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


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(a(),h(x)) -> g#(x)
   f#(a(),h(x)) -> f#(g(x),h(x))
   h#(g(x)) -> h#(a())
   g#(h(x)) -> g#(x)
  TRS:
   f(a(),h(x)) -> f(g(x),h(x))
   h(g(x)) -> h(a())
   g(h(x)) -> g(x)
   h(h(x)) -> x
  TDG Processor:
   DPs:
    f#(a(),h(x)) -> g#(x)
    f#(a(),h(x)) -> f#(g(x),h(x))
    h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x)
   TRS:
    f(a(),h(x)) -> f(g(x),h(x))
    h(g(x)) -> h(a())
    g(h(x)) -> g(x)
    h(h(x)) -> x
   graph:
    h#(g(x)) -> h#(a()) -> h#(g(x)) -> h#(a())
    g#(h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
    f#(a(),h(x)) -> g#(x) -> g#(h(x)) -> g#(x)
    f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> f#(g(x),h(x))
    f#(a(),h(x)) -> f#(g(x),h(x)) -> f#(a(),h(x)) -> g#(x)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 5/16
    DPs:
     f#(a(),h(x)) -> f#(g(x),h(x))
    TRS:
     f(a(),h(x)) -> f(g(x),h(x))
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    EDG Processor:
     DPs:
      f#(a(),h(x)) -> f#(g(x),h(x))
     TRS:
      f(a(),h(x)) -> f(g(x),h(x))
      h(g(x)) -> h(a())
      g(h(x)) -> g(x)
      h(h(x)) -> x
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1
      
    
    DPs:
     g#(h(x)) -> g#(x)
    TRS:
     f(a(),h(x)) -> f(g(x),h(x))
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       f(a(),h(x)) -> f(g(x),h(x))
       h(g(x)) -> h(a())
       g(h(x)) -> g(x)
       h(h(x)) -> x
     Qed
    
    DPs:
     h#(g(x)) -> h#(a())
    TRS:
     f(a(),h(x)) -> f(g(x),h(x))
     h(g(x)) -> h(a())
     g(h(x)) -> g(x)
     h(h(x)) -> x
    EDG Processor:
     DPs:
      h#(g(x)) -> h#(a())
     TRS:
      f(a(),h(x)) -> f(g(x),h(x))
      h(g(x)) -> h(a())
      g(h(x)) -> g(x)
      h(h(x)) -> x
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1