21.50/21.89	YES
21.50/21.89	
21.50/21.89	Problem 1: 
21.50/21.89	
21.50/21.89	(VAR v_NonEmpty:S x1:S)
21.50/21.89	(RULES
21.50/21.89	0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	)
21.50/21.89	
21.50/21.89	Problem 1: 
21.50/21.89	
21.50/21.89	Dependency Pairs Processor:
21.50/21.89	-> Pairs:
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(0(1(x1:S)))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(2(0(0(1(x1:S)))))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(0(1(x1:S)))) -> 0#(3(0(1(x1:S))))
21.50/21.89	 1#(0(0(1(x1:S)))) -> 1#(0(3(0(1(x1:S)))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(2(0(x1:S)))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(3(2(0(x1:S))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(0(0(4(x1:S)))) -> 1#(4(0(2(0(x1:S)))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 1#(4(0(3(2(0(x1:S))))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 4#(0(2(0(x1:S))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 4#(0(3(2(0(x1:S)))))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 0#(0(3(1(x1:S))))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 0#(3(1(x1:S)))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(3(0(0(3(1(x1:S))))))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 0#(3(1(2(4(x1:S)))))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(0(3(1(2(4(x1:S))))))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.89	 1#(0(1(5(x1:S)))) -> 0#(2(1(5(x1:S))))
21.50/21.89	 1#(0(1(5(x1:S)))) -> 1#(0(2(1(5(x1:S)))))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(4(3(4(0(x1:S)))))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 1#(0(4(3(4(0(x1:S))))))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(3(4(0(x1:S))))
21.50/21.89	 1#(0(4(1(x1:S)))) -> 0#(3(4(1(x1:S))))
21.50/21.89	 1#(0(4(1(x1:S)))) -> 1#(0(3(4(1(x1:S)))))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 1#(2(5(2(0(0(x1:S))))))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 5#(2(0(0(x1:S))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 0#(0(3(1(x1:S))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 0#(3(1(x1:S)))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(0(0(3(1(x1:S)))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(1(0(0(3(1(x1:S))))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 0#(2(1(x1:S)))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 0#(3(1(x1:S)))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(4(0(2(1(x1:S)))))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(4(0(3(1(x1:S)))))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 4#(0(2(1(x1:S))))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 4#(0(3(1(x1:S))))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 0#(5(0(2(1(x1:S)))))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 0#(2(1(x1:S)))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 4#(0(5(0(2(1(x1:S))))))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 5#(0(2(1(x1:S))))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 0#(2(1(2(5(x1:S)))))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 4#(0(2(1(2(5(x1:S))))))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 0#(3(1(2(5(4(x1:S))))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(3(1(3(x1:S))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(5(0(3(1(3(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(0(3(1(3(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(2(0(4(x1:S)))) -> 1#(3(4(2(0(x1:S)))))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 4#(2(0(x1:S)))
21.50/21.89	 1#(2(0(5(0(x1:S))))) -> 0#(2(0(x1:S)))
21.50/21.89	 1#(2(0(5(0(x1:S))))) -> 1#(0(2(0(x1:S))))
21.50/21.89	 1#(2(0(5(0(x1:S))))) -> 5#(2(1(0(2(0(x1:S))))))
21.50/21.89	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(3(0(4(x1:S)))) -> 1#(3(4(2(0(x1:S)))))
21.50/21.89	 1#(3(0(4(x1:S)))) -> 4#(2(0(x1:S)))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 0#(4(0(3(1(x1:S)))))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 0#(3(1(x1:S)))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 1#(0(4(0(3(1(x1:S))))))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 4#(0(3(1(x1:S))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(2(4(2(0(1(x1:S))))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(3(4(3(0(1(x1:S))))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 4#(1(0(0(x1:S)))) -> 4#(2(0(1(x1:S))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 4#(3(0(1(x1:S))))
21.50/21.89	 4#(1(0(5(x1:S)))) -> 0#(2(1(5(x1:S))))
21.50/21.89	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(0(5(x1:S)))) -> 4#(0(2(1(5(x1:S)))))
21.50/21.89	 4#(1(5(3(1(x1:S))))) -> 1#(5(4(3(1(x1:S)))))
21.50/21.89	 4#(1(5(3(1(x1:S))))) -> 4#(3(1(x1:S)))
21.50/21.89	 4#(1(5(3(1(x1:S))))) -> 5#(4(3(1(x1:S))))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 0#(0(2(1(x1:S))))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 0#(2(1(x1:S)))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 4#(2(0(0(2(1(x1:S))))))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 0#(2(1(3(4(x1:S)))))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 0#(0(5(3(1(x1:S)))))
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 0#(5(3(1(x1:S))))
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 4#(0(0(5(3(1(x1:S))))))
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 5#(3(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(2(1(5(1(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(2(1(5(1(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 1#(5(5(3(1(x1:S)))))
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 4#(1(5(5(3(1(x1:S))))))
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 5#(5(3(1(x1:S))))
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 5#(3(1(x1:S)))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(3(0(1(x1:S))))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 4#(0(3(0(1(x1:S)))))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 5#(4(0(3(0(1(x1:S))))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(0(3(5(5(x1:S)))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(3(4(0(5(5(x1:S))))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(3(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(0(3(5(5(x1:S))))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(2(0(x1:S)))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(0(4(x1:S)))) -> 4#(0(2(0(x1:S))))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 5#(4(0(2(0(x1:S)))))
21.50/21.89	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(1(4(x1:S)))) -> 1#(5(4(3(0(x1:S)))))
21.50/21.89	 5#(0(1(4(x1:S)))) -> 4#(3(0(x1:S)))
21.50/21.89	 5#(0(1(4(x1:S)))) -> 5#(4(3(0(x1:S))))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 0#(4(0(3(1(x1:S)))))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 0#(3(1(x1:S)))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 4#(0(3(1(x1:S))))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 5#(0(4(0(3(1(x1:S))))))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 0#(3(5(1(1(x1:S)))))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(0(3(5(1(1(x1:S))))))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 4#(3(1(5(5(x1:S)))))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 4#(2(0(x1:S)))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 5#(5(3(4(2(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 5#(3(4(2(0(x1:S)))))
21.50/21.89	-> Rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	
21.50/21.89	Problem 1: 
21.50/21.89	
21.50/21.89	SCC Processor:
21.50/21.89	-> Pairs:
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(0(1(x1:S)))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(2(0(0(1(x1:S)))))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(0(1(x1:S)))) -> 0#(3(0(1(x1:S))))
21.50/21.89	 1#(0(0(1(x1:S)))) -> 1#(0(3(0(1(x1:S)))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(2(0(x1:S)))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(3(2(0(x1:S))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(0(0(4(x1:S)))) -> 1#(4(0(2(0(x1:S)))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 1#(4(0(3(2(0(x1:S))))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 4#(0(2(0(x1:S))))
21.50/21.89	 1#(0(0(4(x1:S)))) -> 4#(0(3(2(0(x1:S)))))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 0#(0(3(1(x1:S))))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 0#(3(1(x1:S)))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(3(0(0(3(1(x1:S))))))
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 0#(3(1(2(4(x1:S)))))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(0(3(1(2(4(x1:S))))))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.89	 1#(0(1(5(x1:S)))) -> 0#(2(1(5(x1:S))))
21.50/21.89	 1#(0(1(5(x1:S)))) -> 1#(0(2(1(5(x1:S)))))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(4(3(4(0(x1:S)))))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 1#(0(4(3(4(0(x1:S))))))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(3(4(0(x1:S))))
21.50/21.89	 1#(0(4(1(x1:S)))) -> 0#(3(4(1(x1:S))))
21.50/21.89	 1#(0(4(1(x1:S)))) -> 1#(0(3(4(1(x1:S)))))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 1#(2(5(2(0(0(x1:S))))))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 5#(2(0(0(x1:S))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 0#(0(3(1(x1:S))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 0#(3(1(x1:S)))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(0(0(3(1(x1:S)))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(1(0(0(3(1(x1:S))))))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 0#(2(1(x1:S)))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 0#(3(1(x1:S)))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(4(0(2(1(x1:S)))))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(4(0(3(1(x1:S)))))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 4#(0(2(1(x1:S))))
21.50/21.89	 1#(4(1(0(x1:S)))) -> 4#(0(3(1(x1:S))))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 0#(5(0(2(1(x1:S)))))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 0#(2(1(x1:S)))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 4#(0(5(0(2(1(x1:S))))))
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 5#(0(2(1(x1:S))))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 0#(2(1(2(5(x1:S)))))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 4#(0(2(1(2(5(x1:S))))))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 0#(3(1(2(5(4(x1:S))))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(3(1(3(x1:S))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(5(0(3(1(3(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(0(3(1(3(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(2(0(4(x1:S)))) -> 1#(3(4(2(0(x1:S)))))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 4#(2(0(x1:S)))
21.50/21.89	 1#(2(0(5(0(x1:S))))) -> 0#(2(0(x1:S)))
21.50/21.89	 1#(2(0(5(0(x1:S))))) -> 1#(0(2(0(x1:S))))
21.50/21.89	 1#(2(0(5(0(x1:S))))) -> 5#(2(1(0(2(0(x1:S))))))
21.50/21.89	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(3(0(4(x1:S)))) -> 1#(3(4(2(0(x1:S)))))
21.50/21.89	 1#(3(0(4(x1:S)))) -> 4#(2(0(x1:S)))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 0#(4(0(3(1(x1:S)))))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 0#(3(1(x1:S)))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 1#(0(4(0(3(1(x1:S))))))
21.50/21.89	 4#(1(0(0(1(x1:S))))) -> 4#(0(3(1(x1:S))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(2(4(2(0(1(x1:S))))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(3(4(3(0(1(x1:S))))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 4#(1(0(0(x1:S)))) -> 4#(2(0(1(x1:S))))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 4#(3(0(1(x1:S))))
21.50/21.89	 4#(1(0(5(x1:S)))) -> 0#(2(1(5(x1:S))))
21.50/21.89	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(0(5(x1:S)))) -> 4#(0(2(1(5(x1:S)))))
21.50/21.89	 4#(1(5(3(1(x1:S))))) -> 1#(5(4(3(1(x1:S)))))
21.50/21.89	 4#(1(5(3(1(x1:S))))) -> 4#(3(1(x1:S)))
21.50/21.89	 4#(1(5(3(1(x1:S))))) -> 5#(4(3(1(x1:S))))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 0#(0(2(1(x1:S))))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 0#(2(1(x1:S)))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 4#(2(0(0(2(1(x1:S))))))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 0#(2(1(3(4(x1:S)))))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 0#(0(5(3(1(x1:S)))))
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 0#(5(3(1(x1:S))))
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 4#(0(0(5(3(1(x1:S))))))
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 5#(3(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(2(1(5(1(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(2(1(5(1(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 1#(5(5(3(1(x1:S)))))
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 4#(1(5(5(3(1(x1:S))))))
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 5#(5(3(1(x1:S))))
21.50/21.89	 4#(5(1(5(1(x1:S))))) -> 5#(3(1(x1:S)))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(3(0(1(x1:S))))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 4#(0(3(0(1(x1:S)))))
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 5#(4(0(3(0(1(x1:S))))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(0(3(5(5(x1:S)))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(3(4(0(5(5(x1:S))))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(3(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(0(3(5(5(x1:S))))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(2(0(x1:S)))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(0(4(x1:S)))) -> 4#(0(2(0(x1:S))))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 5#(4(0(2(0(x1:S)))))
21.50/21.89	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(1(4(x1:S)))) -> 1#(5(4(3(0(x1:S)))))
21.50/21.89	 5#(0(1(4(x1:S)))) -> 4#(3(0(x1:S)))
21.50/21.89	 5#(0(1(4(x1:S)))) -> 5#(4(3(0(x1:S))))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 0#(4(0(3(1(x1:S)))))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 0#(3(1(x1:S)))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 4#(0(3(1(x1:S))))
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 5#(0(4(0(3(1(x1:S))))))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 0#(3(5(1(1(x1:S)))))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(0(3(5(1(1(x1:S))))))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 4#(3(1(5(5(x1:S)))))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 4#(2(0(x1:S)))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 5#(5(3(4(2(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 5#(3(4(2(0(x1:S)))))
21.50/21.89	-> Rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	->Strongly Connected Components:
21.50/21.89	->->Cycle:
21.50/21.89	->->-> Pairs:
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(0(1(x1:S)))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	->->-> Rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	
21.50/21.89	Problem 1: 
21.50/21.89	
21.50/21.89	Reduction Pair Processor:
21.50/21.89	-> Pairs:
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(0(1(x1:S)))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	-> Rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	-> Usable rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	->Interpretation type:
21.50/21.89	 Linear
21.50/21.89	->Coefficients:
21.50/21.89	 Natural Numbers
21.50/21.89	->Dimension:
21.50/21.89	 1
21.50/21.89	->Bound:
21.50/21.89	 2
21.50/21.89	->Interpretation:
21.50/21.89	 
21.50/21.89	[0](X) = 2.X + 2
21.50/21.89	[1](X) = 2.X + 2
21.50/21.89	[4](X) = 2.X + 2
21.50/21.89	[5](X) = 2.X + 2
21.50/21.89	[2](X) = X
21.50/21.89	[3](X) = X
21.50/21.89	[0#](X) = 2.X + 1
21.50/21.89	[1#](X) = 2.X + 2
21.50/21.89	[4#](X) = 2.X + 2
21.50/21.89	[5#](X) = 2.X + 2
21.50/21.89	
21.50/21.89	Problem 1: 
21.50/21.89	
21.50/21.89	SCC Processor:
21.50/21.89	-> Pairs:
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	-> Rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.89	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.89	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.89	->Strongly Connected Components:
21.50/21.89	->->Cycle:
21.50/21.89	->->-> Pairs:
21.50/21.89	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.89	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.89	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.89	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.89	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.89	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.89	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.89	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.89	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.89	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.89	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.89	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.89	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.89	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.89	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.89	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.89	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.89	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.89	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.89	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.89	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.89	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.89	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.89	->->-> Rules:
21.50/21.89	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.89	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.89	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.89	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.89	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.89	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.89	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.89	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.89	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.89	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.89	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.89	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.89	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.89	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.89	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.89	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.89	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.89	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.89	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.89	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.89	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.89	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.89	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.89	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.89	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.89	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.89	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.89	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.89	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.89	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.89	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.89	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.89	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.89	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.89	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.89	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.89	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.89	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.89	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.89	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	Reduction Pair Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 0#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.90	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	-> Usable rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Interpretation type:
21.50/21.90	 Linear
21.50/21.90	->Coefficients:
21.50/21.90	 Natural Numbers
21.50/21.90	->Dimension:
21.50/21.90	 1
21.50/21.90	->Bound:
21.50/21.90	 2
21.50/21.90	->Interpretation:
21.50/21.90	 
21.50/21.90	[0](X) = 2.X + 2
21.50/21.90	[1](X) = 2.X + 2
21.50/21.90	[4](X) = 2.X + 2
21.50/21.90	[5](X) = 2.X + 2
21.50/21.90	[2](X) = X
21.50/21.90	[3](X) = X
21.50/21.90	[0#](X) = 2.X + 2
21.50/21.90	[1#](X) = 2.X + 2
21.50/21.90	[4#](X) = 2.X + 2
21.50/21.90	[5#](X) = 2.X + 2
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	SCC Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Strongly Connected Components:
21.50/21.90	->->Cycle:
21.50/21.90	->->-> Pairs:
21.50/21.90	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	->->-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	Reduction Pair Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 0#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	-> Usable rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Interpretation type:
21.50/21.90	 Linear
21.50/21.90	->Coefficients:
21.50/21.90	 Natural Numbers
21.50/21.90	->Dimension:
21.50/21.90	 1
21.50/21.90	->Bound:
21.50/21.90	 2
21.50/21.90	->Interpretation:
21.50/21.90	 
21.50/21.90	[0](X) = 2.X + 2
21.50/21.90	[1](X) = 2.X + 2
21.50/21.90	[4](X) = 2.X + 2
21.50/21.90	[5](X) = 2.X + 2
21.50/21.90	[2](X) = X
21.50/21.90	[3](X) = X
21.50/21.90	[0#](X) = 2.X + 2
21.50/21.90	[1#](X) = 2.X + 2
21.50/21.90	[4#](X) = 2.X + 2
21.50/21.90	[5#](X) = 2.X + 2
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	SCC Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(3(1(5(4(0(x1:S))))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(1(4(x1:S)))) -> 1#(2(4(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(5(0(x1:S)))) -> 0#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 1#(2(5(x1:S)))
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 1#(2(5(4(x1:S))))
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 0#(1(3(1(3(5(x1:S))))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(1(3(5(x1:S)))))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(5(x1:S)))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 1#(3(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 0#(5(1(5(x1:S))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 1#(2(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 1#(3(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 4#(1(0(0(x1:S)))) -> 0#(1(x1:S))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 1#(3(4(x1:S)))
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 1#(3(4(4(0(1(x1:S))))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(4(0(5(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 0#(5(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(3(4(0(5(x1:S)))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(1(x1:S))))) -> 0#(1(x1:S))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 0#(5(5(x1:S)))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(0(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(1(4(x1:S)))) -> 0#(x1:S)
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 0#(1(5(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(2(4(0(1(5(x1:S))))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 1#(3(4(0(x1:S))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	 5#(5(2(0(4(x1:S))))) -> 0#(x1:S)
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Strongly Connected Components:
21.50/21.90	->->Cycle:
21.50/21.90	->->-> Pairs:
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	->->-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	Reduction Pair Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	-> Usable rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Interpretation type:
21.50/21.90	 Linear
21.50/21.90	->Coefficients:
21.50/21.90	 Natural Numbers
21.50/21.90	->Dimension:
21.50/21.90	 1
21.50/21.90	->Bound:
21.50/21.90	 2
21.50/21.90	->Interpretation:
21.50/21.90	 
21.50/21.90	[0](X) = 2.X + 2
21.50/21.90	[1](X) = 2.X + 2
21.50/21.90	[4](X) = 2.X + 2
21.50/21.90	[5](X) = X
21.50/21.90	[2](X) = X
21.50/21.90	[3](X) = X
21.50/21.90	[1#](X) = X + 2
21.50/21.90	[4#](X) = X + 2
21.50/21.90	[5#](X) = X + 1
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	SCC Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Strongly Connected Components:
21.50/21.90	->->Cycle:
21.50/21.90	->->-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	->->-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	Reduction Pair Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 1#(5(4(0(x1:S))))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	-> Usable rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Interpretation type:
21.50/21.90	 Linear
21.50/21.90	->Coefficients:
21.50/21.90	 Natural Numbers
21.50/21.90	->Dimension:
21.50/21.90	 1
21.50/21.90	->Bound:
21.50/21.90	 2
21.50/21.90	->Interpretation:
21.50/21.90	 
21.50/21.90	[0](X) = 2.X + 2
21.50/21.90	[1](X) = 2.X + 2
21.50/21.90	[4](X) = 2.X + 2
21.50/21.90	[5](X) = 2.X + 2
21.50/21.90	[2](X) = X
21.50/21.90	[3](X) = X
21.50/21.90	[1#](X) = 2.X + 2
21.50/21.90	[4#](X) = 2.X + 2
21.50/21.90	[5#](X) = X + 2
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	SCC Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Strongly Connected Components:
21.50/21.90	->->Cycle:
21.50/21.90	->->-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	->->-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	Reduction Pair Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	-> Usable rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Interpretation type:
21.50/21.90	 Linear
21.50/21.90	->Coefficients:
21.50/21.90	 Natural Numbers
21.50/21.90	->Dimension:
21.50/21.90	 1
21.50/21.90	->Bound:
21.50/21.90	 2
21.50/21.90	->Interpretation:
21.50/21.90	 
21.50/21.90	[0](X) = 2.X + 2
21.50/21.90	[1](X) = 2.X + 2
21.50/21.90	[4](X) = 2.X + 2
21.50/21.90	[5](X) = X
21.50/21.90	[2](X) = X
21.50/21.90	[3](X) = X
21.50/21.90	[1#](X) = 2.X + 2
21.50/21.90	[4#](X) = 2.X + 2
21.50/21.90	[5#](X) = 2.X
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	SCC Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	->Strongly Connected Components:
21.50/21.90	->->Cycle:
21.50/21.90	->->-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.90	->->-> Rules:
21.50/21.90	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.90	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.90	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.90	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.90	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.90	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.90	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.90	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.90	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.90	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.90	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.90	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.90	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.90	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.90	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.90	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.90	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.90	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.90	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.90	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.90	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.90	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.90	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.90	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.90	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.90	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.90	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.90	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.90	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.90	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.90	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.90	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.90	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.90	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.90	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.90	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.90	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.90	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.90	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.90	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.90	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.90	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.90	
21.50/21.90	Problem 1: 
21.50/21.90	
21.50/21.90	Reduction Pair Processor:
21.50/21.90	-> Pairs:
21.50/21.90	 1#(0(1(4(5(x1:S))))) -> 5#(4(0(x1:S)))
21.50/21.90	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.90	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.90	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.90	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.90	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.90	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.90	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.90	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.90	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.90	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.90	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.90	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.90	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.90	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.90	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.90	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	-> Usable rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Interpretation type:
21.50/21.91	 Linear
21.50/21.91	->Coefficients:
21.50/21.91	 Natural Numbers
21.50/21.91	->Dimension:
21.50/21.91	 1
21.50/21.91	->Bound:
21.50/21.91	 2
21.50/21.91	->Interpretation:
21.50/21.91	 
21.50/21.91	[0](X) = 2.X + 2
21.50/21.91	[1](X) = 2.X + 2
21.50/21.91	[4](X) = 2.X + 2
21.50/21.91	[5](X) = X
21.50/21.91	[2](X) = X
21.50/21.91	[3](X) = X
21.50/21.91	[1#](X) = 2.X + 2
21.50/21.91	[4#](X) = 2.X + 2
21.50/21.91	[5#](X) = 2.X + 2
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	SCC Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Strongly Connected Components:
21.50/21.91	->->Cycle:
21.50/21.91	->->-> Pairs:
21.50/21.91	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	->->-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	Reduction Pair Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(0(4(0(4(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	-> Usable rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Interpretation type:
21.50/21.91	 Linear
21.50/21.91	->Coefficients:
21.50/21.91	 Natural Numbers
21.50/21.91	->Dimension:
21.50/21.91	 1
21.50/21.91	->Bound:
21.50/21.91	 2
21.50/21.91	->Interpretation:
21.50/21.91	 
21.50/21.91	[0](X) = 2.X + 2
21.50/21.91	[1](X) = 2.X + 2
21.50/21.91	[4](X) = 2.X + 2
21.50/21.91	[5](X) = 2.X + 2
21.50/21.91	[2](X) = X
21.50/21.91	[3](X) = X
21.50/21.91	[1#](X) = 2.X
21.50/21.91	[4#](X) = 2.X
21.50/21.91	[5#](X) = 2.X
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	SCC Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Strongly Connected Components:
21.50/21.91	->->Cycle:
21.50/21.91	->->-> Pairs:
21.50/21.91	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	->->-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	Reduction Pair Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(1(1(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	-> Usable rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Interpretation type:
21.50/21.91	 Linear
21.50/21.91	->Coefficients:
21.50/21.91	 Natural Numbers
21.50/21.91	->Dimension:
21.50/21.91	 1
21.50/21.91	->Bound:
21.50/21.91	 2
21.50/21.91	->Interpretation:
21.50/21.91	 
21.50/21.91	[0](X) = 2.X + 2
21.50/21.91	[1](X) = 2.X + 2
21.50/21.91	[4](X) = 2.X + 2
21.50/21.91	[5](X) = 2.X + 2
21.50/21.91	[2](X) = X
21.50/21.91	[3](X) = X
21.50/21.91	[1#](X) = 2.X + 2
21.50/21.91	[4#](X) = 2.X + 2
21.50/21.91	[5#](X) = 2.X + 1
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	SCC Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Strongly Connected Components:
21.50/21.91	->->Cycle:
21.50/21.91	->->-> Pairs:
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	->->-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	Reduction Pair Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	-> Usable rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Interpretation type:
21.50/21.91	 Linear
21.50/21.91	->Coefficients:
21.50/21.91	 Natural Numbers
21.50/21.91	->Dimension:
21.50/21.91	 1
21.50/21.91	->Bound:
21.50/21.91	 2
21.50/21.91	->Interpretation:
21.50/21.91	 
21.50/21.91	[0](X) = 2.X + 2
21.50/21.91	[1](X) = 2.X + 2
21.50/21.91	[4](X) = 2.X + 2
21.50/21.91	[5](X) = X
21.50/21.91	[2](X) = X
21.50/21.91	[3](X) = X
21.50/21.91	[1#](X) = 2.X + 2
21.50/21.91	[4#](X) = 2.X + 2
21.50/21.91	[5#](X) = 2.X + 2
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	SCC Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	->Strongly Connected Components:
21.50/21.91	->->Cycle:
21.50/21.91	->->-> Pairs:
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	->->-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.50/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.50/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.50/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.50/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.50/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.50/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.50/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.50/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.50/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.50/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.50/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.50/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.50/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.50/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.50/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.50/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.50/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.50/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.50/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.50/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.50/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.50/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.50/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.50/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.50/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.50/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.50/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.50/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.50/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.50/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.50/21.91	
21.50/21.91	Problem 1: 
21.50/21.91	
21.50/21.91	Reduction Pair Processor:
21.50/21.91	-> Pairs:
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 1#(1(4(5(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.50/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.50/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.50/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.50/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.50/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.50/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.50/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.50/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.50/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.50/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.50/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.50/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.50/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.50/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.50/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.50/21.91	-> Rules:
21.50/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.50/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.50/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.50/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.50/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.50/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.50/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.50/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.50/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.50/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.50/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.50/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	-> Usable rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	->Interpretation type:
21.52/21.91	 Linear
21.52/21.91	->Coefficients:
21.52/21.91	 Natural Numbers
21.52/21.91	->Dimension:
21.52/21.91	 1
21.52/21.91	->Bound:
21.52/21.91	 2
21.52/21.91	->Interpretation:
21.52/21.91	 
21.52/21.91	[0](X) = 2.X + 2
21.52/21.91	[1](X) = 2.X + 2
21.52/21.91	[4](X) = 2.X + 2
21.52/21.91	[5](X) = 2.X + 2
21.52/21.91	[2](X) = X
21.52/21.91	[3](X) = X
21.52/21.91	[1#](X) = 2.X + 2
21.52/21.91	[4#](X) = 2.X + 2
21.52/21.91	[5#](X) = 2.X + 2
21.52/21.91	
21.52/21.91	Problem 1: 
21.52/21.91	
21.52/21.91	SCC Processor:
21.52/21.91	-> Pairs:
21.52/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.91	-> Rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	->Strongly Connected Components:
21.52/21.91	->->Cycle:
21.52/21.91	->->-> Pairs:
21.52/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.91	->->-> Rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	
21.52/21.91	Problem 1: 
21.52/21.91	
21.52/21.91	Reduction Pair Processor:
21.52/21.91	-> Pairs:
21.52/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 1#(4(1(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.91	-> Rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	-> Usable rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	->Interpretation type:
21.52/21.91	 Linear
21.52/21.91	->Coefficients:
21.52/21.91	 Natural Numbers
21.52/21.91	->Dimension:
21.52/21.91	 1
21.52/21.91	->Bound:
21.52/21.91	 2
21.52/21.91	->Interpretation:
21.52/21.91	 
21.52/21.91	[0](X) = 2.X + 2
21.52/21.91	[1](X) = 2.X + 2
21.52/21.91	[4](X) = X
21.52/21.91	[5](X) = 2.X + 2
21.52/21.91	[2](X) = X
21.52/21.91	[3](X) = X
21.52/21.91	[1#](X) = 2.X + 2
21.52/21.91	[4#](X) = X
21.52/21.91	[5#](X) = 2.X + 2
21.52/21.91	
21.52/21.91	Problem 1: 
21.52/21.91	
21.52/21.91	SCC Processor:
21.52/21.91	-> Pairs:
21.52/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.91	-> Rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.91	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.91	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.91	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.91	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.91	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.91	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.91	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.91	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.91	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.91	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.91	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.91	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.91	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.91	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.91	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.91	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.91	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.91	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.91	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.91	->Strongly Connected Components:
21.52/21.91	->->Cycle:
21.52/21.91	->->-> Pairs:
21.52/21.91	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.91	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.91	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.91	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.91	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.91	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.91	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.91	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.91	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.91	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.91	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.91	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.91	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.91	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.91	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.91	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.91	->->-> Rules:
21.52/21.91	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.91	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.91	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.91	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.91	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.91	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.91	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.91	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.91	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.91	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.91	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.91	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.91	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.91	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.91	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.91	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.91	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.91	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.91	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.91	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.91	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.91	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	Reduction Pair Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	-> Usable rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Interpretation type:
21.52/21.92	 Linear
21.52/21.92	->Coefficients:
21.52/21.92	 Natural Numbers
21.52/21.92	->Dimension:
21.52/21.92	 1
21.52/21.92	->Bound:
21.52/21.92	 2
21.52/21.92	->Interpretation:
21.52/21.92	 
21.52/21.92	[0](X) = 2.X + 2
21.52/21.92	[1](X) = 2.X + 2
21.52/21.92	[4](X) = 2.X + 2
21.52/21.92	[5](X) = 2.X + 2
21.52/21.92	[2](X) = X
21.52/21.92	[3](X) = X
21.52/21.92	[1#](X) = 2.X + 2
21.52/21.92	[4#](X) = 2.X + 2
21.52/21.92	[5#](X) = 2.X + 2
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	SCC Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Strongly Connected Components:
21.52/21.92	->->Cycle:
21.52/21.92	->->-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	->->-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	Reduction Pair Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	-> Usable rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Interpretation type:
21.52/21.92	 Linear
21.52/21.92	->Coefficients:
21.52/21.92	 Natural Numbers
21.52/21.92	->Dimension:
21.52/21.92	 1
21.52/21.92	->Bound:
21.52/21.92	 2
21.52/21.92	->Interpretation:
21.52/21.92	 
21.52/21.92	[0](X) = 2.X + 2
21.52/21.92	[1](X) = 2.X + 2
21.52/21.92	[4](X) = 2.X + 2
21.52/21.92	[5](X) = 2.X + 2
21.52/21.92	[2](X) = X
21.52/21.92	[3](X) = X
21.52/21.92	[1#](X) = 2.X + 2
21.52/21.92	[4#](X) = 2.X + 2
21.52/21.92	[5#](X) = 2.X + 2
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	SCC Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Strongly Connected Components:
21.52/21.92	->->Cycle:
21.52/21.92	->->-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	->->-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	Reduction Pair Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 4#(x1:S)
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	-> Usable rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Interpretation type:
21.52/21.92	 Linear
21.52/21.92	->Coefficients:
21.52/21.92	 Natural Numbers
21.52/21.92	->Dimension:
21.52/21.92	 1
21.52/21.92	->Bound:
21.52/21.92	 2
21.52/21.92	->Interpretation:
21.52/21.92	 
21.52/21.92	[0](X) = 2.X + 2
21.52/21.92	[1](X) = 2.X + 2
21.52/21.92	[4](X) = 2.X + 2
21.52/21.92	[5](X) = 2.X + 2
21.52/21.92	[2](X) = X
21.52/21.92	[3](X) = X
21.52/21.92	[1#](X) = 2.X
21.52/21.92	[4#](X) = 2.X
21.52/21.92	[5#](X) = 2.X
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	SCC Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Strongly Connected Components:
21.52/21.92	->->Cycle:
21.52/21.92	->->-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	->->-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	Reduction Pair Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(4(5(2(0(x1:S))))) -> 5#(4(x1:S))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	-> Usable rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Interpretation type:
21.52/21.92	 Linear
21.52/21.92	->Coefficients:
21.52/21.92	 Natural Numbers
21.52/21.92	->Dimension:
21.52/21.92	 1
21.52/21.92	->Bound:
21.52/21.92	 2
21.52/21.92	->Interpretation:
21.52/21.92	 
21.52/21.92	[0](X) = 2.X + 2
21.52/21.92	[1](X) = 2.X + 2
21.52/21.92	[4](X) = 2.X + 2
21.52/21.92	[5](X) = 2.X + 2
21.52/21.92	[2](X) = X
21.52/21.92	[3](X) = X
21.52/21.92	[1#](X) = 2.X + 2
21.52/21.92	[4#](X) = 2.X + 2
21.52/21.92	[5#](X) = 2.X + 2
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	SCC Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Strongly Connected Components:
21.52/21.92	->->Cycle:
21.52/21.92	->->-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	->->-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	Reduction Pair Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(1(x1:S)))) -> 5#(x1:S)
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	-> Usable rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Interpretation type:
21.52/21.92	 Linear
21.52/21.92	->Coefficients:
21.52/21.92	 Natural Numbers
21.52/21.92	->Dimension:
21.52/21.92	 1
21.52/21.92	->Bound:
21.52/21.92	 2
21.52/21.92	->Interpretation:
21.52/21.92	 
21.52/21.92	[0](X) = 2.X + 2
21.52/21.92	[1](X) = 2.X + 2
21.52/21.92	[4](X) = 2.X + 2
21.52/21.92	[5](X) = 2.X + 2
21.52/21.92	[2](X) = X
21.52/21.92	[3](X) = X
21.52/21.92	[1#](X) = 2.X + 2
21.52/21.92	[4#](X) = 2.X + 2
21.52/21.92	[5#](X) = 2.X + 2
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	SCC Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Strongly Connected Components:
21.52/21.92	->->Cycle:
21.52/21.92	->->-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	->->-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	Reduction Pair Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	-> Usable rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Interpretation type:
21.52/21.92	 Linear
21.52/21.92	->Coefficients:
21.52/21.92	 Natural Numbers
21.52/21.92	->Dimension:
21.52/21.92	 1
21.52/21.92	->Bound:
21.52/21.92	 2
21.52/21.92	->Interpretation:
21.52/21.92	 
21.52/21.92	[0](X) = 2.X + 2
21.52/21.92	[1](X) = 2.X + 2
21.52/21.92	[4](X) = 2.X + 2
21.52/21.92	[5](X) = 2.X + 2
21.52/21.92	[2](X) = X
21.52/21.92	[3](X) = X
21.52/21.92	[1#](X) = 2.X + 2
21.52/21.92	[4#](X) = 2.X + 2
21.52/21.92	[5#](X) = 2.X + 2
21.52/21.92	
21.52/21.92	Problem 1: 
21.52/21.92	
21.52/21.92	SCC Processor:
21.52/21.92	-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.92	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.92	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.92	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.92	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.92	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.92	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.92	->Strongly Connected Components:
21.52/21.92	->->Cycle:
21.52/21.92	->->-> Pairs:
21.52/21.92	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.92	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.92	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.92	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.92	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.92	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.92	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.92	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.92	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.92	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.92	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.92	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.92	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.92	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.92	->->-> Rules:
21.52/21.92	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.92	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.92	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.92	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.92	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.92	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.92	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.92	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.92	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.92	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.92	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.92	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.92	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.92	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.92	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.92	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.92	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.92	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.92	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.92	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.92	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.92	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.92	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.92	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.92	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.92	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.92	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.92	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.92	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.92	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.92	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.92	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.92	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.92	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.92	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.92	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	Reduction Pair Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 5#(1(5(x1:S)))
21.52/21.93	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	-> Usable rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Interpretation type:
21.52/21.93	 Linear
21.52/21.93	->Coefficients:
21.52/21.93	 Natural Numbers
21.52/21.93	->Dimension:
21.52/21.93	 1
21.52/21.93	->Bound:
21.52/21.93	 2
21.52/21.93	->Interpretation:
21.52/21.93	 
21.52/21.93	[0](X) = 2.X + 2
21.52/21.93	[1](X) = 2.X + 2
21.52/21.93	[4](X) = 2.X + 2
21.52/21.93	[5](X) = 2.X + 2
21.52/21.93	[2](X) = X
21.52/21.93	[3](X) = X
21.52/21.93	[1#](X) = 2.X
21.52/21.93	[4#](X) = 2.X
21.52/21.93	[5#](X) = X + 2
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	SCC Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Strongly Connected Components:
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	Reduction Pair Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(0(0(x1:S)))) -> 1#(x1:S)
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	-> Usable rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Interpretation type:
21.52/21.93	 Linear
21.52/21.93	->Coefficients:
21.52/21.93	 Natural Numbers
21.52/21.93	->Dimension:
21.52/21.93	 1
21.52/21.93	->Bound:
21.52/21.93	 2
21.52/21.93	->Interpretation:
21.52/21.93	 
21.52/21.93	[0](X) = 2.X + 2
21.52/21.93	[1](X) = 2.X + 2
21.52/21.93	[4](X) = X
21.52/21.93	[5](X) = 2.X + 2
21.52/21.93	[2](X) = X
21.52/21.93	[3](X) = X
21.52/21.93	[1#](X) = 2.X + 2
21.52/21.93	[4#](X) = X
21.52/21.93	[5#](X) = 2.X + 2
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	SCC Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Strongly Connected Components:
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	Reduction Pair Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(0(5(x1:S)))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	-> Usable rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Interpretation type:
21.52/21.93	 Linear
21.52/21.93	->Coefficients:
21.52/21.93	 Natural Numbers
21.52/21.93	->Dimension:
21.52/21.93	 1
21.52/21.93	->Bound:
21.52/21.93	 2
21.52/21.93	->Interpretation:
21.52/21.93	 
21.52/21.93	[0](X) = 2.X + 2
21.52/21.93	[1](X) = 2.X + 2
21.52/21.93	[4](X) = 2.X + 2
21.52/21.93	[5](X) = 2.X + 2
21.52/21.93	[2](X) = X
21.52/21.93	[3](X) = X
21.52/21.93	[1#](X) = X + 2
21.52/21.93	[4#](X) = X + 2
21.52/21.93	[5#](X) = 2.X + 2
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	SCC Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Strongly Connected Components:
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	Reduction Pair Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(2(0(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	-> Usable rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Interpretation type:
21.52/21.93	 Linear
21.52/21.93	->Coefficients:
21.52/21.93	 Natural Numbers
21.52/21.93	->Dimension:
21.52/21.93	 1
21.52/21.93	->Bound:
21.52/21.93	 2
21.52/21.93	->Interpretation:
21.52/21.93	 
21.52/21.93	[0](X) = 2.X + 2
21.52/21.93	[1](X) = 2.X + 2
21.52/21.93	[4](X) = 2.X + 2
21.52/21.93	[5](X) = 2.X + 2
21.52/21.93	[2](X) = X
21.52/21.93	[3](X) = X
21.52/21.93	[1#](X) = 2.X + 1
21.52/21.93	[4#](X) = 2.X + 1
21.52/21.93	[5#](X) = 2.X + 2
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	SCC Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Strongly Connected Components:
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	Reduction Pair Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(2(0(x1:S)))) -> 4#(x1:S)
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	-> Usable rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Interpretation type:
21.52/21.93	 Linear
21.52/21.93	->Coefficients:
21.52/21.93	 Natural Numbers
21.52/21.93	->Dimension:
21.52/21.93	 1
21.52/21.93	->Bound:
21.52/21.93	 2
21.52/21.93	->Interpretation:
21.52/21.93	 
21.52/21.93	[0](X) = 2.X + 2
21.52/21.93	[1](X) = 2.X + 2
21.52/21.93	[4](X) = 2.X + 2
21.52/21.93	[5](X) = 2.X + 2
21.52/21.93	[2](X) = X
21.52/21.93	[3](X) = X
21.52/21.93	[1#](X) = 2.X + 2
21.52/21.93	[4#](X) = 2.X + 2
21.52/21.93	[5#](X) = 2.X
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	SCC Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Strongly Connected Components:
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	Reduction Pair Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 1#(5(0(4(5(x1:S))))) -> 4#(0(5(1(5(x1:S)))))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	-> Usable rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Interpretation type:
21.52/21.93	 Linear
21.52/21.93	->Coefficients:
21.52/21.93	 Natural Numbers
21.52/21.93	->Dimension:
21.52/21.93	 1
21.52/21.93	->Bound:
21.52/21.93	 2
21.52/21.93	->Interpretation:
21.52/21.93	 
21.52/21.93	[0](X) = 0
21.52/21.93	[1](X) = 2
21.52/21.93	[4](X) = 2
21.52/21.93	[5](X) = 2
21.52/21.93	[2](X) = 0
21.52/21.93	[3](X) = 1
21.52/21.93	[1#](X) = 2
21.52/21.93	[4#](X) = 2.X + 1
21.52/21.93	[5#](X) = 2
21.52/21.93	
21.52/21.93	Problem 1: 
21.52/21.93	
21.52/21.93	SCC Processor:
21.52/21.93	-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(0(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(5(1(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(0(4(1(0(x1:S))))) -> 1#(x1:S)
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 1#(1(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 1#(5(x1:S))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 1#(5(5(x1:S)))
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->Strongly Connected Components:
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.93	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.93	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.93	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.93	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.93	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.93	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.93	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.93	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.93	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.93	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.93	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.93	->->Cycle:
21.52/21.93	->->-> Pairs:
21.52/21.93	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.93	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.93	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.93	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.93	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.93	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.93	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.93	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.93	->->-> Rules:
21.52/21.93	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.93	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.93	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.93	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.93	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.93	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.93	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.93	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.93	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.93	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.93	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.93	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.93	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.93	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.93	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.93	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.93	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.93	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.93	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.93	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.93	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.93	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.93	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.93	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.93	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.93	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.93	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.93	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.93	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.93	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.93	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	
21.52/21.94	
21.52/21.94	The problem is decomposed in 2 subproblems.
21.52/21.94	
21.52/21.94	Problem 1.1: 
21.52/21.94	
21.52/21.94	Reduction Pair Processor:
21.52/21.94	-> Pairs:
21.52/21.94	 1#(1(4(5(0(x1:S))))) -> 1#(1(3(4(0(5(x1:S))))))
21.52/21.94	-> Rules:
21.52/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	-> Usable rules:
21.52/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	->Interpretation type:
21.52/21.94	 Linear
21.52/21.94	->Coefficients:
21.52/21.94	 Natural Numbers
21.52/21.94	->Dimension:
21.52/21.94	 1
21.52/21.94	->Bound:
21.52/21.94	 2
21.52/21.94	->Interpretation:
21.52/21.94	 
21.52/21.94	[0](X) = X
21.52/21.94	[1](X) = 2.X + 2
21.52/21.94	[4](X) = 2.X
21.52/21.94	[5](X) = 2.X + 2
21.52/21.94	[2](X) = 0
21.52/21.94	[3](X) = 0
21.52/21.94	[1#](X) = X
21.52/21.94	
21.52/21.94	Problem 1.1: 
21.52/21.94	
21.52/21.94	SCC Processor:
21.52/21.94	-> Pairs:
21.52/21.94	 Empty
21.52/21.94	-> Rules:
21.52/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	->Strongly Connected Components:
21.52/21.94	 There is no strongly connected component
21.52/21.94	
21.52/21.94	The problem is finite.
21.52/21.94	
21.52/21.94	Problem 1.2: 
21.52/21.94	
21.52/21.94	Reduction Pair Processor:
21.52/21.94	-> Pairs:
21.52/21.94	 4#(1(3(0(5(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.94	-> Rules:
21.52/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	-> Usable rules:
21.52/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	->Interpretation type:
21.52/21.94	 Linear
21.52/21.94	->Coefficients:
21.52/21.94	 Natural Numbers
21.52/21.94	->Dimension:
21.52/21.94	 1
21.52/21.94	->Bound:
21.52/21.94	 2
21.52/21.94	->Interpretation:
21.52/21.94	 
21.52/21.94	[0](X) = 0
21.52/21.94	[1](X) = 2
21.52/21.94	[4](X) = 2
21.52/21.94	[5](X) = 2
21.52/21.94	[2](X) = 0
21.52/21.94	[3](X) = 0
21.52/21.94	[4#](X) = 2.X + 2
21.52/21.94	[5#](X) = 2
21.52/21.94	
21.52/21.94	Problem 1.2: 
21.52/21.94	
21.52/21.94	SCC Processor:
21.52/21.94	-> Pairs:
21.52/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.52/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.52/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.52/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.52/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.52/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.52/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.52/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.52/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.52/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.52/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.52/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.52/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.52/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.52/21.94	-> Rules:
21.52/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.52/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.52/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.52/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.52/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.52/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.52/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.52/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.52/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.52/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.52/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.52/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.52/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.52/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.52/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.52/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.52/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.52/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.52/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.52/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.52/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.52/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.52/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.52/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.52/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.52/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.52/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.52/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.52/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.52/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.52/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.52/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.52/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.52/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.52/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.52/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.52/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.52/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.52/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.52/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.52/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.52/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.52/21.94	->Strongly Connected Components:
21.52/21.94	->->Cycle:
21.52/21.94	->->-> Pairs:
21.52/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.52/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	->->-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	Reduction Pair Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(0(1(x1:S)))
21.53/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	-> Usable rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Interpretation type:
21.53/21.94	 Linear
21.53/21.94	->Coefficients:
21.53/21.94	 Natural Numbers
21.53/21.94	->Dimension:
21.53/21.94	 1
21.53/21.94	->Bound:
21.53/21.94	 2
21.53/21.94	->Interpretation:
21.53/21.94	 
21.53/21.94	[0](X) = 0
21.53/21.94	[1](X) = 2
21.53/21.94	[4](X) = 2
21.53/21.94	[5](X) = 2
21.53/21.94	[2](X) = X
21.53/21.94	[3](X) = 2
21.53/21.94	[4#](X) = X + 1
21.53/21.94	[5#](X) = 1
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	SCC Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Strongly Connected Components:
21.53/21.94	->->Cycle:
21.53/21.94	->->-> Pairs:
21.53/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	->->-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	Reduction Pair Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(4(1(0(1(x1:S))))) -> 4#(4(0(1(x1:S))))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	-> Usable rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Interpretation type:
21.53/21.94	 Linear
21.53/21.94	->Coefficients:
21.53/21.94	 Natural Numbers
21.53/21.94	->Dimension:
21.53/21.94	 1
21.53/21.94	->Bound:
21.53/21.94	 2
21.53/21.94	->Interpretation:
21.53/21.94	 
21.53/21.94	[0](X) = X + 2
21.53/21.94	[1](X) = 2.X
21.53/21.94	[4](X) = 2.X + 2
21.53/21.94	[5](X) = 2.X
21.53/21.94	[2](X) = 0
21.53/21.94	[3](X) = 0
21.53/21.94	[4#](X) = 2.X + 2
21.53/21.94	[5#](X) = 2.X + 2
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	SCC Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Strongly Connected Components:
21.53/21.94	->->Cycle:
21.53/21.94	->->-> Pairs:
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	->->-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	Reduction Pair Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(0(0(x1:S)))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	-> Usable rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Interpretation type:
21.53/21.94	 Linear
21.53/21.94	->Coefficients:
21.53/21.94	 Natural Numbers
21.53/21.94	->Dimension:
21.53/21.94	 1
21.53/21.94	->Bound:
21.53/21.94	 2
21.53/21.94	->Interpretation:
21.53/21.94	 
21.53/21.94	[0](X) = 2.X + 1
21.53/21.94	[1](X) = 2.X + 1
21.53/21.94	[4](X) = 2.X + 1
21.53/21.94	[5](X) = X
21.53/21.94	[2](X) = X
21.53/21.94	[3](X) = 0
21.53/21.94	[4#](X) = 2.X
21.53/21.94	[5#](X) = 2.X + 1
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	SCC Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Strongly Connected Components:
21.53/21.94	->->Cycle:
21.53/21.94	->->-> Pairs:
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	->->-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	Reduction Pair Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(0(0(x1:S)))) -> 5#(x1:S)
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	-> Usable rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Interpretation type:
21.53/21.94	 Linear
21.53/21.94	->Coefficients:
21.53/21.94	 Natural Numbers
21.53/21.94	->Dimension:
21.53/21.94	 1
21.53/21.94	->Bound:
21.53/21.94	 2
21.53/21.94	->Interpretation:
21.53/21.94	 
21.53/21.94	[0](X) = 0
21.53/21.94	[1](X) = 2
21.53/21.94	[4](X) = 2.X
21.53/21.94	[5](X) = 2.X + 2
21.53/21.94	[2](X) = 0
21.53/21.94	[3](X) = 2.X
21.53/21.94	[4#](X) = X
21.53/21.94	[5#](X) = 0
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	SCC Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Strongly Connected Components:
21.53/21.94	->->Cycle:
21.53/21.94	->->-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	->->-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	Reduction Pair Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 4#(0(5(x1:S)))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	-> Usable rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Interpretation type:
21.53/21.94	 Linear
21.53/21.94	->Coefficients:
21.53/21.94	 Natural Numbers
21.53/21.94	->Dimension:
21.53/21.94	 1
21.53/21.94	->Bound:
21.53/21.94	 2
21.53/21.94	->Interpretation:
21.53/21.94	 
21.53/21.94	[0](X) = 2
21.53/21.94	[1](X) = 2.X + 2
21.53/21.94	[4](X) = X
21.53/21.94	[5](X) = 2.X + 2
21.53/21.94	[2](X) = 2
21.53/21.94	[3](X) = 0
21.53/21.94	[4#](X) = X
21.53/21.94	[5#](X) = 2
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	SCC Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Strongly Connected Components:
21.53/21.94	->->Cycle:
21.53/21.94	->->-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	->->-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	Reduction Pair Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(1(x1:S))
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	-> Usable rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Interpretation type:
21.53/21.94	 Linear
21.53/21.94	->Coefficients:
21.53/21.94	 Natural Numbers
21.53/21.94	->Dimension:
21.53/21.94	 1
21.53/21.94	->Bound:
21.53/21.94	 2
21.53/21.94	->Interpretation:
21.53/21.94	 
21.53/21.94	[0](X) = 2.X + 2
21.53/21.94	[1](X) = 2.X + 2
21.53/21.94	[4](X) = 2.X + 1
21.53/21.94	[5](X) = 2.X + 2
21.53/21.94	[2](X) = 0
21.53/21.94	[3](X) = 0
21.53/21.94	[4#](X) = 2.X + 2
21.53/21.94	[5#](X) = 2.X + 2
21.53/21.94	
21.53/21.94	Problem 1.2: 
21.53/21.94	
21.53/21.94	SCC Processor:
21.53/21.94	-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.94	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.94	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.94	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.94	-> Rules:
21.53/21.94	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.94	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.94	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.94	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.94	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.94	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.94	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.94	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.94	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.94	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.94	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.94	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.94	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.94	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.94	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.94	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.94	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.94	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.94	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.94	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.94	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.94	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.94	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.94	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.94	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.94	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.94	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.94	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.94	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.94	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.94	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.94	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.94	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.94	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.94	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.94	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.94	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.94	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.94	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.94	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.94	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.94	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.94	->Strongly Connected Components:
21.53/21.94	->->Cycle:
21.53/21.94	->->-> Pairs:
21.53/21.94	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.94	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 4#(5(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = X
21.53/21.95	[1](X) = 2.X + 2
21.53/21.95	[4](X) = 2.X + 2
21.53/21.95	[5](X) = 2.X + 2
21.53/21.95	[2](X) = X
21.53/21.95	[3](X) = X
21.53/21.95	[4#](X) = 2.X + 2
21.53/21.95	[5#](X) = 2.X + 2
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 4#(0(5(5(x1:S))))
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 4#(0(1(5(x1:S))))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 4#(0(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	->->Cycle:
21.53/21.95	->->-> Pairs:
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(0(0(4(5(x1:S))))) -> 5#(5(x1:S))
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = 2.X
21.53/21.95	[1](X) = 2.X + 2
21.53/21.95	[4](X) = 2.X + 2
21.53/21.95	[5](X) = X
21.53/21.95	[2](X) = 0
21.53/21.95	[3](X) = 0
21.53/21.95	[5#](X) = 2.X
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	->->Cycle:
21.53/21.95	->->-> Pairs:
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(1(5(0(1(x1:S))))) -> 5#(1(1(x1:S)))
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = 2.X + 1
21.53/21.95	[1](X) = X
21.53/21.95	[4](X) = 2.X + 1
21.53/21.95	[5](X) = 2.X + 1
21.53/21.95	[2](X) = X
21.53/21.95	[3](X) = X
21.53/21.95	[5#](X) = X
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	->->Cycle:
21.53/21.95	->->-> Pairs:
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(1(1(0(x1:S))))) -> 5#(x1:S)
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = 2.X + 2
21.53/21.95	[1](X) = 2.X + 2
21.53/21.95	[4](X) = 2.X + 2
21.53/21.95	[5](X) = 2.X
21.53/21.95	[2](X) = 0
21.53/21.95	[3](X) = 0
21.53/21.95	[5#](X) = 2.X
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	->->Cycle:
21.53/21.95	->->-> Pairs:
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(1(5(x1:S)))) -> 5#(5(x1:S))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = 2
21.53/21.95	[1](X) = 2.X + 2
21.53/21.95	[4](X) = X
21.53/21.95	[5](X) = 2.X + 2
21.53/21.95	[2](X) = 0
21.53/21.95	[3](X) = 0
21.53/21.95	[5#](X) = X
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	->->Cycle:
21.53/21.95	->->-> Pairs:
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(1(3(4(0(x1:S)))))
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = 2.X + 2
21.53/21.95	[1](X) = X + 2
21.53/21.95	[4](X) = 2.X + 1
21.53/21.95	[5](X) = 2.X + 2
21.53/21.95	[2](X) = 0
21.53/21.95	[3](X) = 0
21.53/21.95	[5#](X) = X
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	->->Cycle:
21.53/21.95	->->-> Pairs:
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	->->-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	Reduction Pair Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 5#(4(5(1(0(x1:S))))) -> 5#(5(1(3(4(0(x1:S))))))
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	-> Usable rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Interpretation type:
21.53/21.95	 Linear
21.53/21.95	->Coefficients:
21.53/21.95	 Natural Numbers
21.53/21.95	->Dimension:
21.53/21.95	 1
21.53/21.95	->Bound:
21.53/21.95	 2
21.53/21.95	->Interpretation:
21.53/21.95	 
21.53/21.95	[0](X) = 2
21.53/21.95	[1](X) = 2.X + 2
21.53/21.95	[4](X) = X
21.53/21.95	[5](X) = 2.X + 2
21.53/21.95	[2](X) = 1
21.53/21.95	[3](X) = 0
21.53/21.95	[5#](X) = 2.X
21.53/21.95	
21.53/21.95	Problem 1.2: 
21.53/21.95	
21.53/21.95	SCC Processor:
21.53/21.95	-> Pairs:
21.53/21.95	 Empty
21.53/21.95	-> Rules:
21.53/21.95	 0(1(0(0(x1:S)))) -> 2(0(2(0(0(1(x1:S))))))
21.53/21.95	 1(0(0(1(x1:S)))) -> 1(0(3(0(1(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(2(0(x1:S)))))
21.53/21.95	 1(0(0(4(x1:S)))) -> 1(4(0(3(2(0(x1:S))))))
21.53/21.95	 1(0(1(0(x1:S)))) -> 1(3(0(0(3(1(x1:S))))))
21.53/21.95	 1(0(1(4(5(x1:S))))) -> 1(3(1(5(4(0(x1:S))))))
21.53/21.95	 1(0(1(4(x1:S)))) -> 1(0(3(1(2(4(x1:S))))))
21.53/21.95	 1(0(1(5(x1:S)))) -> 1(0(2(1(5(x1:S)))))
21.53/21.95	 1(0(4(0(4(x1:S))))) -> 1(0(4(3(4(0(x1:S))))))
21.53/21.95	 1(0(4(1(x1:S)))) -> 1(0(3(4(1(x1:S)))))
21.53/21.95	 1(0(5(0(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
21.53/21.95	 1(1(1(0(0(x1:S))))) -> 1(1(0(0(3(1(x1:S))))))
21.53/21.95	 1(1(4(5(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(2(1(x1:S)))))
21.53/21.95	 1(4(1(0(x1:S)))) -> 1(4(0(3(1(x1:S)))))
21.53/21.95	 1(4(5(0(0(x1:S))))) -> 4(0(5(0(2(1(x1:S))))))
21.53/21.95	 1(4(5(0(x1:S)))) -> 4(0(2(1(2(5(x1:S))))))
21.53/21.95	 1(4(5(2(0(x1:S))))) -> 0(3(1(2(5(4(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 0(1(3(1(3(5(x1:S))))))
21.53/21.95	 1(5(0(1(x1:S)))) -> 1(5(0(3(1(3(x1:S))))))
21.53/21.95	 1(5(0(4(5(x1:S))))) -> 3(4(0(5(1(5(x1:S))))))
21.53/21.95	 1(2(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 1(2(0(5(0(x1:S))))) -> 5(2(1(0(2(0(x1:S))))))
21.53/21.95	 1(3(0(4(x1:S)))) -> 1(3(4(2(0(x1:S)))))
21.53/21.95	 4(1(0(0(1(x1:S))))) -> 1(0(4(0(3(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(2(4(2(0(1(x1:S))))))
21.53/21.95	 4(1(0(0(x1:S)))) -> 0(3(4(3(0(1(x1:S))))))
21.53/21.95	 4(1(0(5(x1:S)))) -> 4(0(2(1(5(x1:S)))))
21.53/21.95	 4(1(5(3(1(x1:S))))) -> 2(1(5(4(3(1(x1:S))))))
21.53/21.95	 4(1(2(0(0(x1:S))))) -> 4(2(0(0(2(1(x1:S))))))
21.53/21.95	 4(1(2(0(x1:S)))) -> 3(0(2(1(3(4(x1:S))))))
21.53/21.95	 4(1(3(0(5(x1:S))))) -> 3(2(4(0(1(5(x1:S))))))
21.53/21.95	 4(4(1(0(1(x1:S))))) -> 1(3(4(4(0(1(x1:S))))))
21.53/21.95	 4(5(0(0(x1:S)))) -> 3(0(4(0(5(x1:S)))))
21.53/21.95	 4(5(0(1(0(x1:S))))) -> 4(0(0(5(3(1(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 1(1(3(4(0(5(x1:S))))))
21.53/21.95	 4(5(1(1(0(x1:S))))) -> 4(0(2(1(5(1(x1:S))))))
21.53/21.95	 4(5(1(5(1(x1:S))))) -> 4(1(5(5(3(1(x1:S))))))
21.53/21.95	 4(5(5(0(4(x1:S))))) -> 5(4(0(5(4(2(x1:S))))))
21.53/21.95	 5(0(0(4(1(x1:S))))) -> 5(4(0(3(0(1(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 0(3(4(0(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(5(x1:S))))) -> 4(0(0(3(5(5(x1:S))))))
21.53/21.95	 5(0(0(4(x1:S)))) -> 5(4(0(2(0(x1:S)))))
21.53/21.95	 5(0(1(4(x1:S)))) -> 1(5(4(3(0(x1:S)))))
21.53/21.95	 5(0(4(1(0(x1:S))))) -> 5(0(4(0(3(1(x1:S))))))
21.53/21.95	 5(1(5(0(1(x1:S))))) -> 5(0(3(5(1(1(x1:S))))))
21.53/21.95	 5(4(1(1(0(x1:S))))) -> 1(2(4(0(1(5(x1:S))))))
21.53/21.95	 5(4(1(5(x1:S)))) -> 4(3(1(5(5(x1:S)))))
21.53/21.95	 5(4(5(1(0(x1:S))))) -> 5(5(1(3(4(0(x1:S))))))
21.53/21.95	 5(5(2(0(4(x1:S))))) -> 5(5(3(4(2(0(x1:S))))))
21.53/21.95	->Strongly Connected Components:
21.53/21.95	 There is no strongly connected component
21.53/21.95	
21.53/21.95	The problem is finite.
21.53/21.95	EOF