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


--------------------------------------------------------------------------------


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