/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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failure 'Failure("No result of SMT solver - maybe due to some flag of the solver? or the solver was not found in PATH?")' in subprocess 14696
YES

Problem:
 o(x) -> a(l(x))
 a(l(x)) -> l(a(a(x)))
 l(o(x)) -> o(l(x))
 a(x) -> x
 H(0(),x) -> o(x)
 a(H(H(0(),y),z)) -> c1(y,z)
 a(H(H(H(0(),x),y),z)) -> c2(x,y,z)
 c2(x,y,z) -> o(H(y,z))
 a(c1(x,y)) -> c1(x,H(x,y))
 a(c2(x,y,z)) -> c2(x,H(x,y),z)
 c1(y,z) -> o(z)

Proof:
 Embedding Processor:
  strict:
   o(x) -> a(l(x))
   a(l(x)) -> l(a(a(x)))
   l(o(x)) -> o(l(x))
   a(x) -> x
   H(0(),x) -> o(x)
   a(H(H(0(),y),z)) -> c1(y,z)
   a(H(H(H(0(),x),y),z)) -> c2(x,y,z)
   c2(x,y,z) -> o(H(y,z))
   a(c1(x,y)) -> c1(x,H(x,y))
   a(c2(x,y,z)) -> c2(x,H(x,y),z)
   c1(y,z) -> o(z)
  weak:
   o(x0) -> x0
   a(x0) -> x0
   l(x0) -> x0
   H(x0,x1) -> x0
   H(x0,x1) -> x1
   c1(x0,x1) -> x0
   c1(x0,x1) -> x1
   c2(x0,x1,x2) -> x0
   c2(x0,x1,x2) -> x1
   c2(x0,x1,x2) -> x2
  Higher Ordinal Interpretation Processor:
   degree: 3
   reverse arguments: false
   interpretation:
    o(x6) =  (+) x6
    a(x7) =  (+) x7
    l(x8) =  (+) x8
    H(x9,x10) = omega^( (+) x9) (+) x10 (+) 1
    0() = 0
    c1(x11,x12) = x12 + omega^( (+) x11 (+) 1)
    c2(x13,x14,x15) = omega^(x14 + omega^(x13 (+) 1) (+) 1) (+) x15
   problem:
    strict:
     o(x) -> a(l(x))
     a(l(x)) -> l(a(a(x)))
     l(o(x)) -> o(l(x))
     a(x) -> x
     a(c1(x,y)) -> c1(x,H(x,y))
     a(c2(x,y,z)) -> c2(x,H(x,y),z)
    weak:
     o(x0) -> x0
     a(x0) -> x0
     l(x0) -> x0
     f7(x11) -> c1(x11,x12)
     f8(x15) -> c2(x13,x14,x15)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                   [0]
     [H](x0, x1) = [0],
     
                [2 2]     [2]
     [f8](x0) = [2 2]x0 + [2],
     
               [1 0]  
     [l](x0) = [1 1]x0,
     
                    [2]
     [c1](x0, x1) = [2],
     
               [2 0]     [1]
     [o](x0) = [1 2]x0 + [0],
     
                [2 0]     [2]
     [f7](x0) = [0 2]x0 + [3],
     
                        [0 0]     [0]
     [c2](x0, x1, x2) = [1 1]x2 + [1],
     
                 
     [a](x0) = x0
    orientation:
            [2 0]    [1]    [1 0]           
     o(x) = [1 2]x + [0] >= [1 1]x = a(l(x))
     
               [1 0]     [1 0]              
     a(l(x)) = [1 1]x >= [1 1]x = l(a(a(x)))
     
               [2 0]    [1]    [2 0]    [1]          
     l(o(x)) = [3 2]x + [1] >= [3 2]x + [0] = o(l(x))
     
                      
     a(x) = x >= x = x
     
                  [2]    [2]               
     a(c1(x,y)) = [2] >= [2] = c1(x,H(x,y))
     
                    [0 0]    [0]    [0 0]    [0]                 
     a(c2(x,y,z)) = [1 1]z + [1] >= [1 1]z + [1] = c2(x,H(x,y),z)
     
             [2 0]     [1]           
     o(x0) = [1 2]x0 + [0] >= x0 = x0
     
                          
     a(x0) = x0 >= x0 = x0
     
             [1 0]             
     l(x0) = [1 1]x0 >= x0 = x0
     
               [2 0]      [2]    [2]              
     f7(x11) = [0 2]x11 + [3] >= [2] = c1(x11,x12)
     
               [2 2]      [2]    [0 0]      [0]                  
     f8(x15) = [2 2]x15 + [2] >= [1 1]x15 + [1] = c2(x13,x14,x15)
    problem:
     strict:
      a(l(x)) -> l(a(a(x)))
      l(o(x)) -> o(l(x))
      a(x) -> x
      a(c1(x,y)) -> c1(x,H(x,y))
      a(c2(x,y,z)) -> c2(x,H(x,y),z)
     weak:
      o(x0) -> x0
      a(x0) -> x0
      l(x0) -> x0
      f7(x11) -> c1(x11,x12)
      f8(x15) -> c2(x13,x14,x15)
      f9() -> c1(x16,x17)
      f10() -> H(x18,x19)
      f11() -> c2(x20,x21,x22)
    Matrix Interpretation Processor: dim=2
     
     interpretation:
                    [0]
      [H](x0, x1) = [0],
      
                 [1 0]     [2]
      [f8](x0) = [2 0]x0 + [2],
      
                [2 2]     [0]
      [l](x0) = [0 2]x0 + [1],
      
                     [0]
      [c1](x0, x1) = [0],
      
              [1]
      [f10] = [2],
      
                     [1]
      [o](x0) = x0 + [0],
      
                 [1 2]     [1]
      [f7](x0) = [2 2]x0 + [0],
      
              [0]
      [f11] = [2],
      
             [0]
      [f9] = [2],
      
                         [0]
      [c2](x0, x1, x2) = [0],
      
                  
      [a](x0) = x0
     orientation:
                [2 2]    [0]    [2 2]    [0]             
      a(l(x)) = [0 2]x + [1] >= [0 2]x + [1] = l(a(a(x)))
      
                [2 2]    [2]    [2 2]    [1]          
      l(o(x)) = [0 2]x + [1] >= [0 2]x + [1] = o(l(x))
      
                       
      a(x) = x >= x = x
      
                   [0]    [0]               
      a(c1(x,y)) = [0] >= [0] = c1(x,H(x,y))
      
                     [0]    [0]                 
      a(c2(x,y,z)) = [0] >= [0] = c2(x,H(x,y),z)
      
                   [1]           
      o(x0) = x0 + [0] >= x0 = x0
      
                           
      a(x0) = x0 >= x0 = x0
      
              [2 2]     [0]           
      l(x0) = [0 2]x0 + [1] >= x0 = x0
      
                [1 2]      [1]    [0]              
      f7(x11) = [2 2]x11 + [0] >= [0] = c1(x11,x12)
      
                [1 0]      [2]    [0]                  
      f8(x15) = [2 0]x15 + [2] >= [0] = c2(x13,x14,x15)
      
             [0]    [0]              
      f9() = [2] >= [0] = c1(x16,x17)
      
              [1]    [0]             
      f10() = [2] >= [0] = H(x18,x19)
      
              [0]    [0]                  
      f11() = [2] >= [0] = c2(x20,x21,x22)
     problem:
      strict:
       a(l(x)) -> l(a(a(x)))
       a(x) -> x
       a(c1(x,y)) -> c1(x,H(x,y))
       a(c2(x,y,z)) -> c2(x,H(x,y),z)
      weak:
       o(x0) -> x0
       a(x0) -> x0
       l(x0) -> x0
       f7(x11) -> c1(x11,x12)
       f8(x15) -> c2(x13,x14,x15)
       f9() -> c1(x16,x17)
       f10() -> H(x18,x19)
       f11() -> c2(x20,x21,x22)
       f12() -> c1(x23,x24)
       f13() -> H(x25,x26)
       f14() -> c2(x27,x28,x29)
     Matrix Interpretation Processor: dim=2
      
      interpretation:
                     [0]
       [H](x0, x1) = [0],
       
                  [2 0]     [2]
       [f8](x0) = [2 1]x0 + [1],
       
                 [1 0]  
       [l](x0) = [0 2]x0,
       
                      [0]
       [c1](x0, x1) = [2],
       
               [2]
       [f10] = [0],
       
                 [2 0]     [0]
       [o](x0) = [0 2]x0 + [1],
       
                  [1 1]     [1]
       [f7](x0) = [2 0]x0 + [2],
       
               [2]
       [f14] = [1],
       
               [0]
       [f12] = [3],
       
               [0]
       [f11] = [0],
       
              [0]
       [f9] = [2],
       
               [0]
       [f13] = [1],
       
                          [0]
       [c2](x0, x1, x2) = [0],
       
                 [1 1]  
       [a](x0) = [0 1]x0
      orientation:
                 [1 2]     [1 2]              
       a(l(x)) = [0 2]x >= [0 2]x = l(a(a(x)))
       
              [1 1]          
       a(x) = [0 1]x >= x = x
       
                    [2]    [0]               
       a(c1(x,y)) = [2] >= [2] = c1(x,H(x,y))
       
                      [0]    [0]                 
       a(c2(x,y,z)) = [0] >= [0] = c2(x,H(x,y),z)
       
               [2 0]     [0]           
       o(x0) = [0 2]x0 + [1] >= x0 = x0
       
               [1 1]             
       a(x0) = [0 1]x0 >= x0 = x0
       
               [1 0]             
       l(x0) = [0 2]x0 >= x0 = x0
       
                 [1 1]      [1]    [0]              
       f7(x11) = [2 0]x11 + [2] >= [2] = c1(x11,x12)
       
                 [2 0]      [2]    [0]                  
       f8(x15) = [2 1]x15 + [1] >= [0] = c2(x13,x14,x15)
       
              [0]    [0]              
       f9() = [2] >= [2] = c1(x16,x17)
       
               [2]    [0]             
       f10() = [0] >= [0] = H(x18,x19)
       
               [0]    [0]                  
       f11() = [0] >= [0] = c2(x20,x21,x22)
       
               [0]    [0]              
       f12() = [3] >= [2] = c1(x23,x24)
       
               [0]    [0]             
       f13() = [1] >= [0] = H(x25,x26)
       
               [2]    [0]                  
       f14() = [1] >= [0] = c2(x27,x28,x29)
      problem:
       strict:
        a(l(x)) -> l(a(a(x)))
        a(x) -> x
        a(c2(x,y,z)) -> c2(x,H(x,y),z)
       weak:
        o(x0) -> x0
        a(x0) -> x0
        l(x0) -> x0
        f7(x11) -> c1(x11,x12)
        f8(x15) -> c2(x13,x14,x15)
        f9() -> c1(x16,x17)
        f10() -> H(x18,x19)
        f11() -> c2(x20,x21,x22)
        f12() -> c1(x23,x24)
        f13() -> H(x25,x26)
        f14() -> c2(x27,x28,x29)
        f15() -> c1(x30,x31)
        f16() -> H(x32,x33)
        f17() -> c2(x34,x35,x36)
      Matrix Interpretation Processor: dim=2
       
       interpretation:
                      [0]
        [H](x0, x1) = [0],
        
                [0]
        [f15] = [0],
        
                   [2 0]     [1]
        [f8](x0) = [0 0]x0 + [0],
        
                  [1 0]     [1]
        [l](x0) = [0 2]x0 + [1],
        
                [0]
        [f16] = [0],
        
                [0]
        [f17] = [0],
        
                       [0]
        [c1](x0, x1) = [0],
        
                [0]
        [f10] = [0],
        
                  [2 1]  
        [o](x0) = [1 1]x0,
        
                   [1 2]     [2]
        [f7](x0) = [0 0]x0 + [0],
        
                [0]
        [f14] = [0],
        
                [0]
        [f12] = [0],
        
                [0]
        [f11] = [0],
        
               [0]
        [f9] = [0],
        
                [0]
        [f13] = [0],
        
                           [0]
        [c2](x0, x1, x2) = [0],
        
                  [1 1]  
        [a](x0) = [0 1]x0
       orientation:
                  [1 2]    [2]    [1 2]    [1]             
        a(l(x)) = [0 2]x + [1] >= [0 2]x + [1] = l(a(a(x)))
        
               [1 1]          
        a(x) = [0 1]x >= x = x
        
                       [0]    [0]                 
        a(c2(x,y,z)) = [0] >= [0] = c2(x,H(x,y),z)
        
                [2 1]             
        o(x0) = [1 1]x0 >= x0 = x0
        
                [1 1]             
        a(x0) = [0 1]x0 >= x0 = x0
        
                [1 0]     [1]           
        l(x0) = [0 2]x0 + [1] >= x0 = x0
        
                  [1 2]      [2]    [0]              
        f7(x11) = [0 0]x11 + [0] >= [0] = c1(x11,x12)
        
                  [2 0]      [1]    [0]                  
        f8(x15) = [0 0]x15 + [0] >= [0] = c2(x13,x14,x15)
        
               [0]    [0]              
        f9() = [0] >= [0] = c1(x16,x17)
        
                [0]    [0]             
        f10() = [0] >= [0] = H(x18,x19)
        
                [0]    [0]                  
        f11() = [0] >= [0] = c2(x20,x21,x22)
        
                [0]    [0]              
        f12() = [0] >= [0] = c1(x23,x24)
        
                [0]    [0]             
        f13() = [0] >= [0] = H(x25,x26)
        
                [0]    [0]                  
        f14() = [0] >= [0] = c2(x27,x28,x29)
        
                [0]    [0]              
        f15() = [0] >= [0] = c1(x30,x31)
        
                [0]    [0]             
        f16() = [0] >= [0] = H(x32,x33)
        
                [0]    [0]                  
        f17() = [0] >= [0] = c2(x34,x35,x36)
       problem:
        strict:
         a(x) -> x
         a(c2(x,y,z)) -> c2(x,H(x,y),z)
        weak:
         o(x0) -> x0
         a(x0) -> x0
         l(x0) -> x0
         f7(x11) -> c1(x11,x12)
         f8(x15) -> c2(x13,x14,x15)
         f9() -> c1(x16,x17)
         f10() -> H(x18,x19)
         f11() -> c2(x20,x21,x22)
         f12() -> c1(x23,x24)
         f13() -> H(x25,x26)
         f14() -> c2(x27,x28,x29)
         f15() -> c1(x30,x31)
         f16() -> H(x32,x33)
         f17() -> c2(x34,x35,x36)
         f18() -> c2(x37,x38,x39)
         f19() -> H(x40,x41)
         f20() -> c1(x42,x43)
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [f18] = 2,
         
         [H](x0, x1) = 0,
         
         [f15] = 0,
         
         [f8](x0) = 2x0 + 2,
         
         [l](x0) = x0,
         
         [f16] = 0,
         
         [f19] = 0,
         
         [f17] = 2,
         
         [c1](x0, x1) = 0,
         
         [f10] = 0,
         
         [o](x0) = x0,
         
         [f7](x0) = 2x0,
         
         [f20] = 0,
         
         [f14] = 2,
         
         [f12] = 0,
         
         [f11] = 2,
         
         [f9] = 0,
         
         [f13] = 0,
         
         [c2](x0, x1, x2) = 2,
         
         [a](x0) = 2x0 + 3
        orientation:
         a(x) = 2x + 3 >= x = x
         
         a(c2(x,y,z)) = 7 >= 2 = c2(x,H(x,y),z)
         
         o(x0) = x0 >= x0 = x0
         
         a(x0) = 2x0 + 3 >= x0 = x0
         
         l(x0) = x0 >= x0 = x0
         
         f7(x11) = 2x11 >= 0 = c1(x11,x12)
         
         f8(x15) = 2x15 + 2 >= 2 = c2(x13,x14,x15)
         
         f9() = 0 >= 0 = c1(x16,x17)
         
         f10() = 0 >= 0 = H(x18,x19)
         
         f11() = 2 >= 2 = c2(x20,x21,x22)
         
         f12() = 0 >= 0 = c1(x23,x24)
         
         f13() = 0 >= 0 = H(x25,x26)
         
         f14() = 2 >= 2 = c2(x27,x28,x29)
         
         f15() = 0 >= 0 = c1(x30,x31)
         
         f16() = 0 >= 0 = H(x32,x33)
         
         f17() = 2 >= 2 = c2(x34,x35,x36)
         
         f18() = 2 >= 2 = c2(x37,x38,x39)
         
         f19() = 0 >= 0 = H(x40,x41)
         
         f20() = 0 >= 0 = c1(x42,x43)
        problem:
         strict:
          
         weak:
          o(x0) -> x0
          a(x0) -> x0
          l(x0) -> x0
          f7(x11) -> c1(x11,x12)
          f8(x15) -> c2(x13,x14,x15)
          f9() -> c1(x16,x17)
          f10() -> H(x18,x19)
          f11() -> c2(x20,x21,x22)
          f12() -> c1(x23,x24)
          f13() -> H(x25,x26)
          f14() -> c2(x27,x28,x29)
          f15() -> c1(x30,x31)
          f16() -> H(x32,x33)
          f17() -> c2(x34,x35,x36)
          f18() -> c2(x37,x38,x39)
          f19() -> H(x40,x41)
          f20() -> c1(x42,x43)
          f21() -> c2(x44,x45,x46)
          f22() -> H(x47,x48)
          f23() -> c1(x49,x50)
        Qed