/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:
 sum(0()) -> 0()
 sum(s(x)) -> +(sqr(s(x)),sum(x))
 sqr(x) -> *(x,x)
 sum(s(x)) -> +(*(s(x),s(x)),sum(x))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [*](x0, x1) = x0 + x1,
   
   [+](x0, x1) = 2x0 + x1,
   
   [sqr](x0) = 2x0,
   
   [s](x0) = 4x0,
   
   [sum](x0) = 6x0 + 2,
   
   [0] = 0
  orientation:
   sum(0()) = 2 >= 0 = 0()
   
   sum(s(x)) = 24x + 2 >= 22x + 2 = +(sqr(s(x)),sum(x))
   
   sqr(x) = 2x >= 2x = *(x,x)
   
   sum(s(x)) = 24x + 2 >= 22x + 2 = +(*(s(x),s(x)),sum(x))
  problem:
   sum(s(x)) -> +(sqr(s(x)),sum(x))
   sqr(x) -> *(x,x)
   sum(s(x)) -> +(*(s(x),s(x)),sum(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [*](x0, x1) = x0 + x1 + 1,
    
    [+](x0, x1) = x0 + x1,
    
    [sqr](x0) = 2x0 + 3,
    
    [s](x0) = 4x0 + 4,
    
    [sum](x0) = 3x0
   orientation:
    sum(s(x)) = 12x + 12 >= 11x + 11 = +(sqr(s(x)),sum(x))
    
    sqr(x) = 2x + 3 >= 2x + 1 = *(x,x)
    
    sum(s(x)) = 12x + 12 >= 11x + 9 = +(*(s(x),s(x)),sum(x))
   problem:
    
   Qed