3.80/3.87	YES
3.80/3.87	
3.80/3.87	Problem 1: 
3.80/3.87	
3.80/3.87	(VAR v_NonEmpty:S x1:S)
3.80/3.87	(RULES
3.80/3.87	1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	)
3.80/3.87	
3.80/3.87	Problem 1: 
3.80/3.87	
3.80/3.87	Dependency Pairs Processor:
3.80/3.87	-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 1#(2(2(1(0(1(x1:S))))))
3.80/3.87	 1#(2(5(x1:S))) -> 1#(0(1(x1:S)))
3.80/3.87	 1#(2(5(x1:S))) -> 1#(0(5(0(5(4(x1:S))))))
3.80/3.87	 1#(2(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 2#(1(0(1(x1:S))))
3.80/3.87	 1#(2(5(x1:S))) -> 2#(2(1(0(1(x1:S)))))
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(2(5(x1:S))) -> 5#(0(5(4(x1:S))))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(2(4(0(2(1(x1:S))))))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 2#(4(0(2(1(x1:S)))))
3.80/3.87	 1#(4(5(x1:S))) -> 4#(0(2(1(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 4#(0(2(2(3(3(x1:S))))))
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 2#(0(4(1(3(3(x1:S))))))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(0(1(x1:S)))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(4(x1:S))) -> 2#(0(5(1(0(1(x1:S))))))
3.80/3.87	 2#(5(4(x1:S))) -> 5#(1(0(1(x1:S))))
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 2#(2(0(5(0(1(x1:S))))))
3.80/3.87	 2#(5(x1:S)) -> 2#(0(5(0(1(x1:S)))))
3.80/3.87	 2#(5(x1:S)) -> 5#(0(1(x1:S)))
3.80/3.87	 3#(2(5(x1:S))) -> 1#(0(5(x1:S)))
3.80/3.87	 3#(2(5(x1:S))) -> 2#(0(1(0(5(x1:S)))))
3.80/3.87	 3#(2(5(x1:S))) -> 3#(2(0(1(0(5(x1:S))))))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(4(2(x1:S))) -> 3#(4(0(2(2(2(x1:S))))))
3.80/3.87	 3#(4(2(x1:S))) -> 4#(0(2(2(2(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 1#(4(1(0(1(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 1#(0(1(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(1(4(1(0(1(x1:S))))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(0(0(5(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(1(0(1(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(0(0(5(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(3(4(0(4(2(x1:S))))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 3#(4(0(4(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(3(x1:S))) -> 4#(0(4(2(x1:S))))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(4(x1:S))) -> 5#(0(0(1(2(x1:S)))))
3.80/3.87	 3#(5(5(x1:S))) -> 1#(0(5(x1:S)))
3.80/3.87	 3#(5(5(x1:S))) -> 4#(1(0(5(x1:S))))
3.80/3.87	 3#(5(5(x1:S))) -> 5#(4(1(0(5(x1:S)))))
3.80/3.87	 3#(5(x1:S)) -> 1#(3(2(0(0(1(x1:S))))))
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 2#(0(0(1(x1:S))))
3.80/3.87	 3#(5(x1:S)) -> 3#(2(0(0(1(x1:S)))))
3.80/3.87	 4#(5(1(x1:S))) -> 1#(0(5(3(3(x1:S)))))
3.80/3.87	 4#(5(1(x1:S))) -> 2#(1(0(5(3(3(x1:S))))))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 1#(0(0(4(x1:S))))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(2(x1:S))) -> 5#(1(0(0(4(x1:S)))))
3.80/3.87	 4#(5(4(x1:S))) -> 1#(0(4(2(x1:S))))
3.80/3.87	 4#(5(4(x1:S))) -> 2#(1(0(4(2(x1:S)))))
3.80/3.87	 4#(5(4(x1:S))) -> 2#(2(1(0(4(2(x1:S))))))
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(0(1(2(2(x1:S)))))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(3(x1:S))) -> 5#(1(0(1(2(2(x1:S))))))
3.80/3.87	 5#(5(4(x1:S))) -> 1#(0(4(2(2(x1:S)))))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	 5#(5(4(x1:S))) -> 5#(1(0(4(2(2(x1:S))))))
3.80/3.87	-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	
3.80/3.87	Problem 1: 
3.80/3.87	
3.80/3.87	SCC Processor:
3.80/3.87	-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 1#(2(2(1(0(1(x1:S))))))
3.80/3.87	 1#(2(5(x1:S))) -> 1#(0(1(x1:S)))
3.80/3.87	 1#(2(5(x1:S))) -> 1#(0(5(0(5(4(x1:S))))))
3.80/3.87	 1#(2(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 2#(1(0(1(x1:S))))
3.80/3.87	 1#(2(5(x1:S))) -> 2#(2(1(0(1(x1:S)))))
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(2(5(x1:S))) -> 5#(0(5(4(x1:S))))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(2(4(0(2(1(x1:S))))))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 2#(4(0(2(1(x1:S)))))
3.80/3.87	 1#(4(5(x1:S))) -> 4#(0(2(1(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 4#(0(2(2(3(3(x1:S))))))
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 2#(0(4(1(3(3(x1:S))))))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(0(1(x1:S)))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(4(x1:S))) -> 2#(0(5(1(0(1(x1:S))))))
3.80/3.87	 2#(5(4(x1:S))) -> 5#(1(0(1(x1:S))))
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 2#(2(0(5(0(1(x1:S))))))
3.80/3.87	 2#(5(x1:S)) -> 2#(0(5(0(1(x1:S)))))
3.80/3.87	 2#(5(x1:S)) -> 5#(0(1(x1:S)))
3.80/3.87	 3#(2(5(x1:S))) -> 1#(0(5(x1:S)))
3.80/3.87	 3#(2(5(x1:S))) -> 2#(0(1(0(5(x1:S)))))
3.80/3.87	 3#(2(5(x1:S))) -> 3#(2(0(1(0(5(x1:S))))))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(4(2(x1:S))) -> 3#(4(0(2(2(2(x1:S))))))
3.80/3.87	 3#(4(2(x1:S))) -> 4#(0(2(2(2(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 1#(4(1(0(1(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 1#(0(1(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(1(4(1(0(1(x1:S))))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(0(0(5(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(1(0(1(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(0(0(5(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(3(4(0(4(2(x1:S))))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 3#(4(0(4(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(3(x1:S))) -> 4#(0(4(2(x1:S))))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(4(x1:S))) -> 5#(0(0(1(2(x1:S)))))
3.80/3.87	 3#(5(5(x1:S))) -> 1#(0(5(x1:S)))
3.80/3.87	 3#(5(5(x1:S))) -> 4#(1(0(5(x1:S))))
3.80/3.87	 3#(5(5(x1:S))) -> 5#(4(1(0(5(x1:S)))))
3.80/3.87	 3#(5(x1:S)) -> 1#(3(2(0(0(1(x1:S))))))
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 2#(0(0(1(x1:S))))
3.80/3.87	 3#(5(x1:S)) -> 3#(2(0(0(1(x1:S)))))
3.80/3.87	 4#(5(1(x1:S))) -> 1#(0(5(3(3(x1:S)))))
3.80/3.87	 4#(5(1(x1:S))) -> 2#(1(0(5(3(3(x1:S))))))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 1#(0(0(4(x1:S))))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(2(x1:S))) -> 5#(1(0(0(4(x1:S)))))
3.80/3.87	 4#(5(4(x1:S))) -> 1#(0(4(2(x1:S))))
3.80/3.87	 4#(5(4(x1:S))) -> 2#(1(0(4(2(x1:S)))))
3.80/3.87	 4#(5(4(x1:S))) -> 2#(2(1(0(4(2(x1:S))))))
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(0(1(2(2(x1:S)))))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(3(x1:S))) -> 5#(1(0(1(2(2(x1:S))))))
3.80/3.87	 5#(5(4(x1:S))) -> 1#(0(4(2(2(x1:S)))))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	 5#(5(4(x1:S))) -> 5#(1(0(4(2(2(x1:S))))))
3.80/3.87	-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	->Strongly Connected Components:
3.80/3.87	->->Cycle:
3.80/3.87	->->-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	->->-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	
3.80/3.87	Problem 1: 
3.80/3.87	
3.80/3.87	Reduction Pair Processor:
3.80/3.87	-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	-> Usable rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	->Interpretation type:
3.80/3.87	 Linear
3.80/3.87	->Coefficients:
3.80/3.87	 Natural Numbers
3.80/3.87	->Dimension:
3.80/3.87	 1
3.80/3.87	->Bound:
3.80/3.87	 2
3.80/3.87	->Interpretation:
3.80/3.87	 
3.80/3.87	[1](X) = X + 1
3.80/3.87	[2](X) = X
3.80/3.87	[3](X) = X
3.80/3.87	[4](X) = 2.X + 1
3.80/3.87	[5](X) = 2.X + 2
3.80/3.87	[0](X) = 0
3.80/3.87	[1#](X) = X
3.80/3.87	[2#](X) = 2.X
3.80/3.87	[3#](X) = 2.X
3.80/3.87	[4#](X) = 2.X + 1
3.80/3.87	[5#](X) = X + 1
3.80/3.87	
3.80/3.87	Problem 1: 
3.80/3.87	
3.80/3.87	SCC Processor:
3.80/3.87	-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	->Strongly Connected Components:
3.80/3.87	->->Cycle:
3.80/3.87	->->-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	->->-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	
3.80/3.87	Problem 1: 
3.80/3.87	
3.80/3.87	Reduction Pair Processor:
3.80/3.87	-> Pairs:
3.80/3.87	 1#(2(5(x1:S))) -> 4#(x1:S)
3.80/3.87	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.87	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.87	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.87	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.87	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.87	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.87	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.87	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.87	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.87	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.87	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.87	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.87	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.87	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.87	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.87	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.87	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.87	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.87	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.87	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.87	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.87	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.87	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.87	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.87	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.87	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.87	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.87	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.87	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.87	-> Rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.87	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.87	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.87	-> Usable rules:
3.80/3.87	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.87	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.87	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.87	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.87	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.87	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.87	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.87	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.87	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.87	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.87	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.87	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.87	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.87	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.87	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.87	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.87	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.87	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.87	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X + 1
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X
3.80/3.88	[4](X) = X + 2
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[1#](X) = 2.X + 2
3.80/3.88	[2#](X) = X + 2
3.80/3.88	[3#](X) = 2.X + 2
3.80/3.88	[4#](X) = 2.X + 2
3.80/3.88	[5#](X) = 2.X + 1
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.88	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.88	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 1#(2(5(x1:S))) -> 5#(4(x1:S))
3.80/3.88	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	-> Usable rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X + 1
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X
3.80/3.88	[4](X) = 2.X
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[1#](X) = X + 1
3.80/3.88	[2#](X) = 2.X + 2
3.80/3.88	[3#](X) = 2.X + 2
3.80/3.88	[4#](X) = 2.X + 2
3.80/3.88	[5#](X) = X + 2
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 1#(4(5(x1:S))) -> 1#(x1:S)
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	-> Usable rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X + 1
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X
3.80/3.88	[4](X) = 2.X + 1
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[1#](X) = 2.X + 1
3.80/3.88	[2#](X) = 2.X + 2
3.80/3.88	[3#](X) = 2.X + 2
3.80/3.88	[4#](X) = 2.X + 2
3.80/3.88	[5#](X) = 2.X + 2
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 1#(4(5(x1:S))) -> 2#(1(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	-> Usable rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X + 1
3.80/3.88	[4](X) = X
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[1#](X) = 2.X + 2
3.80/3.88	[2#](X) = 2.X
3.80/3.88	[3#](X) = 2.X
3.80/3.88	[4#](X) = 2.X
3.80/3.88	[5#](X) = 2.X
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 1#(2(3(x1:S)))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 1#(3(3(x1:S)))
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 2#(5(4(x1:S))) -> 1#(x1:S)
3.80/3.88	 2#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 1#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 1#(3(2(1(x1:S))))
3.80/3.88	 4#(5(x1:S)) -> 1#(x1:S)
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 1#(2(2(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(1(2(3(x1:S))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	-> Usable rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X
3.80/3.88	[4](X) = 2.X + 2
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[2#](X) = 2.X + 2
3.80/3.88	[3#](X) = 2.X + 2
3.80/3.88	[4#](X) = 2.X
3.80/3.88	[5#](X) = X + 2
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(1(2(3(x1:S)))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	-> Usable rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X + 1
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X
3.80/3.88	[4](X) = X + 2
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[2#](X) = 2.X + 2
3.80/3.88	[3#](X) = 2.X
3.80/3.88	[4#](X) = 2.X + 2
3.80/3.88	[5#](X) = 2.X + 2
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(2(2(1(2(3(x1:S))))))
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	-> Usable rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Interpretation type:
3.80/3.88	 Linear
3.80/3.88	->Coefficients:
3.80/3.88	 Natural Numbers
3.80/3.88	->Dimension:
3.80/3.88	 1
3.80/3.88	->Bound:
3.80/3.88	 2
3.80/3.88	->Interpretation:
3.80/3.88	 
3.80/3.88	[1](X) = X + 1
3.80/3.88	[2](X) = X
3.80/3.88	[3](X) = X
3.80/3.88	[4](X) = X + 2
3.80/3.88	[5](X) = 2.X + 2
3.80/3.88	[0](X) = 0
3.80/3.88	[2#](X) = X + 2
3.80/3.88	[3#](X) = 2.X
3.80/3.88	[4#](X) = 2.X + 2
3.80/3.88	[5#](X) = 2.X + 2
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	SCC Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	->Strongly Connected Components:
3.80/3.88	->->Cycle:
3.80/3.88	->->-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.88	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.88	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.88	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.88	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.88	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.88	->->-> Rules:
3.80/3.88	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.88	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.88	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.88	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.88	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.88	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.88	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.88	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.88	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.88	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.88	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.88	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.88	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.88	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.88	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.88	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.88	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.88	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.88	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.88	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.88	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.88	
3.80/3.88	Problem 1: 
3.80/3.88	
3.80/3.88	Reduction Pair Processor:
3.80/3.88	-> Pairs:
3.80/3.88	 2#(5(1(x1:S))) -> 2#(3(x1:S))
3.80/3.88	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.88	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.88	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.88	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.88	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.88	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.88	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.88	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.88	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.88	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.88	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.88	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.88	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = X + 2
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X + 1
3.80/3.89	[3#](X) = 2.X + 2
3.80/3.89	[4#](X) = 2.X + 2
3.80/3.89	[5#](X) = X
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = 2.X + 1
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X
3.80/3.89	[3#](X) = 2.X + 1
3.80/3.89	[4#](X) = 2.X
3.80/3.89	[5#](X) = 2.X + 2
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 2#(2(3(3(x1:S))))
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = 2.X + 2
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X
3.80/3.89	[3#](X) = 2.X
3.80/3.89	[4#](X) = 2.X
3.80/3.89	[5#](X) = 2.X + 2
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 2#(3(3(x1:S)))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = 2.X + 1
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = X
3.80/3.89	[3#](X) = 2.X + 2
3.80/3.89	[4#](X) = 2.X
3.80/3.89	[5#](X) = 2.X + 2
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = 2.X + 1
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X + 2
3.80/3.89	[3#](X) = 2.X + 2
3.80/3.89	[4#](X) = 2.X + 2
3.80/3.89	[5#](X) = 2.X + 2
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(2(x1:S))) -> 3#(x1:S)
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = X + 2
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X + 2
3.80/3.89	[3#](X) = 2.X
3.80/3.89	[4#](X) = 2.X + 2
3.80/3.89	[5#](X) = 2.X
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(3(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = 2.X + 1
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X
3.80/3.89	[3#](X) = 2.X
3.80/3.89	[4#](X) = 2.X + 2
3.80/3.89	[5#](X) = 2.X + 2
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Strongly Connected Components:
3.80/3.89	->->Cycle:
3.80/3.89	->->-> Pairs:
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	->->-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	Reduction Pair Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 2#(5(3(x1:S))) -> 4#(1(3(3(x1:S))))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.89	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.89	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.89	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.89	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.89	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.89	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.89	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.89	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.89	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.89	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.89	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.89	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.89	-> Rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	-> Usable rules:
3.80/3.89	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.89	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.89	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.89	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.89	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.89	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.89	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.89	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.89	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.89	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.89	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.89	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.89	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.89	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.89	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.89	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.89	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.89	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.89	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.89	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.89	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.89	->Interpretation type:
3.80/3.89	 Linear
3.80/3.89	->Coefficients:
3.80/3.89	 Natural Numbers
3.80/3.89	->Dimension:
3.80/3.89	 1
3.80/3.89	->Bound:
3.80/3.89	 2
3.80/3.89	->Interpretation:
3.80/3.89	 
3.80/3.89	[1](X) = X + 1
3.80/3.89	[2](X) = X
3.80/3.89	[3](X) = X
3.80/3.89	[4](X) = X + 2
3.80/3.89	[5](X) = 2.X + 2
3.80/3.89	[0](X) = 0
3.80/3.89	[2#](X) = 2.X + 2
3.80/3.89	[3#](X) = 2.X + 2
3.80/3.89	[4#](X) = 2.X + 2
3.80/3.89	[5#](X) = 2.X
3.80/3.89	
3.80/3.89	Problem 1: 
3.80/3.89	
3.80/3.89	SCC Processor:
3.80/3.89	-> Pairs:
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.89	 3#(4(2(x1:S))) -> 2#(2(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(2(3(4(x1:S))))
3.80/3.89	 3#(5(1(x1:S))) -> 2#(3(4(x1:S)))
3.80/3.89	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.89	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 2#(1(2(x1:S)))
3.80/3.90	 3#(5(2(x1:S))) -> 2#(2(2(x1:S)))
3.80/3.90	 3#(5(2(x1:S))) -> 2#(2(x1:S))
3.80/3.90	 3#(5(2(x1:S))) -> 2#(3(3(2(1(2(x1:S))))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 3#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 2#(1(3(2(1(x1:S)))))
3.80/3.90	 4#(5(x1:S)) -> 2#(1(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 2#(2(1(3(2(1(x1:S))))))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(3(x1:S))) -> 2#(2(x1:S))
3.80/3.90	 5#(5(3(x1:S))) -> 2#(x1:S)
3.80/3.90	 5#(5(4(x1:S))) -> 2#(2(x1:S))
3.80/3.90	 5#(5(4(x1:S))) -> 2#(x1:S)
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 3#(4(x1:S))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X + 1
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2.X
3.80/3.90	[4](X) = X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 2
3.80/3.90	[4#](X) = 2.X + 1
3.80/3.90	[5#](X) = X + 1
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 4#(2(2(3(4(x1:S)))))
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X + 1
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2.X
3.80/3.90	[4](X) = X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 2
3.80/3.90	[4#](X) = 2.X
3.80/3.90	[5#](X) = X
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 4#(x1:S)
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = 2.X
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = X
3.80/3.90	[4](X) = 2.X
3.80/3.90	[5](X) = 2.X + 1
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = X + 2
3.80/3.90	[4#](X) = X + 2
3.80/3.90	[5#](X) = X + 2
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(1(x1:S))) -> 5#(x1:S)
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = X + 1
3.80/3.90	[4](X) = 2.X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 1
3.80/3.90	[4#](X) = X + 2
3.80/3.90	[5#](X) = 2.X
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(1(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X + 1
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2.X
3.80/3.90	[4](X) = X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 1
3.80/3.90	[4#](X) = 2.X + 2
3.80/3.90	[5#](X) = X + 2
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(2(2(2(x1:S))))
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X + 1
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2.X
3.80/3.90	[4](X) = 2.X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 2
3.80/3.90	[4#](X) = 2.X + 1
3.80/3.90	[5#](X) = X
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 3#(3(2(1(2(x1:S)))))
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2.X
3.80/3.90	[4](X) = 2.X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 1
3.80/3.90	[4#](X) = 2.X + 1
3.80/3.90	[5#](X) = X + 2
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(2(x1:S))) -> 4#(3(2(2(2(x1:S)))))
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = 2.X
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = X
3.80/3.90	[4](X) = 2.X + 1
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = 2.X + 2
3.80/3.90	[4#](X) = 2.X + 1
3.80/3.90	[5#](X) = 2.X + 2
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 3#(5(3(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X + 1
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2.X
3.80/3.90	[4](X) = 2.X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[3#](X) = X + 2
3.80/3.90	[4#](X) = 2.X
3.80/3.90	[5#](X) = X
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 4#(5(1(x1:S))) -> 3#(3(x1:S))
3.80/3.90	 4#(5(1(x1:S))) -> 3#(x1:S)
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 4#(5(x1:S)) -> 3#(2(1(x1:S)))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	Reduction Pair Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 4#(5(1(x1:S))) -> 5#(3(3(x1:S)))
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	-> Usable rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Interpretation type:
3.80/3.90	 Linear
3.80/3.90	->Coefficients:
3.80/3.90	 Natural Numbers
3.80/3.90	->Dimension:
3.80/3.90	 1
3.80/3.90	->Bound:
3.80/3.90	 2
3.80/3.90	->Interpretation:
3.80/3.90	 
3.80/3.90	[1](X) = X
3.80/3.90	[2](X) = X
3.80/3.90	[3](X) = 2
3.80/3.90	[4](X) = 2.X + 2
3.80/3.90	[5](X) = 2.X + 2
3.80/3.90	[0](X) = 0
3.80/3.90	[4#](X) = 2.X + 1
3.80/3.90	[5#](X) = X + 2
3.80/3.90	
3.80/3.90	Problem 1: 
3.80/3.90	
3.80/3.90	SCC Processor:
3.80/3.90	-> Pairs:
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	 5#(5(4(x1:S))) -> 4#(2(2(x1:S)))
3.80/3.90	-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.90	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.90	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.90	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.90	->Strongly Connected Components:
3.80/3.90	->->Cycle:
3.80/3.90	->->-> Pairs:
3.80/3.90	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.90	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.90	->->-> Rules:
3.80/3.90	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.90	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.90	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.90	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.90	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.90	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.90	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.90	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.90	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.90	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.90	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.90	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.90	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.90	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.90	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.90	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.90	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.90	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	
3.80/3.91	Problem 1: 
3.80/3.91	
3.80/3.91	Reduction Pair Processor:
3.80/3.91	-> Pairs:
3.80/3.91	 4#(5(2(x1:S))) -> 4#(x1:S)
3.80/3.91	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.91	-> Rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	-> Usable rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	->Interpretation type:
3.80/3.91	 Linear
3.80/3.91	->Coefficients:
3.80/3.91	 Natural Numbers
3.80/3.91	->Dimension:
3.80/3.91	 1
3.80/3.91	->Bound:
3.80/3.91	 2
3.80/3.91	->Interpretation:
3.80/3.91	 
3.80/3.91	[1](X) = 1
3.80/3.91	[2](X) = X + 1
3.80/3.91	[3](X) = X
3.80/3.91	[4](X) = 2.X + 1
3.80/3.91	[5](X) = X + 2
3.80/3.91	[0](X) = 0
3.80/3.91	[4#](X) = X
3.80/3.91	
3.80/3.91	Problem 1: 
3.80/3.91	
3.80/3.91	SCC Processor:
3.80/3.91	-> Pairs:
3.80/3.91	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.91	-> Rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	->Strongly Connected Components:
3.80/3.91	->->Cycle:
3.80/3.91	->->-> Pairs:
3.80/3.91	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.91	->->-> Rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	
3.80/3.91	Problem 1: 
3.80/3.91	
3.80/3.91	Reduction Pair Processor:
3.80/3.91	-> Pairs:
3.80/3.91	 4#(5(4(x1:S))) -> 4#(2(x1:S))
3.80/3.91	-> Rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	-> Usable rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	->Interpretation type:
3.80/3.91	 Linear
3.80/3.91	->Coefficients:
3.80/3.91	 Natural Numbers
3.80/3.91	->Dimension:
3.80/3.91	 1
3.80/3.91	->Bound:
3.80/3.91	 2
3.80/3.91	->Interpretation:
3.80/3.91	 
3.80/3.91	[1](X) = 2
3.80/3.91	[2](X) = 2
3.80/3.91	[3](X) = 2
3.80/3.91	[4](X) = 2
3.80/3.91	[5](X) = 2.X
3.80/3.91	[0](X) = 2
3.80/3.91	[4#](X) = X
3.80/3.91	
3.80/3.91	Problem 1: 
3.80/3.91	
3.80/3.91	SCC Processor:
3.80/3.91	-> Pairs:
3.80/3.91	 Empty
3.80/3.91	-> Rules:
3.80/3.91	 1(2(5(x1:S))) -> 1(2(2(1(0(1(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 1(0(5(0(5(4(x1:S))))))
3.80/3.91	 1(2(5(x1:S))) -> 2(0(1(3(1(0(x1:S))))))
3.80/3.91	 1(4(5(x1:S))) -> 1(2(4(0(2(1(x1:S))))))
3.80/3.91	 2(5(1(x1:S))) -> 2(2(2(1(2(3(x1:S))))))
3.80/3.91	 2(5(2(x1:S))) -> 4(0(2(2(3(3(x1:S))))))
3.80/3.91	 2(5(3(x1:S))) -> 2(0(4(1(3(3(x1:S))))))
3.80/3.91	 2(5(4(x1:S))) -> 2(0(5(1(0(1(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 1(3(3(0(1(0(x1:S))))))
3.80/3.91	 2(5(x1:S)) -> 2(2(0(5(0(1(x1:S))))))
3.80/3.91	 3(2(5(x1:S))) -> 3(2(0(1(0(5(x1:S))))))
3.80/3.91	 3(4(2(x1:S))) -> 3(4(0(2(2(2(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 2(1(4(1(0(1(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(2(3(4(x1:S))))))
3.80/3.91	 3(5(1(x1:S))) -> 0(4(2(0(0(5(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(3(3(2(1(2(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 2(0(2(2(3(0(x1:S))))))
3.80/3.91	 3(5(2(x1:S))) -> 0(4(3(2(2(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 2(3(4(0(4(2(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(2(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(3(x1:S))) -> 0(5(4(3(3(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(2(0(5(0(0(x1:S))))))
3.80/3.91	 3(5(4(x1:S))) -> 0(5(0(0(1(2(x1:S))))))
3.80/3.91	 3(5(5(x1:S))) -> 0(5(4(1(0(5(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 1(3(2(0(0(1(x1:S))))))
3.80/3.91	 3(5(x1:S)) -> 3(2(0(5(3(0(x1:S))))))
3.80/3.91	 4(5(1(x1:S))) -> 2(1(0(5(3(3(x1:S))))))
3.80/3.91	 4(5(2(x1:S))) -> 0(5(1(0(0(4(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 2(2(1(0(4(2(x1:S))))))
3.80/3.91	 4(5(4(x1:S))) -> 3(2(0(3(2(0(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 2(2(1(3(2(1(x1:S))))))
3.80/3.91	 4(5(x1:S)) -> 3(2(0(5(0(0(x1:S))))))
3.80/3.91	 5(5(3(x1:S))) -> 5(1(0(1(2(2(x1:S))))))
3.80/3.91	 5(5(4(x1:S))) -> 5(1(0(4(2(2(x1:S))))))
3.80/3.91	->Strongly Connected Components:
3.80/3.91	 There is no strongly connected component
3.80/3.91	
3.80/3.91	The problem is finite.
3.80/3.91	EOF