/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:
 strict:
  a() -> b()
 weak:
  f(s(x)) -> c(x,f(x))
  c(x,c(y(),z())) -> c(y(),c(x,z()))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                 [2 1]     [1 0]  
   [c](x0, x1) = [2 1]x0 + [1 0]x1,
   
         [0]
   [b] = [0],
   
             [1 0]     [1]
   [f](x0) = [1 0]x0 + [1],
   
         [0]
   [y] = [2],
   
         [1]
   [a] = [0],
   
         [0]
   [z] = [0],
   
             [3 2]  
   [s](x0) = [0 0]x0
  orientation:
         [1]    [0]      
   a() = [0] >= [0] = b()
   
             [3 2]    [1]    [3 1]    [1]            
   f(s(x)) = [3 2]x + [1] >= [3 1]x + [1] = c(x,f(x))
   
                     [2 1]    [2]    [2 1]    [2]                  
   c(x,c(y(),z())) = [2 1]x + [2] >= [2 1]x + [2] = c(y(),c(x,z()))
  problem:
   strict:
    
   weak:
    f(s(x)) -> c(x,f(x))
    c(x,c(y(),z())) -> c(y(),c(x,z()))
  Qed