/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:
 a(a(x1)) -> b(b(b(x1)))
 b(x1) -> c(c(d(x1)))
 c(x1) -> d(d(d(x1)))
 b(c(x1)) -> c(b(x1))
 b(c(d(x1))) -> a(x1)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0) = x0 + 8,
   
   [c](x0) = x0 + 4,
   
   [a](x0) = x0 + 12,
   
   [d](x0) = x0
  orientation:
   a(a(x1)) = x1 + 24 >= x1 + 24 = b(b(b(x1)))
   
   b(x1) = x1 + 8 >= x1 + 8 = c(c(d(x1)))
   
   c(x1) = x1 + 4 >= x1 = d(d(d(x1)))
   
   b(c(x1)) = x1 + 12 >= x1 + 12 = c(b(x1))
   
   b(c(d(x1))) = x1 + 12 >= x1 + 12 = a(x1)
  problem:
   a(a(x1)) -> b(b(b(x1)))
   b(x1) -> c(c(d(x1)))
   b(c(x1)) -> c(b(x1))
   b(c(d(x1))) -> a(x1)
  WPO Processor:
   algebra: Sum
   weight function:
    w0 = 0
    w(a) = 2
    w(d) = w(b) = 1
    w(c) = 0
   status function:
    st(c) = st(d) = st(b) = st(a) = [0]
   precedence:
    b > c ~ d ~ a
   problem:
    
   Qed