/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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NO

Problem:
 f(x,x) -> f(i(x),g(g(x)))
 f(x,y) -> x
 g(x) -> i(x)
 f(x,i(x)) -> f(x,x)
 f(i(x),i(g(x))) -> a()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a] = 1,
   
   [g](x0) = x0,
   
   [i](x0) = x0,
   
   [f](x0, x1) = 4x0 + 4x1 + 1
  orientation:
   f(x,x) = 8x + 1 >= 8x + 1 = f(i(x),g(g(x)))
   
   f(x,y) = 4x + 4y + 1 >= x = x
   
   g(x) = x >= x = i(x)
   
   f(x,i(x)) = 8x + 1 >= 8x + 1 = f(x,x)
   
   f(i(x),i(g(x))) = 8x + 1 >= 1 = a()
  problem:
   f(x,x) -> f(i(x),g(g(x)))
   g(x) -> i(x)
   f(x,i(x)) -> f(x,x)
   f(i(x),i(g(x))) -> a()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a] = 0,
    
    [g](x0) = x0,
    
    [i](x0) = x0,
    
    [f](x0, x1) = 2x0 + 2x1 + 1
   orientation:
    f(x,x) = 4x + 1 >= 4x + 1 = f(i(x),g(g(x)))
    
    g(x) = x >= x = i(x)
    
    f(x,i(x)) = 4x + 1 >= 4x + 1 = f(x,x)
    
    f(i(x),i(g(x))) = 4x + 1 >= 0 = a()
   problem:
    f(x,x) -> f(i(x),g(g(x)))
    g(x) -> i(x)
    f(x,i(x)) -> f(x,x)
   Unfolding Processor:
    loop length: 4
    terms:
     f(x141,x141)
     f(i(x141),g(g(x141)))
     f(i(x141),i(g(x141)))
     f(i(x141),i(i(x141)))
    context: []
    substitution:
     x141 -> i(x141)
    Qed