/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(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: {8,1}
      transitions:
       f{#,0}(6,5) -> 8*
       f{#,0}(7,10) -> 8*
       f{#,0}(7,7) -> 1*
       f{#,0}(4,5) -> 8*
       f{#,0}(5,5) -> 1*
       f{#,0}(10,10) -> 8*
       f{#,0}(10,7) -> 1*
       f{#,0}(6,7) -> 1*
       f{#,0}(5,7) -> 8*
       f{#,0}(5,10) -> 1*
       a0() -> 2*
       f0(4,5) -> 10*
       f0(5,7) -> 7*
       f0(10,7) -> 7*
       f0(6,5) -> 7*
       f0(5,10) -> 7*
       f0(7,10) -> 7*
       f0(2,4) -> 5*
       f0(5,5) -> 7*
       f0(10,10) -> 7*
       f0(3,2) -> 4*
       h1(12) -> 13*
       a1() -> 12*
       f40() -> 6*
       h0(2) -> 3*
       f1(4,15) -> 16*
       f1(13,12) -> 14*
       f1(12,14) -> 15*
       f{#,1}(5,16) -> 8*
       f{#,1}(4,15) -> 8*
       f{#,1}(7,16) -> 8*
       f{#,1}(10,16) -> 8*
       f{#,1}(16,16) -> 8*
       8 -> 1*
       1 -> 8*
     problem:
      DPs:
       
      TRS:
       f(f(a(),x),y) -> f(y,f(x,f(a(),f(h(a()),a()))))
     Qed