/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:
 a(x1) -> x1
 a(x1) -> b(c(x1))
 a(b(b(x1))) -> b(b(a(a(x1))))

Proof:
 DP Processor:
  DPs:
   a#(b(b(x1))) -> a#(x1)
   a#(b(b(x1))) -> a#(a(x1))
  TRS:
   a(x1) -> x1
   a(x1) -> b(c(x1))
   a(b(b(x1))) -> b(b(a(a(x1))))
  Arctic Interpretation Processor:
   dimension: 2
   usable rules:
    a(x1) -> x1
    a(x1) -> b(c(x1))
    a(b(b(x1))) -> b(b(a(a(x1))))
   interpretation:
    [a#](x0) = [1 0]x0 + [0],
    
              [-& 1 ]     [0]
    [b](x0) = [0  -&]x0 + [3],
    
              [0  0 ]     [1]
    [c](x0) = [-& -&]x0 + [0],
    
              [0  -&]     [3]
    [a](x0) = [1  0 ]x0 + [3]
   orientation:
    a#(b(b(x1))) = [2 1]x1 + [5] >= [1 0]x1 + [0] = a#(x1)
    
    a#(b(b(x1))) = [2 1]x1 + [5] >= [1 0]x1 + [4] = a#(a(x1))
    
            [0  -&]     [3]           
    a(x1) = [1  0 ]x1 + [3] >= x1 = x1
    
            [0  -&]     [3]    [-& -&]     [1]           
    a(x1) = [1  0 ]x1 + [3] >= [0  0 ]x1 + [3] = b(c(x1))
    
                  [1  -&]     [4]    [1  -&]     [4]                 
    a(b(b(x1))) = [2  1 ]x1 + [5] >= [2  1 ]x1 + [5] = b(b(a(a(x1))))
   problem:
    DPs:
     
    TRS:
     a(x1) -> x1
     a(x1) -> b(c(x1))
     a(b(b(x1))) -> b(b(a(a(x1))))
   Qed