/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))

Proof:
 DP Processor:
  DPs:
   p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(x0)),x3)
   p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(a(a(b(x1))),p(a(a(x0)),x3))
   p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
  TRS:
   p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
  Subterm Criterion Processor:
   simple projection:
    pi(p) = [1,1]
    pi(p#) = [1,1]
   problem:
    DPs:
     p#(a(a(x0)),p(x1,p(a(x2),x3))) -> p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
    TRS:
     p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
   Matrix Interpretation Processor: dim=3
    
    usable rules:
     p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
    interpretation:
                   [0 0 0]     [0 0 1]  
     [p](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 1]     [1 0 0]  ,
     
     [p#](x0, x1) = [1 0 1]x0 + [1 0 0]x1,
     
               [0 1 0]     [0]
     [a](x0) = [0 0 0]x0 + [1]
               [1 0 1]     [0],
     
               [0]
     [b](x0) = [0]
               [0]
    orientation:
     p#(a(a(x0)),p(x1,p(a(x2),x3))) = [1 1 1]x0 + [1 0 1]x2 + [1 0 0]x3 + [1] >= [1 1 1]x0 + [1 0 1]x2 + [1 0 0]x3 = p#(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
     
                                     [0 0 0]     [0 0 1]     [0 0 0]     [0 0 1]      [0 0 0]     [0 0 0]     [0 0 1]                                        
     p(a(a(x0)),p(x1,p(a(x2),x3))) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [0 0 0]x3 >= [0 0 0]x0 + [0 0 0]x2 + [0 0 0]x3 = p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
                                     [1 1 1]     [0 0 0]     [1 0 1]     [1 0 0]      [1 1 1]     [0 0 1]     [1 0 0]                                        
    problem:
     DPs:
      
     TRS:
      p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
    Qed