/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(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),x)
   f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
   f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
   f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
  TRS:
   f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
   TRS:
    f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
   graph:
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y)) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),h(f(a(),x)))
    f#(x,f(a(),y)) -> f#(a(),x) ->
    f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
     f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
     f#(x,f(a(),y)) -> f#(a(),x)
    TRS:
     f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {14}
      transitions:
       f1(31,37) -> 38*
       f1(38,22) -> 16*
       f1(31,31) -> 36*
       f{#,0}(16,15) -> 14*
       h1(36) -> 37*
       f0(16,16) -> 21*
       f0(16,22) -> 16*
       f0(16,15) -> 15*
       a0() -> 16*
       h0(21) -> 22*
       f{#,1}(31,16) -> 14*
       f{#,1}(38,22) -> 14*
       f{#,1}(31,31) -> 14*
       a1() -> 31*
       f40() -> 15*
     problem:
      DPs:
       f#(x,f(a(),y)) -> f#(f(a(),h(f(a(),x))),y)
       f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
      TRS:
       f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
     Subterm Criterion Processor:
      simple projection:
       pi(f) = [1,1]
       pi(f#) = [1,1]
      problem:
       DPs:
        f#(x,f(a(),y)) -> f#(a(),f(f(a(),h(f(a(),x))),y))
       TRS:
        f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
      Semantic Labeling Processor:
       dimension: 2
       usable rules:
        
       interpretation:
                  [1 0]     [1]
        [h](x0) = [1 0]x0 + [0],
        
                      [0 1]     [1 0]  
        [f](x0, x1) = [1 0]x0 + [0 0]x1,
        
              [0]
        [a] = [1]
        labeled:
         f#
        usable (for model):
         f#
         f
         a
         h
        argument filtering:
         pi(a) = []
         pi(f) = 1
         pi(h) = 0
         pi(f#) = []
       precedence:
        f# ~ h ~ f ~ a
       problem:
        DPs:
         
        TRS:
         f(x,f(a(),y)) -> f(a(),f(f(a(),h(f(a(),x))),y))
       Qed