/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:
 f(0(x1)) -> s(0(x1))
 d(0(x1)) -> 0(x1)
 d(s(x1)) -> s(s(d(p(s(x1)))))
 f(s(x1)) -> d(f(p(s(x1))))
 p(s(x1)) -> x1

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]     [0]
   [p](x0) = [1 0 0]x0 + [0]
             [1 0 0]     [1],
   
             [1 0 0]     [1]
   [f](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [0],
   
             [1 0 0]  
   [d](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]     [1]
   [0](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [0],
   
             [1 1 1]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  
  orientation:
              [1 0 0]     [2]    [1 0 0]     [1]           
   f(0(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = s(0(x1))
              [0 0 0]     [0]    [0 0 0]     [0]           
   
              [1 0 0]     [1]    [1 0 0]     [1]        
   d(0(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 0(x1)
              [0 0 0]     [0]    [0 0 0]     [0]        
   
              [1 1 1]      [1 1 1]                      
   d(s(x1)) = [0 0 0]x1 >= [0 0 0]x1 = s(s(d(p(s(x1)))))
              [0 0 0]      [0 0 0]                      
   
              [1 1 1]     [1]    [1 1 1]     [1]                 
   f(s(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d(f(p(s(x1))))
              [0 0 0]     [0]    [0 0 0]     [0]                 
   
              [1 1 1]     [0]           
   p(s(x1)) = [1 1 1]x1 + [0] >= x1 = x1
              [1 1 1]     [1]           
  problem:
   d(0(x1)) -> 0(x1)
   d(s(x1)) -> s(s(d(p(s(x1)))))
   f(s(x1)) -> d(f(p(s(x1))))
   p(s(x1)) -> x1
  Bounds Processor:
   bound: 0
   enrichment: match
   automaton:
    final states: {2,8,3,1}
    transitions:
     f50() -> 2*
     s0(7) -> 3*
     s0(6) -> 7*
     s0(2) -> 4*
     f0(5) -> 9*
     p0(4) -> 5*
     d0(5) -> 6*
     d0(9) -> 8*
     00(2) -> 1*
     2 -> 5*
     8 -> 9*
     1 -> 6*
     3 -> 6*
   problem:
    
   Qed