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

Proof:
 DP Processor:
  DPs:
   f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y)
   f#(a(x),y) -> f#(x,a(y))
   f#(b(x),y) -> f#(x,b(y))
   f#(c(x),y) -> f#(x,c(y))
  TRS:
   f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y)
   f(a(x),y) -> f(x,a(y))
   f(b(x),y) -> f(x,b(y))
   f(c(x),y) -> f(x,c(y))
  EDG Processor:
   DPs:
    f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y)
    f#(a(x),y) -> f#(x,a(y))
    f#(b(x),y) -> f#(x,b(y))
    f#(c(x),y) -> f#(x,c(y))
   TRS:
    f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y)
    f(a(x),y) -> f(x,a(y))
    f(b(x),y) -> f(x,b(y))
    f(c(x),y) -> f(x,c(y))
   graph:
    f#(a(x),y) -> f#(x,a(y)) -> f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y)
    f#(a(x),y) -> f#(x,a(y)) -> f#(a(x),y) -> f#(x,a(y))
    f#(a(x),y) -> f#(x,a(y)) -> f#(b(x),y) -> f#(x,b(y))
    f#(a(x),y) -> f#(x,a(y)) -> f#(c(x),y) -> f#(x,c(y))
    f#(b(x),y) -> f#(x,b(y)) -> f#(a(x),y) -> f#(x,a(y))
    f#(b(x),y) -> f#(x,b(y)) -> f#(b(x),y) -> f#(x,b(y))
    f#(b(x),y) -> f#(x,b(y)) -> f#(c(x),y) -> f#(x,c(y))
    f#(c(x),y) -> f#(x,c(y)) -> f#(a(x),y) -> f#(x,a(y))
    f#(c(x),y) -> f#(x,c(y)) -> f#(b(x),y) -> f#(x,b(y))
    f#(c(x),y) -> f#(x,c(y)) -> f#(c(x),y) -> f#(x,c(y))
    f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y) ->
    f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y)
    f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y) -> f#(b(x),y) -> f#(x,b(y))
   Bounds Processor:
    bound: 1
    enrichment: match-dp
    automaton:
     final states: {13}
     transitions:
      a1(31) -> 32*
      f50() -> 14*
      b1(32) -> 33*
      b1(33) -> 38*
      f{#,0}(14,32) -> 13*
      f{#,0}(25,15) -> 13*
      f{#,0}(14,38) -> 13*
      f{#,0}(25,23) -> 13*
      f{#,0}(26,14) -> 13*
      f{#,0}(26,38) -> 13*
      f{#,0}(14,15) -> 13*
      f{#,0}(14,31) -> 13*
      f{#,0}(26,15) -> 13*
      f{#,0}(26,23) -> 13*
      f{#,0}(26,31) -> 13*
      c1(15) -> 31*
      c1(38) -> 31*
      c1(33) -> 31*
      c1(23) -> 31*
      b0(25) -> 26*
      b0(15) -> 15*
      b0(14) -> 23*
      b0(31) -> 15*
      b0(26) -> 23*
      b0(38) -> 15*
      b0(23) -> 15*
      c0(15) -> 15*
      c0(32) -> 15*
      c0(24) -> 25*
      c0(14) -> 15*
      c0(31) -> 15*
      a0(15) -> 15*
      a0(32) -> 15*
      a0(26) -> 24*
      a0(38) -> 15*
      a0(33) -> 15*
      a0(23) -> 24*
      f{#,1}(25,33) -> 13*
      f{#,1}(26,32) -> 13*
      f{#,1}(23,32) -> 13*
      f{#,1}(24,31) -> 13*
      f{#,1}(14,33) -> 13*
      f{#,1}(25,38) -> 13*
      f{#,1}(26,33) -> 13*
    problem:
     DPs:
      f#(x,a(b(c(y)))) -> f#(b(c(a(b(x)))),y)
      f#(a(x),y) -> f#(x,a(y))
      f#(b(x),y) -> f#(x,b(y))
     TRS:
      f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y)
      f(a(x),y) -> f(x,a(y))
      f(b(x),y) -> f(x,b(y))
      f(c(x),y) -> f(x,c(y))
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       a0(3) -> 4*
       f230() -> 2*
       f{#,0}(5,3) -> 1*
       f{#,0}(6,2) -> 1*
       b0(5) -> 6*
       b0(2) -> 3*
       b0(6) -> 3*
       c0(4) -> 5*
     problem:
      DPs:
       f#(a(x),y) -> f#(x,a(y))
       f#(b(x),y) -> f#(x,b(y))
      TRS:
       f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y)
       f(a(x),y) -> f(x,a(y))
       f(b(x),y) -> f(x,b(y))
       f(c(x),y) -> f(x,c(y))
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {4}
       transitions:
        f{#,0}(5,6) -> 4*
        f250() -> 5*
        b0(5) -> 6*
        b0(6) -> 6*
        a0(6) -> 6*
      problem:
       DPs:
        f#(a(x),y) -> f#(x,a(y))
       TRS:
        f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y)
        f(a(x),y) -> f(x,a(y))
        f(b(x),y) -> f(x,b(y))
        f(c(x),y) -> f(x,c(y))
      Bounds Processor:
       bound: 0
       enrichment: match-dp
       automaton:
        final states: {1}
        transitions:
         f{#,0}(2,3) -> 1*
         f270() -> 2*
         a0(2) -> 3*
         a0(3) -> 3*
       problem:
        DPs:
         
        TRS:
         f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y)
         f(a(x),y) -> f(x,a(y))
         f(b(x),y) -> f(x,b(y))
         f(c(x),y) -> f(x,c(y))
       Qed