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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0) = x0 + 2,
   
   [c](x0) = x0,
   
   [d](x0) = x0 + 1,
   
   [a](x0) = x0 + 3,
   
   [b](x0) = 3x0
  orientation:
   a(b(x1)) = 3x1 + 3 >= 3x1 + 3 = b(d(x1))
   
   a(c(x1)) = x1 + 3 >= x1 + 3 = d(d(d(x1)))
   
   b(d(x1)) = 3x1 + 3 >= 3x1 + 3 = a(c(b(x1)))
   
   c(f(x1)) = x1 + 2 >= x1 + 2 = d(d(c(x1)))
   
   d(d(x1)) = x1 + 2 >= x1 + 2 = f(x1)
   
   f(f(x1)) = x1 + 4 >= x1 + 3 = a(x1)
  problem:
   a(b(x1)) -> b(d(x1))
   a(c(x1)) -> d(d(d(x1)))
   b(d(x1)) -> a(c(b(x1)))
   c(f(x1)) -> d(d(c(x1)))
   d(d(x1)) -> f(x1)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0) = x0 + 2,
    
    [c](x0) = x0,
    
    [d](x0) = x0 + 1,
    
    [a](x0) = x0 + 8,
    
    [b](x0) = 8x0
   orientation:
    a(b(x1)) = 8x1 + 8 >= 8x1 + 8 = b(d(x1))
    
    a(c(x1)) = x1 + 8 >= x1 + 3 = d(d(d(x1)))
    
    b(d(x1)) = 8x1 + 8 >= 8x1 + 8 = a(c(b(x1)))
    
    c(f(x1)) = x1 + 2 >= x1 + 2 = d(d(c(x1)))
    
    d(d(x1)) = x1 + 2 >= x1 + 2 = f(x1)
   problem:
    a(b(x1)) -> b(d(x1))
    b(d(x1)) -> a(c(b(x1)))
    c(f(x1)) -> d(d(c(x1)))
    d(d(x1)) -> f(x1)
   Bounds Processor:
    bound: 1
    enrichment: match
    automaton:
     final states: {10,7,4,1}
     transitions:
      f50() -> 2*
      b0(2) -> 5*
      b0(3) -> 1*
      d0(2) -> 3*
      d0(9) -> 7*
      d0(8) -> 9*
      a0(6) -> 4*
      c0(5) -> 6*
      c0(2) -> 8*
      f0(2) -> 10*
      f1(25) -> 26*
      f1(19) -> 20*
      a1(17) -> 18*
      c1(16) -> 17*
      b1(15) -> 16*
      2 -> 15*
      4 -> 16,5
      7 -> 8,19
      8 -> 19*
      9 -> 25*
      10 -> 3*
      18 -> 1*
      20 -> 7*
      26 -> 9*
    problem:
     
    Qed