40.13/10.53	YES
40.44/10.54	
40.44/10.54	Problem:
40.44/10.54	 a(b(x1)) -> b(r(x1))
40.44/10.54	 r(a(x1)) -> d(r(x1))
40.44/10.54	 r(x1) -> d(x1)
40.44/10.54	 d(a(x1)) -> a(a(d(x1)))
40.44/10.54	 d(x1) -> a(x1)
40.44/10.54	
40.44/10.54	Proof:
40.44/10.54	 DP Processor:
40.44/10.54	  DPs:
40.44/10.54	   a#(b(x1)) -> r#(x1)
40.44/10.54	   r#(a(x1)) -> r#(x1)
40.44/10.54	   r#(a(x1)) -> d#(r(x1))
40.44/10.54	   r#(x1) -> d#(x1)
40.44/10.54	   d#(a(x1)) -> d#(x1)
40.44/10.54	   d#(a(x1)) -> a#(d(x1))
40.44/10.54	   d#(a(x1)) -> a#(a(d(x1)))
40.44/10.54	   d#(x1) -> a#(x1)
40.44/10.54	  TRS:
40.44/10.54	   a(b(x1)) -> b(r(x1))
40.44/10.54	   r(a(x1)) -> d(r(x1))
40.44/10.54	   r(x1) -> d(x1)
40.44/10.54	   d(a(x1)) -> a(a(d(x1)))
40.44/10.54	   d(x1) -> a(x1)
40.44/10.54	  TDG Processor:
40.44/10.54	   DPs:
40.44/10.54	    a#(b(x1)) -> r#(x1)
40.44/10.54	    r#(a(x1)) -> r#(x1)
40.44/10.54	    r#(a(x1)) -> d#(r(x1))
40.44/10.54	    r#(x1) -> d#(x1)
40.44/10.54	    d#(a(x1)) -> d#(x1)
40.44/10.54	    d#(a(x1)) -> a#(d(x1))
40.44/10.54	    d#(a(x1)) -> a#(a(d(x1)))
40.44/10.54	    d#(x1) -> a#(x1)
40.44/10.54	   TRS:
40.44/10.54	    a(b(x1)) -> b(r(x1))
40.44/10.54	    r(a(x1)) -> d(r(x1))
40.44/10.54	    r(x1) -> d(x1)
40.44/10.54	    d(a(x1)) -> a(a(d(x1)))
40.44/10.54	    d(x1) -> a(x1)
40.44/10.54	   graph:
40.44/10.54	    d#(a(x1)) -> d#(x1) -> d#(x1) -> a#(x1)
40.44/10.54	    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> a#(a(d(x1)))
40.44/10.54	    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> a#(d(x1))
40.44/10.54	    d#(a(x1)) -> d#(x1) -> d#(a(x1)) -> d#(x1)
40.44/10.54	    d#(a(x1)) -> a#(d(x1)) -> a#(b(x1)) -> r#(x1)
40.44/10.54	    d#(a(x1)) -> a#(a(d(x1))) -> a#(b(x1)) -> r#(x1)
40.44/10.54	    d#(x1) -> a#(x1) -> a#(b(x1)) -> r#(x1)
40.44/10.54	    r#(a(x1)) -> d#(r(x1)) -> d#(x1) -> a#(x1)
40.44/10.54	    r#(a(x1)) -> d#(r(x1)) -> d#(a(x1)) -> a#(a(d(x1)))
40.44/10.54	    r#(a(x1)) -> d#(r(x1)) -> d#(a(x1)) -> a#(d(x1))
40.44/10.54	    r#(a(x1)) -> d#(r(x1)) -> d#(a(x1)) -> d#(x1)
40.44/10.54	    r#(a(x1)) -> r#(x1) -> r#(x1) -> d#(x1)
40.44/10.54	    r#(a(x1)) -> r#(x1) -> r#(a(x1)) -> d#(r(x1))
40.44/10.54	    r#(a(x1)) -> r#(x1) -> r#(a(x1)) -> r#(x1)
40.44/10.54	    r#(x1) -> d#(x1) -> d#(x1) -> a#(x1)
40.44/10.54	    r#(x1) -> d#(x1) -> d#(a(x1)) -> a#(a(d(x1)))
40.44/10.54	    r#(x1) -> d#(x1) -> d#(a(x1)) -> a#(d(x1))
40.44/10.54	    r#(x1) -> d#(x1) -> d#(a(x1)) -> d#(x1)
40.44/10.54	    a#(b(x1)) -> r#(x1) -> r#(x1) -> d#(x1)
40.44/10.54	    a#(b(x1)) -> r#(x1) -> r#(a(x1)) -> d#(r(x1))
40.44/10.54	    a#(b(x1)) -> r#(x1) -> r#(a(x1)) -> r#(x1)
40.44/10.54	   Polynomial Interpretation Processor:
40.44/10.54	    dimension: 1
40.44/10.54	    interpretation:
40.44/10.54	     [d#](x0) = x0,
40.44/10.54	     
40.44/10.54	     [r#](x0) = x0,
40.44/10.54	     
40.44/10.54	     [a#](x0) = x0,
40.44/10.54	     
40.44/10.54	     [d](x0) = x0,
40.44/10.54	     
40.44/10.54	     [r](x0) = x0,
40.44/10.54	     
40.44/10.54	     [a](x0) = x0,
40.44/10.54	     
40.44/10.54	     [b](x0) = x0 + 1
40.44/10.54	    orientation:
40.44/10.54	     a#(b(x1)) = x1 + 1 >= x1 = r#(x1)
40.44/10.54	     
40.44/10.54	     r#(a(x1)) = x1 >= x1 = r#(x1)
40.44/10.54	     
40.44/10.54	     r#(a(x1)) = x1 >= x1 = d#(r(x1))
40.44/10.54	     
40.44/10.54	     r#(x1) = x1 >= x1 = d#(x1)
40.44/10.54	     
40.44/10.54	     d#(a(x1)) = x1 >= x1 = d#(x1)
40.44/10.54	     
40.44/10.54	     d#(a(x1)) = x1 >= x1 = a#(d(x1))
40.44/10.54	     
40.44/10.54	     d#(a(x1)) = x1 >= x1 = a#(a(d(x1)))
40.44/10.54	     
40.44/10.54	     d#(x1) = x1 >= x1 = a#(x1)
40.44/10.54	     
40.44/10.54	     a(b(x1)) = x1 + 1 >= x1 + 1 = b(r(x1))
40.44/10.54	     
40.44/10.54	     r(a(x1)) = x1 >= x1 = d(r(x1))
40.44/10.54	     
40.44/10.54	     r(x1) = x1 >= x1 = d(x1)
40.44/10.54	     
40.44/10.54	     d(a(x1)) = x1 >= x1 = a(a(d(x1)))
40.44/10.54	     
40.44/10.54	     d(x1) = x1 >= x1 = a(x1)
40.44/10.54	    problem:
40.44/10.54	     DPs:
40.44/10.54	      r#(a(x1)) -> r#(x1)
40.44/10.54	      r#(a(x1)) -> d#(r(x1))
40.44/10.54	      r#(x1) -> d#(x1)
40.44/10.54	      d#(a(x1)) -> d#(x1)
40.44/10.54	      d#(a(x1)) -> a#(d(x1))
40.44/10.54	      d#(a(x1)) -> a#(a(d(x1)))
40.44/10.54	      d#(x1) -> a#(x1)
40.44/10.54	     TRS:
40.44/10.54	      a(b(x1)) -> b(r(x1))
40.44/10.54	      r(a(x1)) -> d(r(x1))
40.44/10.54	      r(x1) -> d(x1)
40.44/10.54	      d(a(x1)) -> a(a(d(x1)))
40.44/10.54	      d(x1) -> a(x1)
40.44/10.54	    SCC Processor:
40.44/10.54	     #sccs: 2
40.44/10.54	     #rules: 2
40.44/10.54	     #arcs: 21/49
40.44/10.54	     DPs:
40.44/10.54	      r#(a(x1)) -> r#(x1)
40.44/10.54	     TRS:
40.44/10.54	      a(b(x1)) -> b(r(x1))
40.44/10.54	      r(a(x1)) -> d(r(x1))
40.44/10.54	      r(x1) -> d(x1)
40.44/10.54	      d(a(x1)) -> a(a(d(x1)))
40.44/10.54	      d(x1) -> a(x1)
40.44/10.54	     Usable Rule Processor:
40.44/10.54	      DPs:
40.44/10.54	       r#(a(x1)) -> r#(x1)
40.44/10.54	      TRS:
40.44/10.54	       
40.44/10.54	      Polynomial Interpretation Processor:
40.44/10.54	       dimension: 1
40.44/10.54	       interpretation:
40.44/10.54	        [r#](x0) = x0,
40.44/10.54	        
40.44/10.54	        [a](x0) = x0 + 1
40.44/10.54	       orientation:
40.44/10.54	        r#(a(x1)) = x1 + 1 >= x1 = r#(x1)
40.44/10.54	       problem:
40.44/10.54	        DPs:
40.44/10.54	         
40.44/10.54	        TRS:
40.44/10.54	         
40.44/10.54	       Qed
40.44/10.54	     
40.44/10.54	     DPs:
40.44/10.54	      d#(a(x1)) -> d#(x1)
40.44/10.54	     TRS:
40.44/10.54	      a(b(x1)) -> b(r(x1))
40.44/10.54	      r(a(x1)) -> d(r(x1))
40.44/10.54	      r(x1) -> d(x1)
40.44/10.54	      d(a(x1)) -> a(a(d(x1)))
40.44/10.54	      d(x1) -> a(x1)
40.44/10.54	     Usable Rule Processor:
40.44/10.54	      DPs:
40.44/10.54	       d#(a(x1)) -> d#(x1)
40.44/10.54	      TRS:
40.44/10.54	       
40.44/10.54	      Polynomial Interpretation Processor:
40.44/10.54	       dimension: 1
40.44/10.54	       interpretation:
40.44/10.54	        [d#](x0) = x0,
40.44/10.54	        
40.44/10.54	        [a](x0) = x0 + 1
40.44/10.54	       orientation:
40.44/10.54	        d#(a(x1)) = x1 + 1 >= x1 = d#(x1)
40.44/10.54	       problem:
40.44/10.54	        DPs:
40.44/10.54	         
40.44/10.54	        TRS:
40.44/10.54	         
40.44/10.54	       Qed
40.44/10.55	EOF