/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 strict:
  g(s(x)) -> f(x)
  f(0()) -> s(0())
  f(s(x)) -> s(s(g(x)))
  g(0()) -> 0()
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [rand](x0) = 2x0,
   
   [0] = 9,
   
   [f](x0) = 8x0,
   
   [g](x0) = 8x0,
   
   [s](x0) = x0
  orientation:
   g(s(x)) = 8x >= 8x = f(x)
   
   f(0()) = 17 >= 9 = s(0())
   
   f(s(x)) = 8x >= 8x = s(s(g(x)))
   
   g(0()) = 17 >= 9 = 0()
   
   rand(x) = 2x >= x = x
   
   rand(x) = 2x >= 2x = rand(s(x))
  problem:
   strict:
    g(s(x)) -> f(x)
    f(s(x)) -> s(s(g(x)))
   weak:
    rand(x) -> rand(s(x))
  String Reversal Processor:
   strict:
    s(g(x)) -> f(x)
    s(f(x)) -> g(s(s(x)))
   weak:
    rand(x) -> s(rand(x))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                  [1 2]  
     [rand](x0) = [0 0]x0,
     
               [1 2]     [1]
     [f](x0) = [0 1]x0 + [2],
     
               [1 1]     [0]
     [g](x0) = [0 1]x0 + [2],
     
               [1 1]  
     [s](x0) = [0 1]x0
    orientation:
               [1 2]    [2]    [1 2]    [1]       
     s(g(x)) = [0 1]x + [2] >= [0 1]x + [2] = f(x)
     
               [1 3]    [3]    [1 3]    [0]             
     s(f(x)) = [0 1]x + [2] >= [0 1]x + [2] = g(s(s(x)))
     
               [1 2]     [1 2]              
     rand(x) = [0 0]x >= [0 0]x = s(rand(x))
    problem:
     strict:
      
     weak:
      rand(x) -> s(rand(x))
    Qed