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


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YES

Problem:
 :(x,x) -> e()
 :(x,e()) -> x
 i(:(x,y)) -> :(y,x)
 :(:(x,y),z) -> :(x,:(z,i(y)))
 :(e(),x) -> i(x)
 i(i(x)) -> x
 i(e()) -> e()
 :(x,:(y,i(x))) -> i(y)
 :(x,:(y,:(i(x),z))) -> :(i(z),y)
 :(i(x),:(y,x)) -> i(y)
 :(i(x),:(y,:(x,z))) -> :(i(z),y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [i](x0) = x0,
   
   [e] = 4,
   
   [:](x0, x1) = x0 + x1 + 4
  orientation:
   :(x,x) = 2x + 4 >= 4 = e()
   
   :(x,e()) = x + 8 >= x = x
   
   i(:(x,y)) = x + y + 4 >= x + y + 4 = :(y,x)
   
   :(:(x,y),z) = x + y + z + 8 >= x + y + z + 8 = :(x,:(z,i(y)))
   
   :(e(),x) = x + 8 >= x = i(x)
   
   i(i(x)) = x >= x = x
   
   i(e()) = 4 >= 4 = e()
   
   :(x,:(y,i(x))) = 2x + y + 8 >= y = i(y)
   
   :(x,:(y,:(i(x),z))) = 2x + y + z + 12 >= y + z + 4 = :(i(z),y)
   
   :(i(x),:(y,x)) = 2x + y + 8 >= y = i(y)
   
   :(i(x),:(y,:(x,z))) = 2x + y + z + 12 >= y + z + 4 = :(i(z),y)
  problem:
   :(x,x) -> e()
   i(:(x,y)) -> :(y,x)
   :(:(x,y),z) -> :(x,:(z,i(y)))
   i(i(x)) -> x
   i(e()) -> e()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [i](x0) = x0,
    
    [e] = 0,
    
    [:](x0, x1) = x0 + x1 + 2
   orientation:
    :(x,x) = 2x + 2 >= 0 = e()
    
    i(:(x,y)) = x + y + 2 >= x + y + 2 = :(y,x)
    
    :(:(x,y),z) = x + y + z + 4 >= x + y + z + 4 = :(x,:(z,i(y)))
    
    i(i(x)) = x >= x = x
    
    i(e()) = 0 >= 0 = e()
   problem:
    i(:(x,y)) -> :(y,x)
    :(:(x,y),z) -> :(x,:(z,i(y)))
    i(i(x)) -> x
    i(e()) -> e()
   KBO Processor:
    weight function:
     w0 = 1
     w(e) = 1
     w(i) = w(:) = 0
    precedence:
     i > e ~ :
    problem:
     
    Qed