165.46/42.30	YES
165.46/42.31	
165.46/42.31	Problem:
165.46/42.31	 a(x1) -> b(x1)
165.46/42.31	 a(b(x1)) -> b(a(c(a(x1))))
165.46/42.31	 b(x1) -> c(x1)
165.46/42.31	 c(c(x1)) -> x1
165.46/42.31	
165.46/42.31	Proof:
165.46/42.31	 DP Processor:
165.46/42.31	  DPs:
165.46/42.31	   a#(x1) -> b#(x1)
165.46/42.31	   a#(b(x1)) -> a#(x1)
165.46/42.31	   a#(b(x1)) -> c#(a(x1))
165.46/42.31	   a#(b(x1)) -> a#(c(a(x1)))
165.46/42.31	   a#(b(x1)) -> b#(a(c(a(x1))))
165.46/42.31	   b#(x1) -> c#(x1)
165.46/42.31	  TRS:
165.46/42.31	   a(x1) -> b(x1)
165.46/42.31	   a(b(x1)) -> b(a(c(a(x1))))
165.46/42.31	   b(x1) -> c(x1)
165.46/42.31	   c(c(x1)) -> x1
165.46/42.31	  TDG Processor:
165.46/42.31	   DPs:
165.46/42.31	    a#(x1) -> b#(x1)
165.46/42.31	    a#(b(x1)) -> a#(x1)
165.46/42.31	    a#(b(x1)) -> c#(a(x1))
165.46/42.31	    a#(b(x1)) -> a#(c(a(x1)))
165.46/42.31	    a#(b(x1)) -> b#(a(c(a(x1))))
165.46/42.31	    b#(x1) -> c#(x1)
165.46/42.31	   TRS:
165.46/42.31	    a(x1) -> b(x1)
165.46/42.31	    a(b(x1)) -> b(a(c(a(x1))))
165.46/42.31	    b(x1) -> c(x1)
165.46/42.31	    c(c(x1)) -> x1
165.46/42.31	   graph:
165.46/42.31	    a#(b(x1)) -> b#(a(c(a(x1)))) -> b#(x1) -> c#(x1)
165.46/42.31	    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> b#(a(c(a(x1))))
165.46/42.31	    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(c(a(x1)))
165.46/42.31	    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> c#(a(x1))
165.46/42.31	    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(x1)
165.46/42.31	    a#(b(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(x1)
165.46/42.31	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(c(a(x1))))
165.46/42.31	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(a(x1)))
165.46/42.31	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
165.46/42.31	    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
165.46/42.31	    a#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
165.46/42.31	    a#(x1) -> b#(x1) -> b#(x1) -> c#(x1)
165.46/42.31	   SCC Processor:
165.46/42.31	    #sccs: 1
165.46/42.31	    #rules: 2
165.46/42.31	    #arcs: 12/36
165.46/42.31	    DPs:
165.46/42.31	     a#(b(x1)) -> a#(c(a(x1)))
165.46/42.31	     a#(b(x1)) -> a#(x1)
165.46/42.31	    TRS:
165.46/42.31	     a(x1) -> b(x1)
165.46/42.31	     a(b(x1)) -> b(a(c(a(x1))))
165.46/42.31	     b(x1) -> c(x1)
165.46/42.31	     c(c(x1)) -> x1
165.46/42.31	    Arctic Interpretation Processor:
165.46/42.31	     dimension: 2
165.46/42.31	     usable rules:
165.46/42.31	      a(x1) -> b(x1)
165.46/42.31	      a(b(x1)) -> b(a(c(a(x1))))
165.46/42.31	      b(x1) -> c(x1)
165.46/42.31	      c(c(x1)) -> x1
165.46/42.31	     interpretation:
165.46/42.31	      [a#](x0) = [0  -&]x0 + [0],
165.46/42.31	      
165.46/42.31	                [-& 0 ]     [0 ]
165.46/42.31	      [c](x0) = [0  -&]x0 + [-&],
165.46/42.31	      
165.46/42.31	                [1  0 ]     [1 ]
165.46/42.31	      [b](x0) = [0  -&]x0 + [-&],
165.46/42.31	      
165.46/42.31	                [1  0 ]     [1 ]
165.46/42.31	      [a](x0) = [0  -&]x0 + [-&]
165.46/42.31	     orientation:
165.46/42.31	      a#(b(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = a#(c(a(x1)))
165.46/42.31	      
165.46/42.31	      a#(b(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = a#(x1)
165.46/42.31	      
165.46/42.31	              [1  0 ]     [1 ]    [1  0 ]     [1 ]        
165.46/42.31	      a(x1) = [0  -&]x1 + [-&] >= [0  -&]x1 + [-&] = b(x1)
165.46/42.31	      
165.46/42.31	                 [2 1]     [2]    [2 1]     [2]                 
165.46/42.31	      a(b(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = b(a(c(a(x1))))
165.46/42.31	      
165.46/42.31	              [1  0 ]     [1 ]    [-& 0 ]     [0 ]        
165.46/42.31	      b(x1) = [0  -&]x1 + [-&] >= [0  -&]x1 + [-&] = c(x1)
165.46/42.31	      
165.46/42.31	                      [0]           
165.46/42.31	      c(c(x1)) = x1 + [0] >= x1 = x1
165.46/42.31	     problem:
165.46/42.31	      DPs:
165.46/42.31	       
165.46/42.31	      TRS:
165.46/42.31	       a(x1) -> b(x1)
165.46/42.31	       a(b(x1)) -> b(a(c(a(x1))))
165.46/42.31	       b(x1) -> c(x1)
165.46/42.31	       c(c(x1)) -> x1
165.46/42.31	     Qed
165.46/42.31	EOF