/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(lambda(x),y) -> lambda(a(x,1()))
 a(lambda(x),y) -> lambda(a(x,a(y,t())))
 a(a(x,y),z) -> a(x,a(y,z))
 lambda(x) -> x
 a(x,y) -> x
 a(x,y) -> y

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [a](x0, x1) = x0 + x1,
   
   [t] = 0,
   
   [lambda](x0) = x0 + 6,
   
   [1] = 0
  orientation:
   a(lambda(x),y) = x + y + 6 >= x + 6 = lambda(a(x,1()))
   
   a(lambda(x),y) = x + y + 6 >= x + y + 6 = lambda(a(x,a(y,t())))
   
   a(a(x,y),z) = x + y + z >= x + y + z = a(x,a(y,z))
   
   lambda(x) = x + 6 >= x = x
   
   a(x,y) = x + y >= x = x
   
   a(x,y) = x + y >= y = y
  problem:
   a(lambda(x),y) -> lambda(a(x,1()))
   a(lambda(x),y) -> lambda(a(x,a(y,t())))
   a(a(x,y),z) -> a(x,a(y,z))
   a(x,y) -> x
   a(x,y) -> y
  WPO Processor:
   algebra: Sum
   weight function:
    w0 = 0
    w(lambda) = 1
    w(t) = w(1) = w(a) = 0
   status function:
    st(t) = st(1) = []
    st(a) = [0, 1]
    st(lambda) = [0]
   precedence:
    a > t ~ 1 ~ lambda
   problem:
    
   Qed