/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(s(x)) -> s(s(f(p(s(x)))))
 f(0()) -> 0()
 p(s(x)) -> x

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 1 1]     [0]
   [f](x0) = [0 0 0]x0 + [1]
             [0 0 0]     [1],
   
         [0]
   [0] = [0]
         [1],
   
             [1 0 0]  
   [s](x0) = [0 0 1]x0
             [0 1 0]  ,
   
             [1 0 0]  
   [p](x0) = [0 0 1]x0
             [0 1 0]  
  orientation:
             [1 1 1]    [0]    [1 1 1]    [0]                   
   f(s(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = s(s(f(p(s(x)))))
             [0 0 0]    [1]    [0 0 0]    [1]                   
   
            [1]    [0]      
   f(0()) = [1] >= [0] = 0()
            [1]    [1]      
   
                       
   p(s(x)) = x >= x = x
                       
  problem:
   f(s(x)) -> s(s(f(p(s(x)))))
   p(s(x)) -> x
  DP Processor:
   DPs:
    f#(s(x)) -> p#(s(x))
    f#(s(x)) -> f#(p(s(x)))
   TRS:
    f(s(x)) -> s(s(f(p(s(x)))))
    p(s(x)) -> x
   TDG Processor:
    DPs:
     f#(s(x)) -> p#(s(x))
     f#(s(x)) -> f#(p(s(x)))
    TRS:
     f(s(x)) -> s(s(f(p(s(x)))))
     p(s(x)) -> x
    graph:
     f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> f#(p(s(x)))
     f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> p#(s(x))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 2/4
     DPs:
      f#(s(x)) -> f#(p(s(x)))
     TRS:
      f(s(x)) -> s(s(f(p(s(x)))))
      p(s(x)) -> x
     Bounds Processor:
      bound: 0
      enrichment: match
      automaton:
       final states: {2,5,1}
       transitions:
        f{#,0}(4) -> 1*
        f0(4) -> 6*
        s0(2) -> 3*
        s0(6) -> 7*
        s0(7) -> 5*
        p0(3) -> 4*
        f60() -> 2*
        2 -> 4*
        5 -> 6*
      problem:
       DPs:
        
       TRS:
        f(s(x)) -> s(s(f(p(s(x)))))
        p(s(x)) -> x
      Qed