40.32/10.58	YES
40.32/10.58	
40.32/10.58	Problem:
40.32/10.58	 a(b(x1)) -> b(c(a(x1)))
40.32/10.58	 b(c(x1)) -> c(b(b(x1)))
40.32/10.58	 a(c(x1)) -> c(a(b(x1)))
40.32/10.58	
40.32/10.58	Proof:
40.32/10.58	 DP Processor:
40.32/10.58	  DPs:
40.32/10.58	   a#(b(x1)) -> a#(x1)
40.32/10.58	   a#(b(x1)) -> b#(c(a(x1)))
40.32/10.58	   b#(c(x1)) -> b#(x1)
40.32/10.58	   b#(c(x1)) -> b#(b(x1))
40.32/10.58	   a#(c(x1)) -> b#(x1)
40.32/10.58	   a#(c(x1)) -> a#(b(x1))
40.32/10.58	  TRS:
40.32/10.58	   a(b(x1)) -> b(c(a(x1)))
40.32/10.58	   b(c(x1)) -> c(b(b(x1)))
40.32/10.58	   a(c(x1)) -> c(a(b(x1)))
40.32/10.58	  TDG Processor:
40.32/10.58	   DPs:
40.32/10.58	    a#(b(x1)) -> a#(x1)
40.32/10.58	    a#(b(x1)) -> b#(c(a(x1)))
40.32/10.58	    b#(c(x1)) -> b#(x1)
40.32/10.58	    b#(c(x1)) -> b#(b(x1))
40.32/10.58	    a#(c(x1)) -> b#(x1)
40.32/10.58	    a#(c(x1)) -> a#(b(x1))
40.32/10.58	   TRS:
40.32/10.58	    a(b(x1)) -> b(c(a(x1)))
40.32/10.58	    b(c(x1)) -> c(b(b(x1)))
40.32/10.58	    a(c(x1)) -> c(a(b(x1)))
40.32/10.58	   graph:
40.32/10.58	    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
40.32/10.58	    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
40.32/10.58	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
40.32/10.58	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
40.32/10.58	    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
40.32/10.58	    a#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
40.32/10.58	    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1))
40.32/10.58	    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1)
40.32/10.58	    a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> b#(c(a(x1)))
40.32/10.58	    a#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
40.32/10.58	    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(b(x1))
40.32/10.58	    a#(b(x1)) -> b#(c(a(x1))) -> b#(c(x1)) -> b#(x1)
40.32/10.58	    a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> a#(b(x1))
40.32/10.58	    a#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
40.32/10.58	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(a(x1)))
40.32/10.58	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
40.32/10.58	   SCC Processor:
40.32/10.58	    #sccs: 2
40.32/10.58	    #rules: 4
40.32/10.58	    #arcs: 16/36
40.32/10.58	    DPs:
40.32/10.58	     a#(c(x1)) -> a#(b(x1))
40.32/10.58	     a#(b(x1)) -> a#(x1)
40.32/10.58	    TRS:
40.32/10.58	     a(b(x1)) -> b(c(a(x1)))
40.32/10.58	     b(c(x1)) -> c(b(b(x1)))
40.32/10.58	     a(c(x1)) -> c(a(b(x1)))
40.32/10.58	    Usable Rule Processor:
40.32/10.58	     DPs:
40.32/10.58	      a#(c(x1)) -> a#(b(x1))
40.32/10.58	      a#(b(x1)) -> a#(x1)
40.32/10.58	     TRS:
40.32/10.58	      b(c(x1)) -> c(b(b(x1)))
40.32/10.58	     Polynomial Interpretation Processor:
40.32/10.58	      dimension: 1
40.32/10.58	      interpretation:
40.32/10.58	       [a#](x0) = x0,
40.32/10.58	       
40.32/10.58	       [c](x0) = x0 + 1,
40.32/10.58	       
40.32/10.58	       [b](x0) = x0
40.32/10.58	      orientation:
40.32/10.58	       a#(c(x1)) = x1 + 1 >= x1 = a#(b(x1))
40.32/10.58	       
40.32/10.58	       a#(b(x1)) = x1 >= x1 = a#(x1)
40.32/10.58	       
40.32/10.58	       b(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1)))
40.32/10.58	      problem:
40.32/10.58	       DPs:
40.32/10.58	        a#(b(x1)) -> a#(x1)
40.32/10.58	       TRS:
40.32/10.58	        b(c(x1)) -> c(b(b(x1)))
40.32/10.58	      Usable Rule Processor:
40.32/10.58	       DPs:
40.32/10.58	        a#(b(x1)) -> a#(x1)
40.32/10.58	       TRS:
40.32/10.58	        
40.32/10.58	       Polynomial Interpretation Processor:
40.32/10.58	        dimension: 1
40.32/10.58	        interpretation:
40.32/10.58	         [a#](x0) = x0,
40.32/10.58	         
40.32/10.58	         [b](x0) = x0 + 1
40.32/10.58	        orientation:
40.32/10.58	         a#(b(x1)) = x1 + 1 >= x1 = a#(x1)
40.32/10.58	        problem:
40.32/10.58	         DPs:
40.32/10.58	          
40.32/10.58	         TRS:
40.32/10.58	          
40.32/10.58	        Qed
40.32/10.58	    
40.32/10.58	    DPs:
40.32/10.58	     b#(c(x1)) -> b#(b(x1))
40.32/10.58	     b#(c(x1)) -> b#(x1)
40.32/10.58	    TRS:
40.32/10.58	     a(b(x1)) -> b(c(a(x1)))
40.32/10.58	     b(c(x1)) -> c(b(b(x1)))
40.32/10.58	     a(c(x1)) -> c(a(b(x1)))
40.32/10.58	    Usable Rule Processor:
40.32/10.58	     DPs:
40.32/10.58	      b#(c(x1)) -> b#(b(x1))
40.32/10.58	      b#(c(x1)) -> b#(x1)
40.32/10.58	     TRS:
40.32/10.58	      b(c(x1)) -> c(b(b(x1)))
40.32/10.58	     Polynomial Interpretation Processor:
40.32/10.58	      dimension: 1
40.32/10.58	      interpretation:
40.32/10.58	       [b#](x0) = x0 + 1,
40.32/10.58	       
40.32/10.58	       [c](x0) = x0 + 1,
40.32/10.58	       
40.32/10.58	       [b](x0) = x0
40.32/10.58	      orientation:
40.32/10.58	       b#(c(x1)) = x1 + 2 >= x1 + 1 = b#(b(x1))
40.32/10.58	       
40.32/10.58	       b#(c(x1)) = x1 + 2 >= x1 + 1 = b#(x1)
40.32/10.58	       
40.32/10.58	       b(c(x1)) = x1 + 1 >= x1 + 1 = c(b(b(x1)))
40.32/10.58	      problem:
40.32/10.58	       DPs:
40.32/10.58	        
40.32/10.58	       TRS:
40.32/10.58	        b(c(x1)) -> c(b(b(x1)))
40.32/10.58	      Qed
40.32/10.59	EOF