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

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