/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),x),y) -> f#(h(a()),a())
   f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
   f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
   f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
  TRS:
   f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
  EDG Processor:
   DPs:
    f#(f(a(),x),y) -> f#(h(a()),a())
    f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
   TRS:
    f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
   graph:
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(h(a()),a())
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a())))) ->
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(h(a()),a())
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(a(),f(h(a()),a()))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a()))) ->
    f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
     f#(f(a(),x),y) -> f#(x,f(a(),f(h(a()),a())))
    TRS:
     f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {8}
      transitions:
       f{#,1}(11,18) -> 8*
       f1(15,17) -> 18*
       f1(16,15) -> 17*
       a1() -> 15*
       h1(15) -> 16*
       f40() -> 13*
       f{#,0}(12,14) -> 8*
       f{#,0}(19,20) -> 8*
       f{#,0}(12,19) -> 8*
       f{#,0}(13,12) -> 8*
       f{#,0}(19,19) -> 8*
       f{#,0}(14,19) -> 8*
       f{#,0}(12,12) -> 8*
       f0(12,14) -> 14*
       f0(19,20) -> 14*
       f0(10,9) -> 11*
       f0(11,12) -> 19*
       f0(12,19) -> 20*
       f0(13,12) -> 14*
       f0(9,11) -> 12*
       f0(19,19) -> 20*
       f0(14,19) -> 14*
       f0(12,12) -> 20*
       a0() -> 9*
       h0(9) -> 10*
     problem:
      DPs:
       f#(f(a(),x),y) -> f#(y,f(x,f(a(),f(h(a()),a()))))
      TRS:
       f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        f140() -> 6*
        f{#,0}(7,7) -> 1*
        f{#,0}(6,7) -> 1*
        f0(8,7) -> 7*
        f0(5,5) -> 7*
        f0(5,7) -> 7*
        f0(3,2) -> 4*
        f0(8,8) -> 7*
        f0(4,5) -> 8*
        f0(5,8) -> 7*
        f0(6,5) -> 7*
        f0(2,4) -> 5*
        f0(7,8) -> 7*
        a0() -> 2*
        h0(2) -> 3*
      problem:
       DPs:
        
       TRS:
        f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
      Qed