3*
       f{#,1}(12,2) -> 3*
       f1(1,6) -> 7*
       f1(2,6) -> 12*
       a1() -> 6*
       f{#,2}(14,7) -> 3*
       f2(7,13) -> 14*
       a2() -> 13*
       f{#,3}(20,14) -> 3*
     problem:
      DPs:
       
      TRS:
       f(x,f(f(f(a(),a()),a()),a())) -> f(f(x,a()),x)
     Qed