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


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(y,f(x,f(a(),x))) -> f#(a(),y)
   f#(y,f(x,f(a(),x))) -> f#(x,a())
   f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
   f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
   f#(x,f(x,y)) -> f#(x,a())
   f#(x,f(x,y)) -> f#(f(x,a()),a())
   f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
  TRS:
   f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
   f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
  EDG Processor:
   DPs:
    f#(y,f(x,f(a(),x))) -> f#(a(),y)
    f#(y,f(x,f(a(),x))) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
    f#(x,f(x,y)) -> f#(x,a())
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
   TRS:
    f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
    f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
   graph:
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),y)
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(x,f(x,y)) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y)) ->
    f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a())) ->
    f#(x,f(x,y)) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a())) ->
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a())) ->
    f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),y)
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(a(),f(x,a()))
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
    f#(y,f(x,f(a(),x))) -> f#(a(),y) -> f#(x,f(x,y)) -> f#(x,a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) ->
    f#(x,f(x,y)) -> f#(f(x,a()),a())
    f#(y,f(x,f(a(),x))) -> f#(a(),y) -> f#(x,f(x,y)) -> f#(f(f(x,a()),a()),a())
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 17/49
    DPs:
     f#(y,f(x,f(a(),x))) -> f#(f(a(),f(x,a())),f(a(),y))
     f#(y,f(x,f(a(),x))) -> f#(a(),y)
    TRS:
     f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
     f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f30() -> 2*
       f{#,0}(22,18) -> 1*
       f{#,0}(22,20) -> 1*
       f{#,0}(22,22) -> 1*
       f{#,0}(3,3) -> 1*
       f{#,0}(23,21) -> 1*
       f{#,0}(18,21) -> 1*
       f{#,0}(23,23) -> 1*
       f{#,0}(3,19) -> 1*
       f{#,0}(18,23) -> 1*
       f{#,0}(19,4) -> 1*
       f{#,0}(3,21) -> 1*
       f{#,0}(3,23) -> 1*
       f{#,0}(4,4) -> 1*
       f{#,0}(4,10) -> 1*
       f{#,0}(19,18) -> 1*
       f{#,0}(19,20) -> 1*
       f{#,0}(4,18) -> 1*
       f{#,0}(19,22) -> 1*
       f{#,0}(4,20) -> 1*
       f{#,0}(4,22) -> 1*
       f{#,0}(20,21) -> 1*
       f{#,0}(20,23) -> 1*
       f{#,0}(21,4) -> 1*
       f{#,0}(6,4) -> 1*
       f{#,0}(21,10) -> 1*
       f{#,0}(21,18) -> 1*
       f{#,0}(21,20) -> 1*
       f{#,0}(6,18) -> 1*
       f{#,0}(21,22) -> 1*
       f{#,0}(6,20) -> 1*
       f{#,0}(6,22) -> 1*
       f{#,0}(22,21) -> 1*
       f{#,0}(22,23) -> 1*
       f{#,0}(23,4) -> 1*
       f{#,0}(18,4) -> 1*
       f{#,0}(3,4) -> 1*
       f{#,0}(23,10) -> 1*
       f{#,0}(3,6) -> 1*
       f{#,0}(18,10) -> 1*
       f{#,0}(23,18) -> 1*
       f{#,0}(18,18) -> 1*
       f{#,0}(23,20) -> 1*
       f{#,0}(18,20) -> 1*
       f{#,0}(23,22) -> 1*
       f{#,0}(3,18) -> 1*
       f{#,0}(18,22) -> 1*
       f{#,0}(3,20) -> 1*
       f{#,0}(3,22) -> 1*
       f{#,0}(19,21) -> 1*
       f{#,0}(19,23) -> 1*
       f{#,0}(20,4) -> 1*
       f{#,0}(4,21) -> 1*
       f{#,0}(4,23) -> 1*
       f{#,0}(20,10) -> 1*
       f{#,0}(20,18) -> 1*
       f{#,0}(20,20) -> 1*
       f{#,0}(20,22) -> 1*
       f{#,0}(21,21) -> 1*
       f{#,0}(21,23) -> 1*
       f{#,0}(22,4) -> 1*
       f{#,0}(6,21) -> 1*
       f{#,0}(6,23) -> 1*
       f{#,0}(22,10) -> 1*
       f0(23,3) -> 5,23*
       f0(18,3) -> 21*
       f0(3,5) -> 6*
       f0(3,11) -> 6*
       f0(3,19) -> 20*,6,4
       f0(3,21) -> 6,20*,4
       f0(3,23) -> 6,4,20*
       f0(19,10) -> 4*
       f0(4,10) -> 4*
       f0(20,3) -> 19*,5
       f0(5,3) -> 18*,4,11
       f0(21,10) -> 4*
       f0(6,10) -> 4*
       f0(22,3) -> 23*
       f0(2,3) -> 5*
       f0(3,2) -> 4*
       f0(3,4) -> 4*
       f0(23,10) -> 4*
       f0(3,6) -> 4*
       f0(18,10) -> 4*
       f0(3,18) -> 20*,6,4
       f0(19,3) -> 22*,5
       f0(3,20) -> 4*
       f0(3,22) -> 4,6,20*
       f0(4,3) -> 19*,6,5
       f0(20,10) -> 4*
       f0(21,3) -> 5,23*
       f0(6,3) -> 5*
       f0(22,10) -> 4*
       f{#,1}(19,10) -> 1*
       f{#,1}(21,10) -> 1*
       f{#,1}(6,10) -> 1*
       f{#,1}(23,10) -> 1*
       f{#,1}(20,10) -> 1*
       a1() -> 3*
       f1(23,3) -> 20*
       f1(18,3) -> 20*
       f1(3,3) -> 10*
       f1(10,3) -> 11*
       f1(22,3) -> 20*
       f1(3,10) -> 6*
       f1(11,3) -> 4,20*,6
     problem:
      DPs:
       f#(y,f(x,f(a(),x))) -> f#(a(),y)
      TRS:
       f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
       f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        a0() -> 3*
        f130() -> 2*
        f{#,0}(3,3) -> 1*
        f{#,0}(3,2) -> 1*
      problem:
       DPs:
        
       TRS:
        f(y,f(x,f(a(),x))) -> f(f(a(),f(x,a())),f(a(),y))
        f(x,f(x,y)) -> f(f(f(x,a()),a()),a())
      Qed