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


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YES

Problem:
 b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
 c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
 b(b(c(b(a(),a()),a(),z),f(a())),y) -> z

Proof:
 DP Processor:
  DPs:
   b#(f(b(x,z)),y) -> b#(y,z)
   b#(f(b(x,z)),y) -> b#(z,b(y,z))
   c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z)
   c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z)))
  TRS:
   b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
   c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
   b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
  TDG Processor:
   DPs:
    b#(f(b(x,z)),y) -> b#(y,z)
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z)
    c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z)))
   TRS:
    b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
    c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
    b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
   graph:
    c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z) ->
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    c#(f(f(c(x,a(),z))),a(),y) -> b#(a(),z) ->
    b#(f(b(x,z)),y) -> b#(y,z)
    c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z))) ->
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    c#(f(f(c(x,a(),z))),a(),y) -> b#(y,f(b(a(),z))) ->
    b#(f(b(x,z)),y) -> b#(y,z)
    b#(f(b(x,z)),y) -> b#(y,z) -> b#(f(b(x,z)),y) -> b#(z,b(y,z))
    b#(f(b(x,z)),y) -> b#(y,z) -> b#(f(b(x,z)),y) -> b#(y,z)
    b#(f(b(x,z)),y) -> b#(z,b(y,z)) ->
    b#(f(b(x,z)),y) -> b#(z,b(y,z))
    b#(f(b(x,z)),y) -> b#(z,b(y,z)) -> b#(f(b(x,z)),y) -> b#(y,z)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     b#(f(b(x,z)),y) -> b#(y,z)
     b#(f(b(x,z)),y) -> b#(z,b(y,z))
    TRS:
     b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
     c(f(f(c(x,a(),z))),a(),y) -> b(y,f(b(a(),z)))
     b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
    Usable Rule Processor:
     DPs:
      b#(f(b(x,z)),y) -> b#(y,z)
      b#(f(b(x,z)),y) -> b#(z,b(y,z))
     TRS:
      b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
      b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
     Matrix Interpretation Processor: dim=2
      
      usable rules:
       b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
       b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
      interpretation:
       [b#](x0, x1) = [0 1]x0 + [0 1]x1,
       
                 [0 0]  
       [f](x0) = [2 0]x0,
       
                         [2 0]     [0 0]  
       [c](x0, x1, x2) = [0 0]x0 + [1 1]x2,
       
                     [0 1]     [0 1]     [2]
       [b](x0, x1) = [0 1]x0 + [0 0]x1 + [0],
       
             [0]
       [a] = [0]
      orientation:
       b#(f(b(x,z)),y) = [0 2]x + [0 1]y + [0 2]z + [4] >= [0 1]y + [0 1]z = b#(y,z)
       
       b#(f(b(x,z)),y) = [0 2]x + [0 1]y + [0 2]z + [4] >= [0 1]y + [0 1]z = b#(z,b(y,z))
       
                        [0 2]    [0 1]    [0 2]    [6]    [0]                       
       b(f(b(x,z)),y) = [0 2]x + [0 0]y + [0 2]z + [4] >= [0] = f(f(f(b(z,b(y,z)))))
       
                                            [0 1]    [1 1]    [2]         
       b(b(c(b(a(),a()),a(),z),f(a())),y) = [0 0]y + [1 1]z + [0] >= z = z
      problem:
       DPs:
        
       TRS:
        b(f(b(x,z)),y) -> f(f(f(b(z,b(y,z)))))
        b(b(c(b(a(),a()),a(),z),f(a())),y) -> z
      Qed