1.72/1.89	YES
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	(VAR v_NonEmpty:S x1:S)
1.72/1.89	(RULES
1.72/1.89	0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	)
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	Dependency Pairs Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(0(x1:S))) -> 3#(0(0(1(0(2(x1:S))))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 0#(1(2(0(x1:S))))
1.72/1.89	 0#(0(x1:S)) -> 0#(2(0(3(x1:S))))
1.72/1.89	 0#(0(x1:S)) -> 0#(2(0(x1:S)))
1.72/1.89	 0#(0(x1:S)) -> 0#(2(2(0(x1:S))))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 0#(2(5(3(0(x1:S)))))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(2(5(3(0(x1:S))))))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(2(0(3(x1:S))))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(0(2(0(3(x1:S)))))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 0#(3(3(0(4(5(x1:S))))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 0#(4(5(3(0(x1:S)))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 0#(4(5(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(4(5(3(0(x1:S))))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(4(5(x1:S))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(3(0(4(5(x1:S)))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 0#(3(1(0(1(5(x1:S))))))
1.72/1.89	 5#(1(0(0(x1:S)))) -> 0#(1(5(x1:S)))
1.72/1.89	 5#(1(0(0(x1:S)))) -> 3#(1(0(1(5(x1:S)))))
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 0#(2(3(3(5(x1:S)))))
1.72/1.89	 5#(2(0(x1:S))) -> 0#(2(3(5(x1:S))))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 0#(2(1(2(4(5(x1:S))))))
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(4(0(3(5(x1:S)))))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	SCC Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(0(x1:S))) -> 3#(0(0(1(0(2(x1:S))))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 0#(1(2(0(x1:S))))
1.72/1.89	 0#(0(x1:S)) -> 0#(2(0(3(x1:S))))
1.72/1.89	 0#(0(x1:S)) -> 0#(2(0(x1:S)))
1.72/1.89	 0#(0(x1:S)) -> 0#(2(2(0(x1:S))))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 0#(2(5(3(0(x1:S)))))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(2(5(3(0(x1:S))))))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(2(0(3(x1:S))))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(0(2(0(3(x1:S)))))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 0#(3(3(0(4(5(x1:S))))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 0#(4(5(3(0(x1:S)))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 0#(4(5(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(4(5(3(0(x1:S))))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(4(5(x1:S))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(3(0(4(5(x1:S)))))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 0#(3(1(0(1(5(x1:S))))))
1.72/1.89	 5#(1(0(0(x1:S)))) -> 0#(1(5(x1:S)))
1.72/1.89	 5#(1(0(0(x1:S)))) -> 3#(1(0(1(5(x1:S)))))
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 0#(2(3(3(5(x1:S)))))
1.72/1.89	 5#(2(0(x1:S))) -> 0#(2(3(5(x1:S))))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 0#(2(1(2(4(5(x1:S))))))
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(4(0(3(5(x1:S)))))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	->Strongly Connected Components:
1.72/1.89	->->Cycle:
1.72/1.89	->->-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(0(x1:S))) -> 3#(0(0(1(0(2(x1:S))))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	->->-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	Reduction Pair Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(0(x1:S))) -> 3#(0(0(1(0(2(x1:S))))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	-> Usable rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	->Interpretation type:
1.72/1.89	 Linear
1.72/1.89	->Coefficients:
1.72/1.89	 Natural Numbers
1.72/1.89	->Dimension:
1.72/1.89	 1
1.72/1.89	->Bound:
1.72/1.89	 2
1.72/1.89	->Interpretation:
1.72/1.89	 
1.72/1.89	[0](X) = 2.X + 1
1.72/1.89	[3](X) = X
1.72/1.89	[5](X) = X
1.72/1.89	[1](X) = X
1.72/1.89	[2](X) = X
1.72/1.89	[4](X) = X
1.72/1.89	[0#](X) = 2.X + 2
1.72/1.89	[3#](X) = X
1.72/1.89	[5#](X) = 2.X
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	SCC Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	->Strongly Connected Components:
1.72/1.89	->->Cycle:
1.72/1.89	->->-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	->->-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	Reduction Pair Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(x1:S)) -> 0#(3(x1:S))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	-> Usable rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	->Interpretation type:
1.72/1.89	 Linear
1.72/1.89	->Coefficients:
1.72/1.89	 Natural Numbers
1.72/1.89	->Dimension:
1.72/1.89	 1
1.72/1.89	->Bound:
1.72/1.89	 2
1.72/1.89	->Interpretation:
1.72/1.89	 
1.72/1.89	[0](X) = 2.X + 2
1.72/1.89	[3](X) = X
1.72/1.89	[5](X) = X
1.72/1.89	[1](X) = X
1.72/1.89	[2](X) = X
1.72/1.89	[4](X) = X
1.72/1.89	[0#](X) = 2.X + 2
1.72/1.89	[3#](X) = 2.X + 2
1.72/1.89	[5#](X) = 2.X + 2
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	SCC Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	->Strongly Connected Components:
1.72/1.89	->->Cycle:
1.72/1.89	->->-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.89	->->-> Rules:
1.72/1.89	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.89	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.89	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.89	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.89	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.89	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.89	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.89	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.89	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.89	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.89	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.89	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.89	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.89	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.89	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.89	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.89	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.89	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.89	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.89	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.89	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.89	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.89	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.89	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.89	
1.72/1.89	Problem 1: 
1.72/1.89	
1.72/1.89	Reduction Pair Processor:
1.72/1.89	-> Pairs:
1.72/1.89	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.89	 0#(0(x1:S)) -> 3#(x1:S)
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.89	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.89	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.89	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.89	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.89	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.89	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.89	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.89	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.89	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.89	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.89	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[0#](X) = 2.X + 2
1.72/1.90	[3#](X) = 2.X + 1
1.72/1.90	[5#](X) = 2.X + 1
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 0#(0(0(x1:S))) -> 0#(0(1(0(2(x1:S)))))
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 3#(0(x1:S))
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[0#](X) = 2.X + 2
1.72/1.90	[3#](X) = X + 2
1.72/1.90	[5#](X) = X + 2
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 0#(3(5(2(0(x1:S))))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[0#](X) = 2.X + 1
1.72/1.90	[3#](X) = X
1.72/1.90	[5#](X) = X + 2
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(0(0(x1:S))) -> 0#(3(x1:S))
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 0#(3(5(x1:S)))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(0(0(x1:S))) -> 3#(x1:S)
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[3#](X) = 2.X + 2
1.72/1.90	[5#](X) = 2.X + 2
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 3#(0(x1:S))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 1
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = 2
1.72/1.90	[1](X) = 1
1.72/1.90	[2](X) = 0
1.72/1.90	[4](X) = 2
1.72/1.90	[3#](X) = X
1.72/1.90	[5#](X) = 2
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(3(0(x1:S)))
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[3#](X) = 2.X + 1
1.72/1.90	[5#](X) = 2.X + 2
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 3#(4(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[3#](X) = 2.X + 2
1.72/1.90	[5#](X) = 2.X + 2
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 3#(5(x1:S))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 3#(3(5(x1:S)))
1.72/1.90	 5#(2(0(x1:S))) -> 3#(5(x1:S))
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 3#(5(x1:S))
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 3#(5(0(x1:S)))
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 5#(1(0(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = 2.X + 2
1.72/1.90	[3](X) = X
1.72/1.90	[5](X) = X
1.72/1.90	[1](X) = X
1.72/1.90	[2](X) = X
1.72/1.90	[4](X) = X
1.72/1.90	[5#](X) = 2.X
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	SCC Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Strongly Connected Components:
1.72/1.90	->->Cycle:
1.72/1.90	->->-> Pairs:
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	->->-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	
1.72/1.90	Problem 1: 
1.72/1.90	
1.72/1.90	Reduction Pair Processor:
1.72/1.90	-> Pairs:
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.90	 5#(1(5(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.90	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.90	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.90	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.90	-> Rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	-> Usable rules:
1.72/1.90	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.90	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.90	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.90	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.90	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.90	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.90	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.90	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.90	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.90	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.90	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.90	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.90	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.90	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.90	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.90	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.90	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.90	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.90	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.90	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.90	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.90	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.90	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.90	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.90	->Interpretation type:
1.72/1.90	 Linear
1.72/1.90	->Coefficients:
1.72/1.90	 Natural Numbers
1.72/1.90	->Dimension:
1.72/1.90	 1
1.72/1.90	->Bound:
1.72/1.90	 2
1.72/1.90	->Interpretation:
1.72/1.90	 
1.72/1.90	[0](X) = X + 2
1.72/1.90	[3](X) = X
1.72/1.91	[5](X) = X
1.72/1.91	[1](X) = X
1.72/1.91	[2](X) = X
1.72/1.91	[4](X) = X
1.72/1.91	[5#](X) = 2.X
1.72/1.91	
1.72/1.91	Problem 1: 
1.72/1.91	
1.72/1.91	SCC Processor:
1.72/1.91	-> Pairs:
1.72/1.91	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.91	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.91	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.91	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.91	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.91	-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	->Strongly Connected Components:
1.72/1.91	->->Cycle:
1.72/1.91	->->-> Pairs:
1.72/1.91	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.91	->->-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	->->Cycle:
1.72/1.91	->->-> Pairs:
1.72/1.91	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.91	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.91	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.91	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.91	->->-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	
1.72/1.91	
1.72/1.91	The problem is decomposed in 2 subproblems.
1.72/1.91	
1.72/1.91	Problem 1.1: 
1.72/1.91	
1.72/1.91	Reduction Pair Processor:
1.72/1.91	-> Pairs:
1.72/1.91	 5#(1(5(0(x1:S)))) -> 5#(1(0(3(5(x1:S)))))
1.72/1.91	-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	-> Usable rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	->Interpretation type:
1.72/1.91	 Linear
1.72/1.91	->Coefficients:
1.72/1.91	 Natural Numbers
1.72/1.91	->Dimension:
1.72/1.91	 1
1.72/1.91	->Bound:
1.72/1.91	 2
1.72/1.91	->Interpretation:
1.72/1.91	 
1.72/1.91	[0](X) = 0
1.72/1.91	[3](X) = 0
1.72/1.91	[5](X) = 2
1.72/1.91	[1](X) = 2.X
1.72/1.91	[2](X) = 0
1.72/1.91	[4](X) = 0
1.72/1.91	[5#](X) = 2.X
1.72/1.91	
1.72/1.91	Problem 1.1: 
1.72/1.91	
1.72/1.91	SCC Processor:
1.72/1.91	-> Pairs:
1.72/1.91	 Empty
1.72/1.91	-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	->Strongly Connected Components:
1.72/1.91	 There is no strongly connected component
1.72/1.91	
1.72/1.91	The problem is finite.
1.72/1.91	
1.72/1.91	Problem 1.2: 
1.72/1.91	
1.72/1.91	Subterm Processor:
1.72/1.91	-> Pairs:
1.72/1.91	 5#(2(0(x1:S))) -> 5#(x1:S)
1.72/1.91	 5#(2(2(0(x1:S)))) -> 5#(x1:S)
1.72/1.91	 5#(4(3(0(0(x1:S))))) -> 5#(x1:S)
1.72/1.91	 5#(4(2(0(x1:S)))) -> 5#(0(x1:S))
1.72/1.91	-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	->Projection:
1.72/1.91	 pi(5#) = 1
1.72/1.91	
1.72/1.91	Problem 1.2: 
1.72/1.91	
1.72/1.91	SCC Processor:
1.72/1.91	-> Pairs:
1.72/1.91	 Empty
1.72/1.91	-> Rules:
1.72/1.91	 0(0(0(x1:S))) -> 0(1(0(4(0(4(x1:S))))))
1.72/1.91	 0(0(0(x1:S))) -> 3(0(0(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(1(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 0(1(0(2(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 3(0(4(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 3(1(0(1(0(4(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(1(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(0(2(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(3(0(1(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(0(1(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(3(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(0(x1:S))))
1.72/1.91	 0(0(x1:S)) -> 1(0(2(2(0(x1:S)))))
1.72/1.91	 0(0(x1:S)) -> 1(0(4(1(0(2(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 1(1(1(0(2(0(x1:S))))))
1.72/1.91	 0(0(x1:S)) -> 2(1(0(2(0(x1:S)))))
1.72/1.91	 0(3(5(2(0(x1:S))))) -> 3(0(2(5(3(0(x1:S))))))
1.72/1.91	 0(5(2(0(x1:S)))) -> 0(5(0(2(2(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(0(3(x1:S)))))
1.72/1.91	 3(0(0(x1:S))) -> 3(0(2(4(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 3(5(2(3(0(2(x1:S))))))
1.72/1.91	 3(3(5(2(0(x1:S))))) -> 4(3(3(5(0(2(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 0(3(3(0(4(5(x1:S))))))
1.72/1.91	 3(4(0(0(x1:S)))) -> 3(0(4(5(3(0(x1:S))))))
1.72/1.91	 5(0(5(2(0(x1:S))))) -> 0(3(5(5(0(2(x1:S))))))
1.72/1.91	 5(3(3(2(0(x1:S))))) -> 5(2(3(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 3(3(5(3(0(2(x1:S))))))
1.72/1.91	 5(3(2(0(x1:S)))) -> 5(3(0(1(2(x1:S)))))
1.72/1.91	 5(1(0(0(x1:S)))) -> 0(3(1(0(1(5(x1:S))))))
1.72/1.91	 5(1(5(0(x1:S)))) -> 5(1(0(3(5(x1:S)))))
1.72/1.91	 5(1(4(0(0(x1:S))))) -> 0(2(5(0(1(4(x1:S))))))
1.72/1.91	 5(1(4(0(x1:S)))) -> 0(1(5(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(3(5(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 0(2(3(5(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 3(5(0(2(x1:S))))
1.72/1.91	 5(2(0(x1:S))) -> 5(0(1(2(2(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(3(5(1(0(2(x1:S))))))
1.72/1.91	 5(2(0(x1:S))) -> 5(1(0(2(4(x1:S)))))
1.72/1.91	 5(2(0(x1:S))) -> 1(0(2(3(5(x1:S)))))
1.72/1.91	 5(2(2(0(x1:S)))) -> 0(2(1(2(4(5(x1:S))))))
1.72/1.91	 5(4(0(0(x1:S)))) -> 0(4(5(5(0(2(x1:S))))))
1.72/1.91	 5(4(3(0(0(x1:S))))) -> 1(0(4(0(3(5(x1:S))))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(0(2(2(4(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 5(4(5(0(2(x1:S)))))
1.72/1.91	 5(4(2(0(x1:S)))) -> 2(4(3(5(0(x1:S)))))
1.72/1.91	->Strongly Connected Components:
1.72/1.91	 There is no strongly connected component
1.72/1.91	
1.72/1.91	The problem is finite.
1.72/1.91	EOF