/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:
 f(x1) -> n(c(n(a(x1))))
 c(f(x1)) -> f(n(a(c(x1))))
 n(a(x1)) -> c(x1)
 c(c(x1)) -> c(x1)
 n(s(x1)) -> f(s(s(x1)))
 n(f(x1)) -> f(n(x1))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]     [0]
   [s](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [1],
   
             [1 0 0]  
   [a](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]  
   [c](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]  
   [f](x0) = [0 1 1]x0
             [0 0 0]  ,
   
             [1 1 1]  
   [n](x0) = [0 1 1]x0
             [0 0 0]  
  orientation:
           [1 0 0]      [1 0 0]                   
   f(x1) = [0 1 1]x1 >= [0 0 0]x1 = n(c(n(a(x1))))
           [0 0 0]      [0 0 0]                   
   
              [1 0 0]      [1 0 0]                   
   c(f(x1)) = [0 0 0]x1 >= [0 0 0]x1 = f(n(a(c(x1))))
              [0 0 0]      [0 0 0]                   
   
              [1 0 0]      [1 0 0]          
   n(a(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(x1)
              [0 0 0]      [0 0 0]          
   
              [1 0 0]      [1 0 0]          
   c(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(x1)
              [0 0 0]      [0 0 0]          
   
              [1 0 0]     [1]    [1 0 0]     [0]              
   n(s(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = f(s(s(x1)))
              [0 0 0]     [0]    [0 0 0]     [0]              
   
              [1 1 1]      [1 1 1]             
   n(f(x1)) = [0 1 1]x1 >= [0 1 1]x1 = f(n(x1))
              [0 0 0]      [0 0 0]             
  problem:
   f(x1) -> n(c(n(a(x1))))
   c(f(x1)) -> f(n(a(c(x1))))
   n(a(x1)) -> c(x1)
   c(c(x1)) -> c(x1)
   n(f(x1)) -> f(n(x1))
  WPO Processor:
   algebra: Sum
   weight function:
    w0 = 0
    w(f) = 1
    w(c) = w(n) = w(a) = 0
   status function:
    st(c) = st(n) = st(a) = st(f) = [0]
   precedence:
    n > c > a ~ f
   problem:
    
   Qed