/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
 f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 0 0]     [1 0 0]  
   [h](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
                      [1 0 0]     [1 0 0]     [1 0 0]  
   [if](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [1 0 0]x2
                      [0 0 0]     [0 0 0]     [0 0 0]  ,
   
          [0]
   [d'] = [1]
          [0],
   
                 [1 1 0]     [1 0 0]  
   [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
         [0]
   [e] = [0]
         [0],
   
                 [1 1 0]     [1 0 0]  
   [f](x0, x1) = [0 1 0]x0 + [0 1 0]x1
                 [0 0 1]     [0 0 0]  ,
   
         [0]
   [d] = [0]
         [0],
   
                 [1 0 0]     [1 0 0]     [0]
   [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                 [0 0 0]     [0 0 0]     [0],
   
         [0]
   [c] = [0]
         [1],
   
                     [1 0 0]     [1 0 0]     [1 0 0]  
   [i](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                     [0 0 0]     [0 0 0]     [0 0 0]  ,
   
          [0]
   [b'] = [1]
          [0],
   
         [0]
   [b] = [0]
         [0],
   
         [0]
   [a] = [0]
         [0]
  orientation:
                                   [1]    [1]                                                 
   f(g(i(a(),b(),b'()),c()),d()) = [1] >= [1] = if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
                                   [0]    [0]                                                 
   
                              [1]    [0]                                                      
   f(g(h(a(),b()),c()),d()) = [1] >= [0] = if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
                              [0]    [0]                                                      
  problem:
   f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                       [1 0 0]     [1 0 0]     [1 0 0]  
    [if](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                       [0 0 0]     [0 0 0]     [0 0 0]  ,
    
           [0]
    [d'] = [0]
           [0],
    
                  [1 0 0]     [1 0 0]  
    [.](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
          [0]
    [e] = [0]
          [0],
    
                  [1 0 0]     [1 0 0]  
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
          [0]
    [d] = [0]
          [0],
    
                  [1 0 0]     [1 0 0]  
    [g](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
          [0]
    [c] = [0]
          [0],
    
                      [1 0 0]     [1 0 0]     [1 0 1]  
    [i](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                      [0 0 0]     [0 0 0]     [0 0 0]  ,
    
           [0]
    [b'] = [0]
           [1],
    
          [0]
    [b] = [0]
          [0],
    
          [0]
    [a] = [0]
          [0]
   orientation:
                                    [1]    [0]                                                 
    f(g(i(a(),b(),b'()),c()),d()) = [0] >= [0] = if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
                                    [0]    [0]                                                 
   problem:
    
   Qed