/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:
 fib(0()) -> 0()
 fib(s(0())) -> s(0())
 fib(s(s(0()))) -> s(0())
 fib(s(s(x))) -> sp(g(x))
 g(0()) -> pair(s(0()),0())
 g(s(0())) -> pair(s(0()),s(0()))
 g(s(x)) -> np(g(x))
 sp(pair(x,y)) -> +(x,y)
 np(pair(x,y)) -> pair(+(x,y),x)
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                      [1 0 0]  
   [+](x0, x1) = x0 + [0 0 0]x1
                      [0 0 0]  ,
   
              [1 1 0]  
   [np](x0) = [0 1 1]x0
              [0 1 0]  ,
   
                    [1 1 0]     [1 0 0]  
   [pair](x0, x1) = [1 0 1]x0 + [1 0 0]x1
                    [1 0 0]     [0 0 1]  ,
   
              [1 0 0]  
   [sp](x0) = [1 0 0]x0
              [0 1 0]  ,
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 0 0]  ,
   
               [1 0 0]     [1]
   [fib](x0) = [1 0 0]x0 + [0]
               [0 0 0]     [0],
   
         [0]
   [0] = [0]
         [0]
  orientation:
              [1]    [0]      
   fib(0()) = [0] >= [0] = 0()
              [0]    [0]      
   
                 [1]    [0]         
   fib(s(0())) = [0] >= [0] = s(0())
                 [0]    [0]         
   
                    [1]    [0]         
   fib(s(s(0()))) = [0] >= [0] = s(0())
                    [0]    [0]         
   
                  [1 0 0]    [1]    [1 0 0]            
   fib(s(s(x))) = [1 0 0]x + [0] >= [1 0 0]x = sp(g(x))
                  [0 0 0]    [0]    [0 0 0]            
   
            [0]    [0]                   
   g(0()) = [0] >= [0] = pair(s(0()),0())
            [0]    [0]                   
   
               [0]    [0]                      
   g(s(0())) = [0] >= [0] = pair(s(0()),s(0()))
               [0]    [0]                      
   
             [1 0 0]     [1 0 0]            
   g(s(x)) = [0 0 0]x >= [0 0 0]x = np(g(x))
             [0 0 0]     [0 0 0]            
   
                   [1 1 0]    [1 0 0]         [1 0 0]          
   sp(pair(x,y)) = [1 1 0]x + [1 0 0]y >= x + [0 0 0]y = +(x,y)
                   [1 0 1]    [1 0 0]         [0 0 0]          
   
                   [2 1 1]    [2 0 0]     [2 1 0]    [1 0 0]                  
   np(pair(x,y)) = [2 0 1]x + [1 0 1]y >= [2 0 1]x + [1 0 0]y = pair(+(x,y),x)
                   [1 0 1]    [1 0 0]     [1 0 1]    [1 0 0]                  
   
                        
   +(x,0()) = x >= x = x
                        
   
                   [1 0 0]     [1 0 0]    [1 0 0]             
   +(x,s(y)) = x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = s(+(x,y))
                   [0 0 0]     [0 0 0]    [0 0 0]             
  problem:
   g(0()) -> pair(s(0()),0())
   g(s(0())) -> pair(s(0()),s(0()))
   g(s(x)) -> np(g(x))
   sp(pair(x,y)) -> +(x,y)
   np(pair(x,y)) -> pair(+(x,y),x)
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                       [1 0 0]  
    [+](x0, x1) = x0 + [0 0 0]x1
                       [0 0 1]  ,
    
               [1 0 1]  
    [np](x0) = [0 0 1]x0
               [0 1 1]  ,
    
                     [1 1 0]     [1 0 0]  
    [pair](x0, x1) = [0 0 0]x0 + [1 0 1]x1
                     [1 0 1]     [0 0 0]  ,
    
               [1 1 1]  
    [sp](x0) = [1 0 0]x0
               [0 1 1]  ,
    
              [1 1 0]     [1]
    [g](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
              [1 0 0]  
    [s](x0) = [0 1 0]x0
              [0 0 0]  ,
    
          [0]
    [0] = [1]
          [0]
   orientation:
             [2]    [1]                   
    g(0()) = [0] >= [0] = pair(s(0()),0())
             [0]    [0]                   
    
                [2]    [1]                      
    g(s(0())) = [0] >= [0] = pair(s(0()),s(0()))
                [0]    [0]                      
    
              [1 1 0]    [1]    [1 1 0]    [1]           
    g(s(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = np(g(x))
              [0 0 0]    [0]    [0 0 0]    [0]           
    
                    [2 1 1]    [2 0 1]         [1 0 0]          
    sp(pair(x,y)) = [1 1 0]x + [1 0 0]y >= x + [0 0 0]y = +(x,y)
                    [1 0 1]    [1 0 1]         [0 0 1]          
    
                    [2 1 1]    [1 0 0]     [2 1 0]    [1 0 0]                  
    np(pair(x,y)) = [1 0 1]x + [0 0 0]y >= [1 0 1]x + [0 0 0]y = pair(+(x,y),x)
                    [1 0 1]    [1 0 1]     [1 0 1]    [1 0 1]                  
    
                         
    +(x,0()) = x >= x = x
                         
    
                    [1 0 0]     [1 0 0]    [1 0 0]             
    +(x,s(y)) = x + [0 0 0]y >= [0 1 0]x + [0 0 0]y = s(+(x,y))
                    [0 0 0]     [0 0 0]    [0 0 0]             
   problem:
    g(s(x)) -> np(g(x))
    sp(pair(x,y)) -> +(x,y)
    np(pair(x,y)) -> pair(+(x,y),x)
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 0 0]  
     [+](x0, x1) = [1 1 0]x0 + [0 1 0]x1
                   [0 0 1]     [0 0 0]  ,
     
                [1 0 1]  
     [np](x0) = [0 1 1]x0
                [0 1 1]  ,
     
                      [1 0 1]     [1 0 0]     [1]
     [pair](x0, x1) = [1 1 0]x0 + [0 0 0]x1 + [1]
                      [1 0 0]     [1 1 0]     [1],
     
                [1 1 0]  
     [sp](x0) = [1 1 1]x0
                [1 1 0]  ,
     
               [1 0 1]  
     [g](x0) = [0 0 0]x0
               [0 0 0]  ,
     
               [1 0 0]  
     [s](x0) = [1 0 0]x0
               [0 0 1]  ,
     
           [0]
     [0] = [0]
           [0]
    orientation:
               [1 0 1]     [1 0 1]            
     g(s(x)) = [0 0 0]x >= [0 0 0]x = np(g(x))
               [0 0 0]     [0 0 0]            
     
                     [2 1 1]    [1 0 0]    [2]    [1 0 0]    [1 0 0]          
     sp(pair(x,y)) = [3 1 1]x + [2 1 0]y + [3] >= [1 1 0]x + [0 1 0]y = +(x,y)
                     [2 1 1]    [1 0 0]    [2]    [0 0 1]    [0 0 0]          
     
                     [2 0 1]    [2 1 0]    [2]    [2 0 1]    [1 0 0]    [1]                 
     np(pair(x,y)) = [2 1 0]x + [1 1 0]y + [2] >= [2 1 0]x + [1 1 0]y + [1] = pair(+(x,y),x)
                     [2 1 0]    [1 1 0]    [2]    [2 1 0]    [1 0 0]    [1]                 
     
                [1 0 0]          
     +(x,0()) = [1 1 0]x >= x = x
                [0 0 1]          
     
                 [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]             
     +(x,s(y)) = [1 1 0]x + [1 0 0]y >= [1 0 0]x + [1 0 0]y = s(+(x,y))
                 [0 0 1]    [0 0 0]     [0 0 1]    [0 0 0]             
    problem:
     g(s(x)) -> np(g(x))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                         [1 1 1]  
      [+](x0, x1) = x0 + [0 1 1]x1
                         [1 0 0]  ,
      
                 [1 0 0]  
      [np](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
                [1 1 0]  
      [g](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                     [0]
      [s](x0) = x0 + [1]
                     [0],
      
            [0]
      [0] = [0]
            [0]
     orientation:
                [1 1 0]    [1]    [1 1 0]            
      g(s(x)) = [0 0 0]x + [0] >= [0 0 0]x = np(g(x))
                [0 0 0]    [0]    [0 0 0]            
      
                           
      +(x,0()) = x >= x = x
                           
      
                      [1 1 1]    [1]        [1 1 1]    [0]            
      +(x,s(y)) = x + [0 1 1]y + [1] >= x + [0 1 1]y + [1] = s(+(x,y))
                      [1 0 0]    [0]        [1 0 0]    [0]            
     problem:
      +(x,0()) -> x
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                          [1 1 0]  
       [+](x0, x1) = x0 + [0 0 0]x1
                          [0 0 0]  ,
       
             [0]
       [0] = [1]
             [0]
      orientation:
                      [1]         
       +(x,0()) = x + [0] >= x = x
                      [0]         
      problem:
       
      Qed