/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:
 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) = 2x0 + x1 + 1,
   
   [sum](x0) = 6x0 + 5,
   
   [sqr](x0) = 2x0,
   
   [*](x0, x1) = x0 + x1,
   
   [0] = 4,
   
   [s](x0) = 3x0 + 1
  orientation:
   sum(0()) = 29 >= 4 = 0()
   
   sum(s(x)) = 18x + 11 >= 18x + 10 = +(sqr(s(x)),sum(x))
   
   sqr(x) = 2x >= 2x = *(x,x)
   
   sum(s(x)) = 18x + 11 >= 18x + 10 = +(*(s(x),s(x)),sum(x))
  problem:
   sqr(x) -> *(x,x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [sqr](x0) = 2x0 + 1,
    
    [*](x0, x1) = x0 + x1
   orientation:
    sqr(x) = 2x + 1 >= 2x = *(x,x)
   problem:
    
   Qed