/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(a(),f(a(),x)) -> f(a(),f(f(a(),a()),f(a(),x)))

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   a ==> a0/0 a1/1 a2/2
   
  uncurry-rules:
   f(a1(x2),x3) -> a2(x2,x3)
   f(a0(),x2) -> a1(x2)
  eta-rules:
   f(f(a(),f(a(),x)),x1) -> f(f(a(),f(f(a(),a()),f(a(),x))),x1)
  problem:
   a1(a1(x)) -> a1(a2(a0(),a1(x)))
   a2(a1(x),x1) -> a2(a2(a0(),a1(x)),x1)
   f(a1(x2),x3) -> a2(x2,x3)
   f(a0(),x2) -> a1(x2)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a2](x0, x1) = x0 + x1,
    
    [f](x0, x1) = 2x0 + 4x1 + 1,
    
    [a1](x0) = 2x0,
    
    [a0] = 0
   orientation:
    a1(a1(x)) = 4x >= 4x = a1(a2(a0(),a1(x)))
    
    a2(a1(x),x1) = 2x + x1 >= 2x + x1 = a2(a2(a0(),a1(x)),x1)
    
    f(a1(x2),x3) = 4x2 + 4x3 + 1 >= x2 + x3 = a2(x2,x3)
    
    f(a0(),x2) = 4x2 + 1 >= 2x2 = a1(x2)
   problem:
    a1(a1(x)) -> a1(a2(a0(),a1(x)))
    a2(a1(x),x1) -> a2(a2(a0(),a1(x)),x1)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                    [1 1 0]     [1 0 0]  
     [a2](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 1 1]  ,
     
                [1 1 0]     [0]
     [a1](x0) = [0 0 0]x0 + [1]
                [0 1 1]     [0],
     
            [0]
     [a0] = [0]
            [0]
    orientation:
                 [1 1 0]    [1]    [1 1 0]    [0]                     
     a1(a1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = a1(a2(a0(),a1(x)))
                 [0 1 1]    [1]    [0 1 1]    [1]                     
     
                    [1 1 0]    [1 0 0]     [1]    [1 1 0]    [1 0 0]                          
     a2(a1(x),x1) = [0 0 0]x + [0 0 0]x1 + [0] >= [0 0 0]x + [0 0 0]x1 = a2(a2(a0(),a1(x)),x1)
                    [0 0 0]    [0 1 1]     [0]    [0 0 0]    [0 1 1]                          
    problem:
     
    Qed