0.64/0.80	YES
0.64/0.80	
0.64/0.80	Problem 1: 
0.64/0.80	
0.64/0.80	(VAR v_NonEmpty:S x1:S)
0.64/0.80	(RULES
0.64/0.80	0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	)
0.64/0.80	
0.64/0.80	Problem 1: 
0.64/0.80	
0.64/0.80	Dependency Pairs Processor:
0.64/0.80	-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(4(1(0(5(x1:S)))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(1(2(0(x1:S))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(1(2(4(2(0(x1:S))))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(2(0(x1:S)))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(3(1(0(x1:S))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(2(0(1(x1:S))))
0.64/0.80	 0#(5(1(x1:S))) -> 0#(2(3(1(5(x1:S)))))
0.64/0.80	 0#(5(1(x1:S))) -> 0#(3(1(5(x1:S))))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 0#(3(5(4(5(x1:S)))))
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(4(5(x1:S)))
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 0#(1(3(0(4(5(x1:S))))))
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 0#(4(5(x1:S)))
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(0(1(x1:S)))) -> 0#(2(0(1(x1:S))))
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 5#(1(2(0(x1:S))))
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 5#(1(2(4(0(x1:S)))))
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 5#(1(2(3(0(x1:S)))))
0.64/0.80	 5#(3(1(5(x1:S)))) -> 5#(3(1(2(5(x1:S)))))
0.64/0.80	-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	
0.64/0.80	Problem 1: 
0.64/0.80	
0.64/0.80	SCC Processor:
0.64/0.80	-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(4(1(0(5(x1:S)))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(1(2(0(x1:S))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(1(2(4(2(0(x1:S))))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(2(0(x1:S)))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(3(1(0(x1:S))))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(2(0(1(x1:S))))
0.64/0.80	 0#(5(1(x1:S))) -> 0#(2(3(1(5(x1:S)))))
0.64/0.80	 0#(5(1(x1:S))) -> 0#(3(1(5(x1:S))))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 0#(3(5(4(5(x1:S)))))
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(4(5(x1:S)))
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 0#(1(3(0(4(5(x1:S))))))
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 0#(4(5(x1:S)))
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(0(1(x1:S)))) -> 0#(2(0(1(x1:S))))
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 5#(1(2(0(x1:S))))
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 5#(1(2(4(0(x1:S)))))
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 5#(1(2(3(0(x1:S)))))
0.64/0.80	 5#(3(1(5(x1:S)))) -> 5#(3(1(2(5(x1:S)))))
0.64/0.80	-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	->Strongly Connected Components:
0.64/0.80	->->Cycle:
0.64/0.80	->->-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	->->-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	
0.64/0.80	Problem 1: 
0.64/0.80	
0.64/0.80	Reduction Pair Processor:
0.64/0.80	-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	-> Usable rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	->Interpretation type:
0.64/0.80	 Linear
0.64/0.80	->Coefficients:
0.64/0.80	 Natural Numbers
0.64/0.80	->Dimension:
0.64/0.80	 1
0.64/0.80	->Bound:
0.64/0.80	 2
0.64/0.80	->Interpretation:
0.64/0.80	 
0.64/0.80	[0](X) = 2.X + 2
0.64/0.80	[5](X) = X
0.64/0.80	[1](X) = 2.X + 2
0.64/0.80	[2](X) = X
0.64/0.80	[3](X) = X
0.64/0.80	[4](X) = X
0.64/0.80	[0#](X) = 2.X + 1
0.64/0.80	[5#](X) = 2.X + 1
0.64/0.80	
0.64/0.80	Problem 1: 
0.64/0.80	
0.64/0.80	SCC Processor:
0.64/0.80	-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	->Strongly Connected Components:
0.64/0.80	->->Cycle:
0.64/0.80	->->-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	->->-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.80	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.80	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.80	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.80	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.80	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.80	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.80	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.80	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.80	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.80	
0.64/0.80	Problem 1: 
0.64/0.80	
0.64/0.80	Reduction Pair Processor:
0.64/0.80	-> Pairs:
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 0#(x1:S)
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.80	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.80	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.80	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.80	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.80	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.80	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.80	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.80	-> Rules:
0.64/0.80	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.80	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.80	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.80	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.80	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.80	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.80	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.80	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.80	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.80	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.80	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.81	-> Usable rules:
0.64/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.81	->Interpretation type:
0.64/0.81	 Linear
0.64/0.81	->Coefficients:
0.64/0.81	 Natural Numbers
0.64/0.81	->Dimension:
0.64/0.81	 1
0.64/0.81	->Bound:
0.64/0.81	 2
0.64/0.81	->Interpretation:
0.64/0.81	 
0.64/0.81	[0](X) = 2.X + 2
0.64/0.81	[5](X) = X + 1
0.64/0.81	[1](X) = X + 2
0.64/0.81	[2](X) = X
0.64/0.81	[3](X) = X
0.64/0.81	[4](X) = X
0.64/0.81	[0#](X) = 2.X + 2
0.64/0.81	[5#](X) = X + 1
0.64/0.81	
0.64/0.81	Problem 1: 
0.64/0.81	
0.64/0.81	SCC Processor:
0.64/0.81	-> Pairs:
0.64/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.81	-> Rules:
0.64/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.64/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.64/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.64/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.64/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.64/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.64/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.64/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.64/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.64/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.64/0.81	->Strongly Connected Components:
0.64/0.81	->->Cycle:
0.64/0.81	->->-> Pairs:
0.64/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.64/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.64/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.64/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.64/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.64/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.64/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.64/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.64/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.64/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.64/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.64/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.64/0.81	->->-> Rules:
0.64/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.64/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.64/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.64/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.64/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.64/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.64/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.64/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.64/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.64/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.64/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.64/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.64/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.64/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	Reduction Pair Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(0(0(x1:S)))
0.66/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	-> Usable rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Interpretation type:
0.66/0.81	 Linear
0.66/0.81	->Coefficients:
0.66/0.81	 Natural Numbers
0.66/0.81	->Dimension:
0.66/0.81	 1
0.66/0.81	->Bound:
0.66/0.81	 2
0.66/0.81	->Interpretation:
0.66/0.81	 
0.66/0.81	[0](X) = 2.X + 2
0.66/0.81	[5](X) = X + 1
0.66/0.81	[1](X) = X + 2
0.66/0.81	[2](X) = X
0.66/0.81	[3](X) = X
0.66/0.81	[4](X) = X
0.66/0.81	[0#](X) = 2.X + 1
0.66/0.81	[5#](X) = X + 2
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	SCC Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Strongly Connected Components:
0.66/0.81	->->Cycle:
0.66/0.81	->->-> Pairs:
0.66/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	->->-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	Reduction Pair Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(5(1(5(x1:S))))) -> 5#(5(0(0(x1:S))))
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	-> Usable rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Interpretation type:
0.66/0.81	 Linear
0.66/0.81	->Coefficients:
0.66/0.81	 Natural Numbers
0.66/0.81	->Dimension:
0.66/0.81	 1
0.66/0.81	->Bound:
0.66/0.81	 2
0.66/0.81	->Interpretation:
0.66/0.81	 
0.66/0.81	[0](X) = X
0.66/0.81	[5](X) = X
0.66/0.81	[1](X) = 2.X + 2
0.66/0.81	[2](X) = X
0.66/0.81	[3](X) = X
0.66/0.81	[4](X) = X
0.66/0.81	[0#](X) = 2.X + 2
0.66/0.81	[5#](X) = 2.X + 1
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	SCC Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Strongly Connected Components:
0.66/0.81	->->Cycle:
0.66/0.81	->->-> Pairs:
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	->->-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	Reduction Pair Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(1(5(x1:S)))) -> 0#(5(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	-> Usable rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Interpretation type:
0.66/0.81	 Linear
0.66/0.81	->Coefficients:
0.66/0.81	 Natural Numbers
0.66/0.81	->Dimension:
0.66/0.81	 1
0.66/0.81	->Bound:
0.66/0.81	 2
0.66/0.81	->Interpretation:
0.66/0.81	 
0.66/0.81	[0](X) = X
0.66/0.81	[5](X) = X
0.66/0.81	[1](X) = 2.X + 2
0.66/0.81	[2](X) = X
0.66/0.81	[3](X) = X
0.66/0.81	[4](X) = X
0.66/0.81	[0#](X) = 2.X
0.66/0.81	[5#](X) = 2.X
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	SCC Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Strongly Connected Components:
0.66/0.81	->->Cycle:
0.66/0.81	->->-> Pairs:
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	->->-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	Reduction Pair Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(1(x1:S))) -> 0#(0(x1:S))
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	-> Usable rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Interpretation type:
0.66/0.81	 Linear
0.66/0.81	->Coefficients:
0.66/0.81	 Natural Numbers
0.66/0.81	->Dimension:
0.66/0.81	 1
0.66/0.81	->Bound:
0.66/0.81	 2
0.66/0.81	->Interpretation:
0.66/0.81	 
0.66/0.81	[0](X) = 2.X + 2
0.66/0.81	[5](X) = X + 1
0.66/0.81	[1](X) = X + 2
0.66/0.81	[2](X) = X
0.66/0.81	[3](X) = X
0.66/0.81	[4](X) = X
0.66/0.81	[0#](X) = 2.X + 1
0.66/0.81	[5#](X) = X + 2
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	SCC Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Strongly Connected Components:
0.66/0.81	->->Cycle:
0.66/0.81	->->-> Pairs:
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	->->-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	Subterm Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 0#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 0#(0(2(1(x1:S)))) -> 0#(1(x1:S))
0.66/0.81	 0#(5(1(x1:S))) -> 5#(x1:S)
0.66/0.81	 0#(5(3(4(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(5(4(0(1(x1:S))))) -> 5#(x1:S)
0.66/0.81	 0#(1(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 0#(1(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	 5#(0(1(x1:S))) -> 0#(x1:S)
0.66/0.81	 5#(3(0(1(x1:S)))) -> 0#(x1:S)
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Projection:
0.66/0.81	 pi(0#) = 1
0.66/0.81	 pi(5#) = 1
0.66/0.81	
0.66/0.81	Problem 1: 
0.66/0.81	
0.66/0.81	SCC Processor:
0.66/0.81	-> Pairs:
0.66/0.81	 Empty
0.66/0.81	-> Rules:
0.66/0.81	 0(0(5(1(5(x1:S))))) -> 1(2(5(5(0(0(x1:S))))))
0.66/0.81	 0(0(1(5(x1:S)))) -> 0(4(1(0(5(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(0(2(2(1(2(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(2(4(2(0(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(1(3(0(4(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(2(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(1(2(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(0(3(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 0(3(1(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 0(4(0(4(1(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(0(4(0(x1:S))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(0(3(0(4(x1:S))))))
0.66/0.81	 0(0(1(x1:S))) -> 1(2(2(0(0(x1:S)))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(0(3(0(2(1(x1:S))))))
0.66/0.81	 0(0(2(1(x1:S)))) -> 2(3(0(2(0(1(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(2(3(1(5(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(2(x1:S)))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(5(x1:S))))
0.66/0.81	 0(5(1(x1:S))) -> 0(3(1(2(5(2(x1:S))))))
0.66/0.81	 0(5(1(x1:S))) -> 0(4(5(1(x1:S))))
0.66/0.81	 0(5(3(0(1(x1:S))))) -> 1(0(5(3(0(4(x1:S))))))
0.66/0.81	 0(5(3(4(1(x1:S))))) -> 1(0(3(5(4(5(x1:S))))))
0.66/0.81	 0(5(4(0(1(x1:S))))) -> 0(1(3(0(4(5(x1:S))))))
0.66/0.81	 0(1(0(1(x1:S)))) -> 1(0(2(0(1(x1:S)))))
0.66/0.81	 0(1(1(1(x1:S)))) -> 1(1(3(1(0(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 0(2(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 0(3(1(1(x1:S))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(3(1(2(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(0(4(2(1(2(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(2(4(3(0(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(1(3(0(4(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(0(2(1(x1:S)))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(1(0(4(4(x1:S))))))
0.66/0.81	 0(1(1(x1:S))) -> 1(2(2(1(3(0(x1:S))))))
0.66/0.81	 5(0(1(1(x1:S)))) -> 1(5(1(2(0(x1:S)))))
0.66/0.81	 5(0(1(x1:S))) -> 5(0(2(1(2(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(3(0(4(x1:S))))))
0.66/0.81	 5(0(1(x1:S))) -> 5(1(2(4(0(x1:S)))))
0.66/0.81	 5(3(0(1(x1:S)))) -> 5(1(2(3(0(x1:S)))))
0.66/0.81	 5(3(1(5(x1:S)))) -> 5(3(1(2(5(x1:S)))))
0.66/0.81	 5(3(2(1(x1:S)))) -> 1(2(3(5(2(x1:S)))))
0.66/0.81	 5(4(0(1(x1:S)))) -> 1(2(5(0(4(x1:S)))))
0.66/0.81	 5(4(2(1(1(x1:S))))) -> 5(4(1(2(1(2(x1:S))))))
0.66/0.81	->Strongly Connected Components:
0.66/0.81	 There is no strongly connected component
0.66/0.81	
0.66/0.81	The problem is finite.
0.66/0.81	EOF