/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)) -> f(X)
 g(cons(0(),Y)) -> g(Y)
 g(cons(s(X),Y)) -> s(X)
 h(cons(X,Y)) -> h(g(cons(X,Y)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = x0,
   
   [f](x0) = 4x0 + 6,
   
   [cons](x0, x1) = 2x0 + x1,
   
   [h](x0) = x0,
   
   [s](x0) = 5x0,
   
   [0] = 1
  orientation:
   f(s(X)) = 20X + 6 >= 4X + 6 = f(X)
   
   g(cons(0(),Y)) = Y + 2 >= Y = g(Y)
   
   g(cons(s(X),Y)) = 10X + Y >= 5X = s(X)
   
   h(cons(X,Y)) = 2X + Y >= 2X + Y = h(g(cons(X,Y)))
  problem:
   f(s(X)) -> f(X)
   g(cons(s(X),Y)) -> s(X)
   h(cons(X,Y)) -> h(g(cons(X,Y)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [g](x0) = [0 1 0]x0
              [0 1 0]  ,
    
              [1 0 1]     [0]
    [f](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [0],
    
                     [1 0 1]     [1 0 0]  
    [cons](x0, x1) = [0 1 0]x0 + [0 1 0]x1
                     [0 1 0]     [0 1 1]  ,
    
              [1 0 1]     [1]
    [h](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
              [1 1 0]     [1]
    [s](x0) = [0 0 1]x0 + [0]
              [0 0 1]     [0]
   orientation:
              [1 1 1]    [1]    [1 0 1]    [0]       
    f(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X)
              [0 0 0]    [0]    [0 0 0]    [0]       
    
                      [1 1 1]    [1 0 0]    [1]    [1 1 0]    [1]       
    g(cons(s(X),Y)) = [0 0 1]X + [0 1 0]Y + [0] >= [0 0 1]X + [0] = s(X)
                      [0 0 1]    [0 1 0]    [0]    [0 0 1]    [0]       
    
                   [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 0]    [1]                  
    h(cons(X,Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y + [0] = h(g(cons(X,Y)))
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                  
   problem:
    g(cons(s(X),Y)) -> s(X)
    h(cons(X,Y)) -> h(g(cons(X,Y)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [0]
     [g](x0) = [0 0 1]x0 + [0]
               [0 0 0]     [1],
     
                      [1 0 1]     [1 0 0]     [0]
     [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1]
                      [0 1 0]     [0 0 0]     [0],
     
               [1 1 0]  
     [h](x0) = [0 1 0]x0
               [0 1 0]  ,
     
               [1 0 0]     [0]
     [s](x0) = [0 0 1]x0 + [0]
               [0 0 0]     [1]
    orientation:
                       [1 0 0]    [1 0 0]    [1]    [1 0 0]    [0]       
     g(cons(s(X),Y)) = [0 0 1]X + [0 0 0]Y + [0] >= [0 0 1]X + [0] = s(X)
                       [0 0 0]    [0 0 0]    [1]    [0 0 0]    [1]       
     
                    [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 0 0]                   
     h(cons(X,Y)) = [0 1 0]X + [0 0 0]Y + [1] >= [0 1 0]X + [0 0 0]Y = h(g(cons(X,Y)))
                    [0 1 0]    [0 0 0]    [1]    [0 1 0]    [0 0 0]                   
    problem:
     
    Qed