11.74/11.89	YES
11.74/11.89	
11.74/11.89	Problem 1: 
11.74/11.89	
11.74/11.89	(VAR v_NonEmpty:S x1:S)
11.74/11.89	(RULES
11.74/11.89	0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	)
11.74/11.89	
11.74/11.89	Problem 1: 
11.74/11.89	
11.74/11.89	Dependency Pairs Processor:
11.74/11.89	-> Pairs:
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 0#(3(4(5(x1:S))))
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 4#(5(x1:S))
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 5#(1(0(3(4(5(x1:S))))))
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(2(1(1(3(0(x1:S))))))
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 2#(1(1(3(0(x1:S)))))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 0#(3(2(x1:S)))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 0#(3(5(x1:S)))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(1(0(3(5(x1:S)))))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 5#(1(0(3(2(x1:S)))))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(1(3(4(5(2(x1:S))))))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(3(0(2(5(x1:S)))))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(1(3(0(2(0(x1:S))))))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(0(4(x1:S)))))
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(0(x1:S))))
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(4(0(4(x1:S))))))
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(4(0(x1:S)))))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(2(1(3(0(x1:S)))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(1(3(0(2(x1:S)))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 2#(1(3(0(x1:S))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 4#(0(2(1(3(0(x1:S))))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 4#(0(1(3(0(2(x1:S))))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(2(1(0(3(4(x1:S))))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(3(4(x1:S)))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 2#(1(0(3(4(x1:S)))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 2#(1(3(4(0(x1:S)))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 0#(1(3(5(1(2(x1:S))))))
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(2(x1:S)))) -> 0#(4(1(2(x1:S))))
11.74/11.89	 0#(1(1(2(x1:S)))) -> 4#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 0#(3(2(1(x1:S))))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 4#(1(0(3(2(1(x1:S))))))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 0#(3(5(x1:S)))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 4#(1(0(3(5(x1:S)))))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 5#(1(3(4(2(2(x1:S))))))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 2#(1(3(0(5(x1:S)))))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 5#(2(1(3(0(5(x1:S))))))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 5#(1(3(2(2(x1:S)))))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 0#(3(2(5(1(x1:S)))))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 0#(3(5(x1:S)))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 2#(4(1(0(3(5(x1:S))))))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 4#(1(0(3(5(x1:S)))))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(1(3(2(x1:S)))))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(1(3(2(x1:S))))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(1(3(2(x1:S))))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 5#(1(3(2(1(x1:S)))))
11.74/11.89	 2#(3(2(0(5(x1:S))))) -> 0#(3(5(x1:S)))
11.74/11.89	 2#(3(2(0(5(x1:S))))) -> 2#(2(1(0(3(5(x1:S))))))
11.74/11.89	 2#(3(2(0(5(x1:S))))) -> 2#(1(0(3(5(x1:S)))))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 0#(3(2(5(x1:S))))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 5#(1(0(3(2(5(x1:S))))))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 5#(1(3(2(x1:S))))
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 2#(2(1(3(0(x1:S)))))
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 2#(1(3(0(x1:S))))
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 4#(2(2(1(3(0(x1:S))))))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 4#(1(5(2(0(2(x1:S))))))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(1(3(4(5(2(x1:S))))))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 5#(1(3(2(4(2(x1:S))))))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(5(1(3(4(2(x1:S))))))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 5#(1(3(4(2(x1:S)))))
11.74/11.89	-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	
11.74/11.89	Problem 1: 
11.74/11.89	
11.74/11.89	SCC Processor:
11.74/11.89	-> Pairs:
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 0#(3(4(5(x1:S))))
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 4#(5(x1:S))
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 5#(1(0(3(4(5(x1:S))))))
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(2(1(1(3(0(x1:S))))))
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 2#(1(1(3(0(x1:S)))))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 0#(3(2(x1:S)))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 0#(3(5(x1:S)))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(1(0(3(5(x1:S)))))
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 5#(1(0(3(2(x1:S)))))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(1(3(4(5(2(x1:S))))))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(3(0(2(5(x1:S)))))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(1(3(0(2(0(x1:S))))))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(0(4(x1:S)))))
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(0(x1:S))))
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(4(0(4(x1:S))))))
11.74/11.89	 0#(1(2(x1:S))) -> 2#(1(3(4(0(x1:S)))))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(2(1(3(0(x1:S)))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(1(3(0(2(x1:S)))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 2#(1(3(0(x1:S))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 4#(0(2(1(3(0(x1:S))))))
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 4#(0(1(3(0(2(x1:S))))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(2(1(0(3(4(x1:S))))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(3(4(x1:S)))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 2#(1(0(3(4(x1:S)))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 2#(1(3(4(0(x1:S)))))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 0#(1(3(5(1(2(x1:S))))))
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(2(x1:S)))) -> 0#(4(1(2(x1:S))))
11.74/11.89	 0#(1(1(2(x1:S)))) -> 4#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 0#(3(2(1(x1:S))))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 4#(1(0(3(2(1(x1:S))))))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 0#(3(5(x1:S)))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 4#(1(0(3(5(x1:S)))))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 5#(1(3(4(2(2(x1:S))))))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 2#(1(3(0(5(x1:S)))))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 5#(2(1(3(0(5(x1:S))))))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 5#(1(3(2(2(x1:S)))))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 0#(3(2(5(1(x1:S)))))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 0#(3(5(x1:S)))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 2#(4(1(0(3(5(x1:S))))))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 4#(1(0(3(5(x1:S)))))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(1(3(2(x1:S)))))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(1(3(2(x1:S))))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(1(3(2(x1:S))))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 5#(1(3(2(1(x1:S)))))
11.74/11.89	 2#(3(2(0(5(x1:S))))) -> 0#(3(5(x1:S)))
11.74/11.89	 2#(3(2(0(5(x1:S))))) -> 2#(2(1(0(3(5(x1:S))))))
11.74/11.89	 2#(3(2(0(5(x1:S))))) -> 2#(1(0(3(5(x1:S)))))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 0#(3(2(5(x1:S))))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 5#(1(0(3(2(5(x1:S))))))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 5#(1(3(2(x1:S))))
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 2#(2(1(3(0(x1:S)))))
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 2#(1(3(0(x1:S))))
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 4#(2(2(1(3(0(x1:S))))))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 4#(1(5(2(0(2(x1:S))))))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(1(3(4(5(2(x1:S))))))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 5#(1(3(2(4(2(x1:S))))))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(5(1(3(4(2(x1:S))))))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 5#(1(3(4(2(x1:S)))))
11.74/11.89	-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	->Strongly Connected Components:
11.74/11.89	->->Cycle:
11.74/11.89	->->-> Pairs:
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 4#(5(x1:S))
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	->->-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	
11.74/11.89	Problem 1: 
11.74/11.89	
11.74/11.89	Reduction Pair Processor:
11.74/11.89	-> Pairs:
11.74/11.89	 0#(4(5(3(5(x1:S))))) -> 4#(5(x1:S))
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	-> Usable rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	->Interpretation type:
11.74/11.89	 Linear
11.74/11.89	->Coefficients:
11.74/11.89	 Natural Numbers
11.74/11.89	->Dimension:
11.74/11.89	 1
11.74/11.89	->Bound:
11.74/11.89	 2
11.74/11.89	->Interpretation:
11.74/11.89	 
11.74/11.89	[0](X) = X
11.74/11.89	[2](X) = 2.X + 2
11.74/11.89	[4](X) = X
11.74/11.89	[5](X) = 2.X + 2
11.74/11.89	[1](X) = X
11.74/11.89	[3](X) = X
11.74/11.89	[0#](X) = 2.X + 2
11.74/11.89	[2#](X) = 2.X
11.74/11.89	[4#](X) = X + 2
11.74/11.89	[5#](X) = X + 2
11.74/11.89	
11.74/11.89	Problem 1: 
11.74/11.89	
11.74/11.89	SCC Processor:
11.74/11.89	-> Pairs:
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	->Strongly Connected Components:
11.74/11.89	->->Cycle:
11.74/11.89	->->-> Pairs:
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	->->-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	
11.74/11.89	Problem 1: 
11.74/11.89	
11.74/11.89	Reduction Pair Processor:
11.74/11.89	-> Pairs:
11.74/11.89	 0#(1(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.89	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.89	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.89	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.89	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.89	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.89	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.89	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.89	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.89	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.89	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.89	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.89	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.89	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.89	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.89	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.89	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.89	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.89	-> Rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	-> Usable rules:
11.74/11.89	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.89	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.89	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.89	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.89	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.89	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.89	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.89	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.89	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.89	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.89	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.89	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.89	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.89	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.89	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.89	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.89	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.89	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.89	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.89	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.89	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.89	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.89	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.89	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.89	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.89	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.89	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.89	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.89	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.89	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.89	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.89	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.89	->Interpretation type:
11.74/11.89	 Linear
11.74/11.89	->Coefficients:
11.74/11.89	 Natural Numbers
11.74/11.89	->Dimension:
11.74/11.89	 1
11.74/11.89	->Bound:
11.74/11.89	 2
11.74/11.89	->Interpretation:
11.74/11.90	 
11.74/11.90	[0](X) = X
11.74/11.90	[2](X) = 2.X + 2
11.74/11.90	[4](X) = X
11.74/11.90	[5](X) = 2.X + 2
11.74/11.90	[1](X) = X
11.74/11.90	[3](X) = X
11.74/11.90	[0#](X) = 2.X
11.74/11.90	[2#](X) = 2.X + 1
11.74/11.90	[4#](X) = 2.X
11.74/11.90	[5#](X) = 2.X + 1
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	SCC Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Strongly Connected Components:
11.74/11.90	->->Cycle:
11.74/11.90	->->-> Pairs:
11.74/11.90	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	->->-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	Reduction Pair Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(5(x1:S)))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	-> Usable rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Interpretation type:
11.74/11.90	 Linear
11.74/11.90	->Coefficients:
11.74/11.90	 Natural Numbers
11.74/11.90	->Dimension:
11.74/11.90	 1
11.74/11.90	->Bound:
11.74/11.90	 2
11.74/11.90	->Interpretation:
11.74/11.90	 
11.74/11.90	[0](X) = X
11.74/11.90	[2](X) = 2.X + 2
11.74/11.90	[4](X) = X
11.74/11.90	[5](X) = 2.X + 2
11.74/11.90	[1](X) = X
11.74/11.90	[3](X) = X
11.74/11.90	[0#](X) = 2.X + 2
11.74/11.90	[2#](X) = 2.X + 2
11.74/11.90	[4#](X) = 2.X + 2
11.74/11.90	[5#](X) = 2.X + 2
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	SCC Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Strongly Connected Components:
11.74/11.90	->->Cycle:
11.74/11.90	->->-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	->->-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	Reduction Pair Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(0(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	-> Usable rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Interpretation type:
11.74/11.90	 Linear
11.74/11.90	->Coefficients:
11.74/11.90	 Natural Numbers
11.74/11.90	->Dimension:
11.74/11.90	 1
11.74/11.90	->Bound:
11.74/11.90	 2
11.74/11.90	->Interpretation:
11.74/11.90	 
11.74/11.90	[0](X) = X
11.74/11.90	[2](X) = 2.X + 2
11.74/11.90	[4](X) = X
11.74/11.90	[5](X) = 2.X + 2
11.74/11.90	[1](X) = X
11.74/11.90	[3](X) = X
11.74/11.90	[0#](X) = 2.X
11.74/11.90	[2#](X) = 2.X + 2
11.74/11.90	[4#](X) = 2.X
11.74/11.90	[5#](X) = 2.X + 2
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	SCC Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Strongly Connected Components:
11.74/11.90	->->Cycle:
11.74/11.90	->->-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	->->-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	Reduction Pair Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	-> Usable rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Interpretation type:
11.74/11.90	 Linear
11.74/11.90	->Coefficients:
11.74/11.90	 Natural Numbers
11.74/11.90	->Dimension:
11.74/11.90	 1
11.74/11.90	->Bound:
11.74/11.90	 2
11.74/11.90	->Interpretation:
11.74/11.90	 
11.74/11.90	[0](X) = X
11.74/11.90	[2](X) = 2.X + 2
11.74/11.90	[4](X) = X
11.74/11.90	[5](X) = 2.X + 2
11.74/11.90	[1](X) = X
11.74/11.90	[3](X) = X
11.74/11.90	[0#](X) = 2.X + 2
11.74/11.90	[2#](X) = 2.X + 2
11.74/11.90	[4#](X) = X + 2
11.74/11.90	[5#](X) = 2.X + 2
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	SCC Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Strongly Connected Components:
11.74/11.90	->->Cycle:
11.74/11.90	->->-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	->->-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	Reduction Pair Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	-> Usable rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Interpretation type:
11.74/11.90	 Linear
11.74/11.90	->Coefficients:
11.74/11.90	 Natural Numbers
11.74/11.90	->Dimension:
11.74/11.90	 1
11.74/11.90	->Bound:
11.74/11.90	 2
11.74/11.90	->Interpretation:
11.74/11.90	 
11.74/11.90	[0](X) = X
11.74/11.90	[2](X) = 2.X + 1
11.74/11.90	[4](X) = X
11.74/11.90	[5](X) = 2.X + 1
11.74/11.90	[1](X) = X
11.74/11.90	[3](X) = X
11.74/11.90	[0#](X) = 2.X + 2
11.74/11.90	[2#](X) = 2.X + 2
11.74/11.90	[4#](X) = 2.X + 2
11.74/11.90	[5#](X) = 2.X + 2
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	SCC Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Strongly Connected Components:
11.74/11.90	->->Cycle:
11.74/11.90	->->-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	->->-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	Reduction Pair Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(5(x1:S))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	-> Usable rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Interpretation type:
11.74/11.90	 Linear
11.74/11.90	->Coefficients:
11.74/11.90	 Natural Numbers
11.74/11.90	->Dimension:
11.74/11.90	 1
11.74/11.90	->Bound:
11.74/11.90	 2
11.74/11.90	->Interpretation:
11.74/11.90	 
11.74/11.90	[0](X) = X
11.74/11.90	[2](X) = 2.X + 2
11.74/11.90	[4](X) = X
11.74/11.90	[5](X) = 2.X + 2
11.74/11.90	[1](X) = X
11.74/11.90	[3](X) = X
11.74/11.90	[0#](X) = 2.X + 2
11.74/11.90	[2#](X) = 2.X + 2
11.74/11.90	[4#](X) = 2.X + 2
11.74/11.90	[5#](X) = 2.X + 2
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	SCC Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	->Strongly Connected Components:
11.74/11.90	->->Cycle:
11.74/11.90	->->-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.90	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.90	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.90	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.90	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.90	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.90	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.90	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.90	->->-> Rules:
11.74/11.90	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.90	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.90	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.90	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.90	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.90	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.90	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.90	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.90	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.90	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.90	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.90	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.90	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.90	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.90	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.90	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.90	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.90	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.90	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.90	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.90	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.90	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.90	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.90	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.90	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.90	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.90	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.90	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.90	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.90	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.90	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.90	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.90	
11.74/11.90	Problem 1: 
11.74/11.90	
11.74/11.90	Reduction Pair Processor:
11.74/11.90	-> Pairs:
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.90	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.90	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.90	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.90	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.90	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.90	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.90	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.90	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.90	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.90	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	-> Rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	-> Usable rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	->Interpretation type:
11.74/11.91	 Linear
11.74/11.91	->Coefficients:
11.74/11.91	 Natural Numbers
11.74/11.91	->Dimension:
11.74/11.91	 1
11.74/11.91	->Bound:
11.74/11.91	 2
11.74/11.91	->Interpretation:
11.74/11.91	 
11.74/11.91	[0](X) = X
11.74/11.91	[2](X) = X
11.74/11.91	[4](X) = X
11.74/11.91	[5](X) = 2.X + 2
11.74/11.91	[1](X) = X
11.74/11.91	[3](X) = X
11.74/11.91	[0#](X) = 2.X + 2
11.74/11.91	[2#](X) = 2.X + 2
11.74/11.91	[4#](X) = 2.X + 2
11.74/11.91	[5#](X) = 2.X + 2
11.74/11.91	
11.74/11.91	Problem 1: 
11.74/11.91	
11.74/11.91	SCC Processor:
11.74/11.91	-> Pairs:
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	-> Rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	->Strongly Connected Components:
11.74/11.91	->->Cycle:
11.74/11.91	->->-> Pairs:
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	->->-> Rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	
11.74/11.91	Problem 1: 
11.74/11.91	
11.74/11.91	Reduction Pair Processor:
11.74/11.91	-> Pairs:
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	-> Rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	-> Usable rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	->Interpretation type:
11.74/11.91	 Linear
11.74/11.91	->Coefficients:
11.74/11.91	 Natural Numbers
11.74/11.91	->Dimension:
11.74/11.91	 1
11.74/11.91	->Bound:
11.74/11.91	 2
11.74/11.91	->Interpretation:
11.74/11.91	 
11.74/11.91	[0](X) = X
11.74/11.91	[2](X) = 2.X + 2
11.74/11.91	[4](X) = X
11.74/11.91	[5](X) = 2.X + 2
11.74/11.91	[1](X) = X
11.74/11.91	[3](X) = X
11.74/11.91	[0#](X) = 2.X + 2
11.74/11.91	[2#](X) = 2.X + 2
11.74/11.91	[4#](X) = X + 2
11.74/11.91	[5#](X) = 2.X + 2
11.74/11.91	
11.74/11.91	Problem 1: 
11.74/11.91	
11.74/11.91	SCC Processor:
11.74/11.91	-> Pairs:
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	-> Rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.74/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.74/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.74/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.74/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.74/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.74/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.74/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.74/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.74/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.74/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.74/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.74/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.74/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.74/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.74/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.74/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.74/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.74/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.74/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.74/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.74/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.74/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.74/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.74/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.74/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.74/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.74/11.91	->Strongly Connected Components:
11.74/11.91	->->Cycle:
11.74/11.91	->->-> Pairs:
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.74/11.91	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.74/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.74/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.74/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.74/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.74/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.74/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.74/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.74/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.74/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.74/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.74/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.74/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.74/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.74/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.74/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.74/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.74/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.74/11.91	->->-> Rules:
11.74/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.74/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.74/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.74/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.74/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.74/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	Reduction Pair Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	-> Usable rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Interpretation type:
11.81/11.91	 Linear
11.81/11.91	->Coefficients:
11.81/11.91	 Natural Numbers
11.81/11.91	->Dimension:
11.81/11.91	 1
11.81/11.91	->Bound:
11.81/11.91	 2
11.81/11.91	->Interpretation:
11.81/11.91	 
11.81/11.91	[0](X) = X
11.81/11.91	[2](X) = 2.X + 2
11.81/11.91	[4](X) = X
11.81/11.91	[5](X) = 2.X + 2
11.81/11.91	[1](X) = X
11.81/11.91	[3](X) = X
11.81/11.91	[0#](X) = 2.X
11.81/11.91	[2#](X) = X + 2
11.81/11.91	[4#](X) = X + 1
11.81/11.91	[5#](X) = X + 2
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	SCC Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Strongly Connected Components:
11.81/11.91	->->Cycle:
11.81/11.91	->->-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	->->-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	Reduction Pair Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(4(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	-> Usable rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Interpretation type:
11.81/11.91	 Linear
11.81/11.91	->Coefficients:
11.81/11.91	 Natural Numbers
11.81/11.91	->Dimension:
11.81/11.91	 1
11.81/11.91	->Bound:
11.81/11.91	 2
11.81/11.91	->Interpretation:
11.81/11.91	 
11.81/11.91	[0](X) = X
11.81/11.91	[2](X) = 2.X + 2
11.81/11.91	[4](X) = X
11.81/11.91	[5](X) = 2.X + 2
11.81/11.91	[1](X) = X
11.81/11.91	[3](X) = X
11.81/11.91	[0#](X) = 2.X
11.81/11.91	[2#](X) = 2.X + 1
11.81/11.91	[4#](X) = 2.X + 1
11.81/11.91	[5#](X) = 2.X + 1
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	SCC Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Strongly Connected Components:
11.81/11.91	->->Cycle:
11.81/11.91	->->-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	->->-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	Reduction Pair Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 0#(x1:S)
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	-> Usable rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Interpretation type:
11.81/11.91	 Linear
11.81/11.91	->Coefficients:
11.81/11.91	 Natural Numbers
11.81/11.91	->Dimension:
11.81/11.91	 1
11.81/11.91	->Bound:
11.81/11.91	 2
11.81/11.91	->Interpretation:
11.81/11.91	 
11.81/11.91	[0](X) = X
11.81/11.91	[2](X) = 2.X + 2
11.81/11.91	[4](X) = X
11.81/11.91	[5](X) = 2.X + 2
11.81/11.91	[1](X) = X
11.81/11.91	[3](X) = X
11.81/11.91	[0#](X) = 2.X + 2
11.81/11.91	[2#](X) = 2.X + 1
11.81/11.91	[4#](X) = X + 2
11.81/11.91	[5#](X) = 2.X + 1
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	SCC Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Strongly Connected Components:
11.81/11.91	->->Cycle:
11.81/11.91	->->-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	->->-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	Reduction Pair Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(4(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	-> Usable rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.91	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.91	->Interpretation type:
11.81/11.91	 Linear
11.81/11.91	->Coefficients:
11.81/11.91	 Natural Numbers
11.81/11.91	->Dimension:
11.81/11.91	 1
11.81/11.91	->Bound:
11.81/11.91	 2
11.81/11.91	->Interpretation:
11.81/11.91	 
11.81/11.91	[0](X) = X
11.81/11.91	[2](X) = 2.X + 2
11.81/11.91	[4](X) = X
11.81/11.91	[5](X) = 2.X + 2
11.81/11.91	[1](X) = X
11.81/11.91	[3](X) = X
11.81/11.91	[0#](X) = X + 1
11.81/11.91	[2#](X) = 2.X + 2
11.81/11.91	[4#](X) = 2.X + 2
11.81/11.91	[5#](X) = 2.X + 2
11.81/11.91	
11.81/11.91	Problem 1: 
11.81/11.91	
11.81/11.91	SCC Processor:
11.81/11.91	-> Pairs:
11.81/11.91	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.91	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.91	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.91	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.91	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.91	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.91	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.91	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.91	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.91	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.91	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.91	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.91	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.91	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.91	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.91	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.91	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.91	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.91	-> Rules:
11.81/11.91	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.91	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.91	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.91	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.91	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.91	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.91	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.91	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.91	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.91	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.91	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.91	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.91	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.91	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.91	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.91	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.91	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.91	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.91	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.91	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.91	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.91	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.91	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.91	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.91	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.91	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.91	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.91	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.91	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.91	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.91	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	Reduction Pair Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	-> Usable rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Interpretation type:
11.81/11.92	 Linear
11.81/11.92	->Coefficients:
11.81/11.92	 Natural Numbers
11.81/11.92	->Dimension:
11.81/11.92	 1
11.81/11.92	->Bound:
11.81/11.92	 2
11.81/11.92	->Interpretation:
11.81/11.92	 
11.81/11.92	[0](X) = X
11.81/11.92	[2](X) = 2.X + 2
11.81/11.92	[4](X) = X
11.81/11.92	[5](X) = 2.X + 2
11.81/11.92	[1](X) = X
11.81/11.92	[3](X) = X
11.81/11.92	[0#](X) = 2.X + 1
11.81/11.92	[2#](X) = 2.X + 2
11.81/11.92	[4#](X) = X + 2
11.81/11.92	[5#](X) = 2.X + 2
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	SCC Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	Reduction Pair Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(2(x1:S))) -> 4#(x1:S)
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	-> Usable rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Interpretation type:
11.81/11.92	 Linear
11.81/11.92	->Coefficients:
11.81/11.92	 Natural Numbers
11.81/11.92	->Dimension:
11.81/11.92	 1
11.81/11.92	->Bound:
11.81/11.92	 2
11.81/11.92	->Interpretation:
11.81/11.92	 
11.81/11.92	[0](X) = X
11.81/11.92	[2](X) = 2.X + 2
11.81/11.92	[4](X) = X
11.81/11.92	[5](X) = 2.X + 2
11.81/11.92	[1](X) = X
11.81/11.92	[3](X) = X
11.81/11.92	[0#](X) = 2.X + 1
11.81/11.92	[2#](X) = 2.X + 2
11.81/11.92	[4#](X) = X
11.81/11.92	[5#](X) = 2.X + 1
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	SCC Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	Reduction Pair Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(0(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	-> Usable rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Interpretation type:
11.81/11.92	 Linear
11.81/11.92	->Coefficients:
11.81/11.92	 Natural Numbers
11.81/11.92	->Dimension:
11.81/11.92	 1
11.81/11.92	->Bound:
11.81/11.92	 2
11.81/11.92	->Interpretation:
11.81/11.92	 
11.81/11.92	[0](X) = X
11.81/11.92	[2](X) = 2.X + 2
11.81/11.92	[4](X) = X
11.81/11.92	[5](X) = 2.X + 2
11.81/11.92	[1](X) = X
11.81/11.92	[3](X) = X
11.81/11.92	[0#](X) = 2.X + 2
11.81/11.92	[2#](X) = 2.X + 2
11.81/11.92	[4#](X) = 2.X + 2
11.81/11.92	[5#](X) = 2.X + 2
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	SCC Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	Reduction Pair Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 0#(x1:S)
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	-> Usable rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Interpretation type:
11.81/11.92	 Linear
11.81/11.92	->Coefficients:
11.81/11.92	 Natural Numbers
11.81/11.92	->Dimension:
11.81/11.92	 1
11.81/11.92	->Bound:
11.81/11.92	 2
11.81/11.92	->Interpretation:
11.81/11.92	 
11.81/11.92	[0](X) = X
11.81/11.92	[2](X) = 2.X + 2
11.81/11.92	[4](X) = X
11.81/11.92	[5](X) = 2.X + 2
11.81/11.92	[1](X) = X
11.81/11.92	[3](X) = X
11.81/11.92	[0#](X) = 2.X
11.81/11.92	[2#](X) = 2.X + 2
11.81/11.92	[4#](X) = 2.X + 1
11.81/11.92	[5#](X) = 2.X + 2
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	SCC Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	Reduction Pair Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(0(x1:S))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	-> Usable rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Interpretation type:
11.81/11.92	 Linear
11.81/11.92	->Coefficients:
11.81/11.92	 Natural Numbers
11.81/11.92	->Dimension:
11.81/11.92	 1
11.81/11.92	->Bound:
11.81/11.92	 2
11.81/11.92	->Interpretation:
11.81/11.92	 
11.81/11.92	[0](X) = X
11.81/11.92	[2](X) = 2.X + 2
11.81/11.92	[4](X) = X
11.81/11.92	[5](X) = 2.X + 2
11.81/11.92	[1](X) = X
11.81/11.92	[3](X) = X
11.81/11.92	[0#](X) = 2.X + 2
11.81/11.92	[2#](X) = 2.X + 2
11.81/11.92	[4#](X) = 2.X + 2
11.81/11.92	[5#](X) = 2.X + 2
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	SCC Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	Reduction Pair Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(4(2(x1:S)))) -> 4#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	-> Usable rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Interpretation type:
11.81/11.92	 Linear
11.81/11.92	->Coefficients:
11.81/11.92	 Natural Numbers
11.81/11.92	->Dimension:
11.81/11.92	 1
11.81/11.92	->Bound:
11.81/11.92	 2
11.81/11.92	->Interpretation:
11.81/11.92	 
11.81/11.92	[0](X) = X
11.81/11.92	[2](X) = 2.X + 2
11.81/11.92	[4](X) = X
11.81/11.92	[5](X) = 2.X + 2
11.81/11.92	[1](X) = X
11.81/11.92	[3](X) = X
11.81/11.92	[0#](X) = 2.X
11.81/11.92	[2#](X) = 2.X + 2
11.81/11.92	[4#](X) = X + 2
11.81/11.92	[5#](X) = 2.X + 2
11.81/11.92	
11.81/11.92	Problem 1: 
11.81/11.92	
11.81/11.92	SCC Processor:
11.81/11.92	-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.92	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.92	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.92	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.92	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.92	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.92	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.92	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.92	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.92	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.92	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.92	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.92	->Strongly Connected Components:
11.81/11.92	->->Cycle:
11.81/11.92	->->-> Pairs:
11.81/11.92	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.92	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.92	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.92	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.92	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.92	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.92	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.92	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.92	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.92	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.92	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.92	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.92	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.92	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.92	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.92	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.92	->->-> Rules:
11.81/11.92	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.92	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.92	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.92	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.92	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.92	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.92	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.92	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.92	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.92	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.92	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.92	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.92	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.92	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.92	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.92	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.92	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.92	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.92	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.92	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.92	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(2(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = X
11.81/11.93	[2](X) = X
11.81/11.93	[4](X) = X
11.81/11.93	[5](X) = 2.X + 2
11.81/11.93	[1](X) = X
11.81/11.93	[3](X) = X
11.81/11.93	[0#](X) = X + 2
11.81/11.93	[2#](X) = X + 2
11.81/11.93	[4#](X) = X + 2
11.81/11.93	[5#](X) = 2.X + 2
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(2(5(x1:S))))) -> 5#(1(2(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = X
11.81/11.93	[2](X) = 2.X + 2
11.81/11.93	[4](X) = X
11.81/11.93	[5](X) = 2.X + 2
11.81/11.93	[1](X) = X
11.81/11.93	[3](X) = X
11.81/11.93	[0#](X) = 2.X + 1
11.81/11.93	[2#](X) = 2.X + 2
11.81/11.93	[4#](X) = 2.X + 2
11.81/11.93	[5#](X) = 2.X + 2
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(4(2(x1:S))))) -> 2#(1(x1:S))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = X
11.81/11.93	[2](X) = 2.X + 2
11.81/11.93	[4](X) = X
11.81/11.93	[5](X) = 2.X + 2
11.81/11.93	[1](X) = X
11.81/11.93	[3](X) = X
11.81/11.93	[0#](X) = 2.X
11.81/11.93	[2#](X) = X + 2
11.81/11.93	[4#](X) = X + 1
11.81/11.93	[5#](X) = X + 1
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 0#(1(1(5(4(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = X
11.81/11.93	[2](X) = 2.X + 2
11.81/11.93	[4](X) = X
11.81/11.93	[5](X) = 2.X + 2
11.81/11.93	[1](X) = X
11.81/11.93	[3](X) = X
11.81/11.93	[0#](X) = 2.X + 1
11.81/11.93	[2#](X) = 2.X + 2
11.81/11.93	[4#](X) = 2.X + 1
11.81/11.93	[5#](X) = 2.X + 2
11.81/11.93	
11.81/11.93	Problem 1: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 4#(2(2(x1:S)))
11.81/11.93	 2#(5(0(3(5(x1:S))))) -> 0#(5(x1:S))
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 4#(4(2(x1:S)))
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 4#(2(0(1(2(x1:S))))) -> 0#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 0#(2(x1:S))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 4#(5(2(x1:S)))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	 5#(1(4(3(2(x1:S))))) -> 4#(2(x1:S))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	
11.81/11.93	The problem is decomposed in 2 subproblems.
11.81/11.93	
11.81/11.93	Problem 1.1: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 0#(1(2(3(5(x1:S))))) -> 0#(2(5(x1:S)))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = 2.X + 2
11.81/11.93	[2](X) = X
11.81/11.93	[4](X) = 0
11.81/11.93	[5](X) = 0
11.81/11.93	[1](X) = 1
11.81/11.93	[3](X) = X + 1
11.81/11.93	[0#](X) = 2.X
11.81/11.93	
11.81/11.93	Problem 1.1: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 Empty
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	 There is no strongly connected component
11.81/11.93	
11.81/11.93	The problem is finite.
11.81/11.93	
11.81/11.93	Problem 1.2: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(2(x1:S))
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = X
11.81/11.93	[2](X) = 2.X + 2
11.81/11.93	[4](X) = X
11.81/11.93	[5](X) = 2.X + 2
11.81/11.93	[1](X) = X
11.81/11.93	[3](X) = X
11.81/11.93	[2#](X) = 2.X + 2
11.81/11.93	[5#](X) = 2.X
11.81/11.93	
11.81/11.93	Problem 1.2: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	Problem 1.2: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 2#(2(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	-> Usable rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Interpretation type:
11.81/11.93	 Linear
11.81/11.93	->Coefficients:
11.81/11.93	 Natural Numbers
11.81/11.93	->Dimension:
11.81/11.93	 1
11.81/11.93	->Bound:
11.81/11.93	 2
11.81/11.93	->Interpretation:
11.81/11.93	 
11.81/11.93	[0](X) = X
11.81/11.93	[2](X) = 2.X + 2
11.81/11.93	[4](X) = X
11.81/11.93	[5](X) = 2.X + 2
11.81/11.93	[1](X) = X
11.81/11.93	[3](X) = X
11.81/11.93	[2#](X) = 2.X + 2
11.81/11.93	[5#](X) = 2.X + 2
11.81/11.93	
11.81/11.93	Problem 1.2: 
11.81/11.93	
11.81/11.93	SCC Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	->Strongly Connected Components:
11.81/11.93	->->Cycle:
11.81/11.93	->->-> Pairs:
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	->->-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.93	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.93	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.93	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.93	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.93	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.93	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.93	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.93	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.93	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.93	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.93	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.93	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.93	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.93	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.93	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.93	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.93	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.93	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.93	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.93	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.93	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.93	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.93	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.93	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.93	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.93	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.93	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.93	
11.81/11.93	Problem 1.2: 
11.81/11.93	
11.81/11.93	Reduction Pair Processor:
11.81/11.93	-> Pairs:
11.81/11.93	 2#(5(3(2(x1:S)))) -> 2#(2(x1:S))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.93	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.93	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.93	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.93	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.93	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.93	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.93	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.93	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.93	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.93	-> Rules:
11.81/11.93	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.93	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.93	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.93	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.93	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = 2.X + 2
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = X + 2
11.81/11.94	[5#](X) = X + 2
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.94	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.94	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 5#(1(x1:S))
11.81/11.94	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = X
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = 2.X + 1
11.81/11.94	[5#](X) = 2.X + 2
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(5(0(x1:S))))) -> 5#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = 2.X + 2
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = 2.X + 1
11.81/11.94	[5#](X) = 2.X
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = 2.X + 2
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = 2.X + 2
11.81/11.94	[5#](X) = X + 2
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(4(3(5(x1:S))))) -> 5#(4(4(2(x1:S))))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = 2
11.81/11.94	[2](X) = 2
11.81/11.94	[4](X) = 1
11.81/11.94	[5](X) = 2
11.81/11.94	[1](X) = 2
11.81/11.94	[3](X) = 0
11.81/11.94	[2#](X) = 2
11.81/11.94	[5#](X) = X
11.81/11.94	
11.81/11.94	Problem 1.2: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 2#(0(2(x1:S)))
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	 5#(1(4(2(2(x1:S))))) -> 2#(4(2(x1:S)))
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.94	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	
11.81/11.94	The problem is decomposed in 2 subproblems.
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(1(1(5(x1:S)))) -> 2#(1(x1:S))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = 2.X + 2
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = 2.X
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(5(5(x1:S)))) -> 2#(5(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = 2.X + 2
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = X
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(0(x1:S))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	-> Usable rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Interpretation type:
11.81/11.94	 Linear
11.81/11.94	->Coefficients:
11.81/11.94	 Natural Numbers
11.81/11.94	->Dimension:
11.81/11.94	 1
11.81/11.94	->Bound:
11.81/11.94	 2
11.81/11.94	->Interpretation:
11.81/11.94	 
11.81/11.94	[0](X) = X
11.81/11.94	[2](X) = 2.X + 2
11.81/11.94	[4](X) = X
11.81/11.94	[5](X) = 2.X + 2
11.81/11.94	[1](X) = X
11.81/11.94	[3](X) = X
11.81/11.94	[2#](X) = X
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	SCC Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	->Strongly Connected Components:
11.81/11.94	->->Cycle:
11.81/11.94	->->-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	->->-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.94	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.94	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.94	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.94	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.94	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.94	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.94	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.94	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.94	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.94	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.94	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.94	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.94	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.94	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.94	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.94	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.94	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.94	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.94	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.94	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.94	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.94	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.94	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.94	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.94	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.94	
11.81/11.94	Problem 1.2.1: 
11.81/11.94	
11.81/11.94	Reduction Pair Processor:
11.81/11.94	-> Pairs:
11.81/11.94	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.94	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.94	 2#(3(3(1(5(x1:S))))) -> 2#(x1:S)
11.81/11.94	-> Rules:
11.81/11.94	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.94	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.94	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.94	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.94	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.94	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.94	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	-> Usable rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Interpretation type:
11.81/11.95	 Linear
11.81/11.95	->Coefficients:
11.81/11.95	 Natural Numbers
11.81/11.95	->Dimension:
11.81/11.95	 1
11.81/11.95	->Bound:
11.81/11.95	 2
11.81/11.95	->Interpretation:
11.81/11.95	 
11.81/11.95	[0](X) = X
11.81/11.95	[2](X) = 2.X + 2
11.81/11.95	[4](X) = X
11.81/11.95	[5](X) = 2.X + 2
11.81/11.95	[1](X) = X
11.81/11.95	[3](X) = X
11.81/11.95	[2#](X) = 2.X
11.81/11.95	
11.81/11.95	Problem 1.2.1: 
11.81/11.95	
11.81/11.95	SCC Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.95	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Strongly Connected Components:
11.81/11.95	->->Cycle:
11.81/11.95	->->-> Pairs:
11.81/11.95	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.95	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.95	->->-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	
11.81/11.95	Problem 1.2.1: 
11.81/11.95	
11.81/11.95	Reduction Pair Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 2#(1(0(1(5(x1:S))))) -> 2#(5(1(x1:S)))
11.81/11.95	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	-> Usable rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Interpretation type:
11.81/11.95	 Linear
11.81/11.95	->Coefficients:
11.81/11.95	 Natural Numbers
11.81/11.95	->Dimension:
11.81/11.95	 1
11.81/11.95	->Bound:
11.81/11.95	 2
11.81/11.95	->Interpretation:
11.81/11.95	 
11.81/11.95	[0](X) = 2
11.81/11.95	[2](X) = X
11.81/11.95	[4](X) = 1
11.81/11.95	[5](X) = 1
11.81/11.95	[1](X) = 2
11.81/11.95	[3](X) = 2
11.81/11.95	[2#](X) = 2.X
11.81/11.95	
11.81/11.95	Problem 1.2.1: 
11.81/11.95	
11.81/11.95	SCC Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 2#(3(1(1(2(x1:S))))) -> 2#(1(2(0(x1:S))))
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Strongly Connected Components:
11.81/11.95	 There is no strongly connected component
11.81/11.95	
11.81/11.95	The problem is finite.
11.81/11.95	
11.81/11.95	Problem 1.2.2: 
11.81/11.95	
11.81/11.95	Reduction Pair Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 5#(0(1(2(2(x1:S))))) -> 5#(2(0(2(x1:S))))
11.81/11.95	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	-> Usable rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Interpretation type:
11.81/11.95	 Linear
11.81/11.95	->Coefficients:
11.81/11.95	 Natural Numbers
11.81/11.95	->Dimension:
11.81/11.95	 1
11.81/11.95	->Bound:
11.81/11.95	 2
11.81/11.95	->Interpretation:
11.81/11.95	 
11.81/11.95	[0](X) = 2.X + 2
11.81/11.95	[2](X) = 2
11.81/11.95	[4](X) = X
11.81/11.95	[5](X) = 2
11.81/11.95	[1](X) = 2
11.81/11.95	[3](X) = 1
11.81/11.95	[5#](X) = 2.X
11.81/11.95	
11.81/11.95	Problem 1.2.2: 
11.81/11.95	
11.81/11.95	SCC Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Strongly Connected Components:
11.81/11.95	->->Cycle:
11.81/11.95	->->-> Pairs:
11.81/11.95	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.95	->->-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	
11.81/11.95	Problem 1.2.2: 
11.81/11.95	
11.81/11.95	Subterm Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 5#(5(4(3(2(x1:S))))) -> 5#(2(x1:S))
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Projection:
11.81/11.95	 pi(5#) = 1
11.81/11.95	
11.81/11.95	Problem 1.2.2: 
11.81/11.95	
11.81/11.95	SCC Processor:
11.81/11.95	-> Pairs:
11.81/11.95	 Empty
11.81/11.95	-> Rules:
11.81/11.95	 0(0(1(2(x1:S)))) -> 0(2(1(0(3(x1:S)))))
11.81/11.95	 0(4(5(3(5(x1:S))))) -> 5(1(0(3(4(5(x1:S))))))
11.81/11.95	 0(1(0(1(2(x1:S))))) -> 0(2(1(1(3(0(x1:S))))))
11.81/11.95	 0(1(2(0(x1:S)))) -> 2(1(0(3(0(3(x1:S))))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 2(1(0(3(5(x1:S)))))
11.81/11.95	 0(1(2(5(x1:S)))) -> 5(1(0(3(2(x1:S)))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(2(5(1(0(3(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 0(1(3(4(5(2(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 5(1(3(0(2(0(x1:S))))))
11.81/11.95	 0(1(2(3(5(x1:S))))) -> 1(0(3(0(2(5(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(0(3(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(4(x1:S)))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(0(x1:S))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(4(x1:S))))))
11.81/11.95	 0(1(2(x1:S))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(2(1(3(0(x1:S))))))
11.81/11.95	 0(1(4(0(2(x1:S))))) -> 4(0(1(3(0(2(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 0(2(1(0(3(4(x1:S))))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(4(1(0(3(x1:S)))))
11.81/11.95	 0(1(4(2(x1:S)))) -> 2(1(3(4(0(x1:S)))))
11.81/11.95	 0(1(1(2(5(x1:S))))) -> 0(1(3(5(1(2(x1:S))))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(0(4(1(2(x1:S)))))
11.81/11.95	 0(1(1(2(x1:S)))) -> 1(2(1(0(3(x1:S)))))
11.81/11.95	 0(1(1(4(2(x1:S))))) -> 4(1(0(3(2(1(x1:S))))))
11.81/11.95	 0(1(1(5(0(x1:S))))) -> 0(1(0(5(4(1(x1:S))))))
11.81/11.95	 0(1(1(5(4(x1:S))))) -> 1(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(2(4(3(5(x1:S))))) -> 5(1(3(4(2(2(x1:S))))))
11.81/11.95	 2(2(3(5(0(x1:S))))) -> 5(2(4(2(0(3(x1:S))))))
11.81/11.95	 2(5(0(3(5(x1:S))))) -> 5(2(1(3(0(5(x1:S))))))
11.81/11.95	 2(5(3(2(x1:S)))) -> 5(1(3(2(2(x1:S)))))
11.81/11.95	 2(1(0(1(5(x1:S))))) -> 1(0(3(2(5(1(x1:S))))))
11.81/11.95	 2(1(2(0(x1:S)))) -> 2(2(1(0(3(x1:S)))))
11.81/11.95	 2(1(4(5(0(x1:S))))) -> 2(4(1(0(3(5(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 5(4(4(1(3(2(x1:S))))))
11.81/11.95	 2(1(4(3(5(x1:S))))) -> 1(3(5(4(4(2(x1:S))))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 2(5(1(4(1(x1:S)))))
11.81/11.95	 2(1(1(5(x1:S)))) -> 5(1(3(2(1(x1:S)))))
11.81/11.95	 2(3(2(0(5(x1:S))))) -> 2(2(1(0(3(5(x1:S))))))
11.81/11.95	 2(3(5(5(x1:S)))) -> 5(1(0(3(2(5(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 4(1(2(2(1(3(x1:S))))))
11.81/11.95	 2(3(1(1(2(x1:S))))) -> 1(3(2(1(2(0(x1:S))))))
11.81/11.95	 2(3(3(1(5(x1:S))))) -> 1(3(5(1(3(2(x1:S))))))
11.81/11.95	 4(2(0(1(2(x1:S))))) -> 4(2(2(1(3(0(x1:S))))))
11.81/11.95	 5(0(1(2(2(x1:S))))) -> 4(1(5(2(0(2(x1:S))))))
11.81/11.95	 5(5(4(3(2(x1:S))))) -> 5(1(3(4(5(2(x1:S))))))
11.81/11.95	 5(1(2(0(x1:S)))) -> 2(5(1(0(3(x1:S)))))
11.81/11.95	 5(1(4(2(2(x1:S))))) -> 5(1(3(2(4(2(x1:S))))))
11.81/11.95	 5(1(4(3(2(x1:S))))) -> 4(5(1(3(4(2(x1:S))))))
11.81/11.95	->Strongly Connected Components:
11.81/11.95	 There is no strongly connected component
11.81/11.95	
11.81/11.95	The problem is finite.
11.81/11.95	EOF