/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

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