/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:
 app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   G ==> G0/0 G1/1
   F ==> F0/0 F1/1 F2/2
   
  uncurry-rules:
   app(F1(x2),x3) -> F2(x2,x3)
   app(F0(),x2) -> F1(x2)
   app(G0(),x5) -> G1(x5)
  eta-rules:
   
  problem:
   F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
   app(F1(x2),x3) -> F2(x2,x3)
   app(F0(),x2) -> F1(x2)
   app(G0(),x5) -> G1(x5)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 1 0]     [1]
    [F1](x0) = [1 1 0]x0 + [1]
               [0 1 0]     [0],
    
                    [1 0 0]     [1 1 0]  
    [app](x0, x1) = [0 1 0]x0 + [1 1 0]x1
                    [1 0 1]     [0 1 0]  ,
    
           [1]
    [F0] = [1]
           [0],
    
                   [1 1 0]     [1 1 0]     [1]
    [F2](x0, x1) = [1 1 0]x0 + [1 1 0]x1 + [1]
                   [0 0 0]     [0 0 0]     [0],
    
               [1 0 0]     [0]
    [G1](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
    
           [1]
    [G0] = [1]
           [0]
   orientation:
                    [2 2 0]    [3 3 0]    [3]    [2 2 0]    [3 3 0]    [3]                           
    F2(F2(f,x),x) = [2 2 0]f + [3 3 0]x + [3] >= [2 2 0]f + [3 3 0]x + [3] = F2(G1(F2(f,x)),app(f,x))
                    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                           
    
                     [1 1 0]     [1 1 0]     [1]    [1 1 0]     [1 1 0]     [1]            
    app(F1(x2),x3) = [1 1 0]x2 + [1 1 0]x3 + [1] >= [1 1 0]x2 + [1 1 0]x3 + [1] = F2(x2,x3)
                     [1 2 0]     [0 1 0]     [1]    [0 0 0]     [0 0 0]     [0]            
    
                   [1 1 0]     [1]    [1 1 0]     [1]         
    app(F0(),x2) = [1 1 0]x2 + [1] >= [1 1 0]x2 + [1] = F1(x2)
                   [0 1 0]     [1]    [0 1 0]     [0]         
    
                   [1 1 0]     [1]    [1 0 0]     [0]         
    app(G0(),x5) = [1 1 0]x5 + [1] >= [0 0 0]x5 + [1] = G1(x5)
                   [0 1 0]     [1]    [0 0 0]     [0]         
   problem:
    F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
    app(F1(x2),x3) -> F2(x2,x3)
    app(F0(),x2) -> F1(x2)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 0 0]     [1]
     [F1](x0) = [1 1 1]x0 + [1]
                [0 1 1]     [1],
     
                     [1 0 1]     [1 0 0]     [0]
     [app](x0, x1) = [0 1 0]x0 + [1 1 1]x1 + [1]
                     [0 1 0]     [0 1 1]     [1],
     
            [0]
     [F0] = [0]
            [1],
     
                    [1 0 1]     [1 0 0]     [0]
     [F2](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [1]
                    [1 1 1]     [0 0 0]     [0],
     
                [1 0 0]  
     [G1](x0) = [0 1 1]x0
                [0 0 0]  
    orientation:
                     [2 1 2]    [2 0 0]    [0]    [2 0 2]    [2 0 0]    [0]                           
     F2(F2(f,x),x) = [1 2 2]f + [0 0 0]x + [2] >= [1 2 2]f + [0 0 0]x + [2] = F2(G1(F2(f,x)),app(f,x))
                     [2 2 3]    [1 0 0]    [1]    [2 2 3]    [1 0 0]    [1]                           
     
                      [1 1 1]     [1 0 0]     [2]    [1 0 1]     [1 0 0]     [0]            
     app(F1(x2),x3) = [1 1 1]x2 + [1 1 1]x3 + [2] >= [0 1 1]x2 + [0 0 0]x3 + [1] = F2(x2,x3)
                      [1 1 1]     [0 1 1]     [2]    [1 1 1]     [0 0 0]     [0]            
     
                    [1 0 0]     [1]    [1 0 0]     [1]         
     app(F0(),x2) = [1 1 1]x2 + [1] >= [1 1 1]x2 + [1] = F1(x2)
                    [0 1 1]     [1]    [0 1 1]     [1]         
    problem:
     F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
     app(F0(),x2) -> F1(x2)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                 [1 0 0]  
      [F1](x0) = [0 0 0]x0
                 [0 0 0]  ,
      
                      [1 0 0]     [1 0 0]     [1]
      [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                      [0 0 0]     [0 0 0]     [0],
      
             [1]
      [F0] = [0]
             [0],
      
                     [1 1 0]     [1 0 0]     [0]
      [F2](x0, x1) = [1 1 0]x0 + [1 0 0]x1 + [1]
                     [0 1 0]     [1 0 0]     [0],
      
                 [1 0 0]  
      [G1](x0) = [0 0 1]x0
                 [0 1 0]  
     orientation:
                      [2 2 0]    [3 0 0]    [1]    [2 2 0]    [3 0 0]    [1]                           
      F2(F2(f,x),x) = [2 2 0]f + [3 0 0]x + [2] >= [2 2 0]f + [3 0 0]x + [2] = F2(G1(F2(f,x)),app(f,x))
                      [1 1 0]    [2 0 0]    [1]    [1 1 0]    [2 0 0]    [1]                           
      
                     [1 0 0]     [2]    [1 0 0]           
      app(F0(),x2) = [0 0 0]x2 + [0] >= [0 0 0]x2 = F1(x2)
                     [0 0 0]     [0]    [0 0 0]           
     problem:
      F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                       [1 0 1]     [1 0 0]  
       [app](x0, x1) = [0 1 0]x0 + [0 1 1]x1
                       [0 0 0]     [0 0 1]  ,
       
                      [1 0 1]     [1 1 0]     [0]
       [F2](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [0]
                      [1 1 1]     [0 0 1]     [1],
       
                  [1 0 0]  
       [G1](x0) = [0 1 1]x0
                  [0 0 0]  
      orientation:
                       [2 1 2]    [2 2 1]    [1]    [2 1 2]    [2 2 1]    [0]                           
       F2(F2(f,x),x) = [1 2 2]f + [0 0 1]x + [1] >= [1 2 2]f + [0 0 1]x + [1] = F2(G1(F2(f,x)),app(f,x))
                       [2 2 3]    [1 1 2]    [2]    [2 2 3]    [1 1 2]    [2]                           
      problem:
       
      Qed