1.15/1.18	YES
1.15/1.18	
1.15/1.18	Problem 1: 
1.15/1.18	
1.15/1.18	(VAR v_NonEmpty:S x1:S)
1.15/1.18	(RULES
1.15/1.18	0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.18	0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.18	0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.18	0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.18	0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.18	0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.18	0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.18	0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.18	0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.18	0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.18	0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.18	0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.18	0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.18	0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.18	0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.18	0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.18	0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.18	0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.18	0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.18	0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.18	0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.18	0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.18	0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.18	0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.18	0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.18	0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.18	0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.18	0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.18	3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.18	3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.18	3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.18	3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.18	3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.18	3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.18	3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.18	3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.18	3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.18	3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.18	3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.18	3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.18	3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.18	3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.18	3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.18	3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.18	3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.18	3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.18	3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.18	3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.18	3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.18	)
1.15/1.18	
1.15/1.18	Problem 1: 
1.15/1.18	
1.15/1.18	Dependency Pairs Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 0#(3(5(x1:S)))
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 0#(4(1(0(3(5(x1:S))))))
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 3#(5(x1:S))
1.15/1.18	 0#(1(3(3(4(x1:S))))) -> 0#(0(3(1(3(4(x1:S))))))
1.15/1.18	 0#(1(3(3(4(x1:S))))) -> 0#(3(1(3(4(x1:S)))))
1.15/1.18	 0#(1(3(3(4(x1:S))))) -> 3#(1(3(4(x1:S))))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(4(1(0(3(x1:S)))))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(4(1(1(3(x1:S)))))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 0#(4(1(0(3(x1:S)))))
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	 0#(1(4(0(2(x1:S))))) -> 0#(4(1(5(0(2(x1:S))))))
1.15/1.18	 0#(2(1(4(4(x1:S))))) -> 0#(4(1(2(4(3(x1:S))))))
1.15/1.18	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	 0#(2(1(4(x1:S)))) -> 0#(4(1(3(2(x1:S)))))
1.15/1.18	 0#(2(1(4(x1:S)))) -> 0#(4(1(2(3(x1:S)))))
1.15/1.18	 0#(2(1(4(x1:S)))) -> 3#(2(x1:S))
1.15/1.18	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.18	 0#(2(4(3(5(x1:S))))) -> 0#(4(5(2(5(3(x1:S))))))
1.15/1.18	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 0#(3(1(0(3(2(x1:S))))))
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 3#(1(0(3(2(x1:S)))))
1.15/1.18	 3#(0(2(1(4(x1:S))))) -> 0#(4(1(3(2(x1:S)))))
1.15/1.18	 3#(0(2(1(4(x1:S))))) -> 3#(2(x1:S))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 0#(4(1(2(0(3(x1:S))))))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(4(0(1(4(x1:S))))) -> 0#(4(1(5(3(4(x1:S))))))
1.15/1.18	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.18	 3#(4(0(1(5(x1:S))))) -> 0#(4(1(5(5(3(x1:S))))))
1.15/1.18	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(4(1(2(4(x1:S))))) -> 0#(4(1(2(4(3(x1:S))))))
1.15/1.18	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	-> Rules:
1.15/1.18	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.18	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.18	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.18	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.18	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.18	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.18	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.18	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.18	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.18	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.18	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.18	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.18	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.18	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.18	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.18	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.18	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.18	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.18	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.18	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.18	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.18	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.18	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.18	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.18	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.18	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.18	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.18	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.18	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.18	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.18	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.18	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.18	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.18	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.18	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.18	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.18	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.18	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.18	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.18	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.18	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.18	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.18	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.18	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.18	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.18	
1.15/1.18	Problem 1: 
1.15/1.18	
1.15/1.18	SCC Processor:
1.15/1.18	-> Pairs:
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 0#(3(5(x1:S)))
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 0#(4(1(0(3(5(x1:S))))))
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 3#(5(x1:S))
1.15/1.18	 0#(1(3(3(4(x1:S))))) -> 0#(0(3(1(3(4(x1:S))))))
1.15/1.18	 0#(1(3(3(4(x1:S))))) -> 0#(3(1(3(4(x1:S)))))
1.15/1.18	 0#(1(3(3(4(x1:S))))) -> 3#(1(3(4(x1:S))))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(4(1(0(3(x1:S)))))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(4(1(1(3(x1:S)))))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 0#(4(1(0(3(x1:S)))))
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	 0#(1(4(0(2(x1:S))))) -> 0#(4(1(5(0(2(x1:S))))))
1.15/1.18	 0#(2(1(4(4(x1:S))))) -> 0#(4(1(2(4(3(x1:S))))))
1.15/1.18	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	 0#(2(1(4(x1:S)))) -> 0#(4(1(3(2(x1:S)))))
1.15/1.18	 0#(2(1(4(x1:S)))) -> 0#(4(1(2(3(x1:S)))))
1.15/1.18	 0#(2(1(4(x1:S)))) -> 3#(2(x1:S))
1.15/1.18	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.18	 0#(2(4(3(5(x1:S))))) -> 0#(4(5(2(5(3(x1:S))))))
1.15/1.18	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 0#(3(1(0(3(2(x1:S))))))
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 3#(1(0(3(2(x1:S)))))
1.15/1.18	 3#(0(2(1(4(x1:S))))) -> 0#(4(1(3(2(x1:S)))))
1.15/1.18	 3#(0(2(1(4(x1:S))))) -> 3#(2(x1:S))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 0#(4(1(2(0(3(x1:S))))))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(4(0(1(4(x1:S))))) -> 0#(4(1(5(3(4(x1:S))))))
1.15/1.18	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.18	 3#(4(0(1(5(x1:S))))) -> 0#(4(1(5(5(3(x1:S))))))
1.15/1.18	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(4(1(2(4(x1:S))))) -> 0#(4(1(2(4(3(x1:S))))))
1.15/1.18	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	-> Rules:
1.15/1.18	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.18	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.18	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.18	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.18	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.18	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.18	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.18	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.18	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.18	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.18	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.18	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.18	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.18	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.18	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.18	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.18	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.18	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.18	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.18	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.18	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.18	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.18	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.18	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.18	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.18	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.18	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.18	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.18	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.18	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.18	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.18	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.18	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.18	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.18	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.18	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.18	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.18	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.18	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.18	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.18	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.18	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.18	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.18	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.18	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.18	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.18	->Strongly Connected Components:
1.15/1.18	->->Cycle:
1.15/1.18	->->-> Pairs:
1.15/1.18	 0#(0(1(4(5(x1:S))))) -> 0#(3(5(x1:S)))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.18	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.18	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.18	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.18	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.18	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.18	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(0(1(4(5(x1:S))))) -> 0#(3(5(x1:S)))
1.15/1.19	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 2.X
1.15/1.19	[3](X) = 0
1.15/1.19	[1](X) = 2
1.15/1.19	[2](X) = 2.X
1.15/1.19	[4](X) = 0
1.15/1.19	[5](X) = 2.X
1.15/1.19	[0#](X) = X + 2
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(3(4(x1:S)))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 1
1.15/1.19	[3](X) = 1
1.15/1.19	[1](X) = 2
1.15/1.19	[2](X) = 1
1.15/1.19	[4](X) = 0
1.15/1.19	[5](X) = 1
1.15/1.19	[0#](X) = 2.X
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(3(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 1
1.15/1.19	[3](X) = 1
1.15/1.19	[1](X) = 2
1.15/1.19	[2](X) = 1
1.15/1.19	[4](X) = 1
1.15/1.19	[5](X) = 1
1.15/1.19	[0#](X) = X + 1
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 2.X
1.15/1.19	[3](X) = 0
1.15/1.19	[1](X) = 2
1.15/1.19	[2](X) = 2
1.15/1.19	[4](X) = 0
1.15/1.19	[5](X) = 0
1.15/1.19	[0#](X) = 2.X + 2
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(1(2(3(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = X
1.15/1.19	[3](X) = 1
1.15/1.19	[1](X) = 2.X + 2
1.15/1.19	[2](X) = 2
1.15/1.19	[4](X) = 1
1.15/1.19	[5](X) = 0
1.15/1.19	[0#](X) = 2.X
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(2(1(4(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 0
1.15/1.19	[3](X) = 0
1.15/1.19	[1](X) = 1
1.15/1.19	[2](X) = X
1.15/1.19	[4](X) = 0
1.15/1.19	[5](X) = 2.X
1.15/1.19	[0#](X) = X + 1
1.15/1.19	[3#](X) = 1
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(2(1(4(x1:S)))) -> 3#(x1:S)
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 2.X
1.15/1.19	[3](X) = 0
1.15/1.19	[1](X) = 2.X + 2
1.15/1.19	[2](X) = 2.X + 2
1.15/1.19	[4](X) = 0
1.15/1.19	[5](X) = 2.X
1.15/1.19	[0#](X) = X + 2
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	Reduction Pair Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 0#(2(4(3(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	-> Usable rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Interpretation type:
1.15/1.19	 Linear
1.15/1.19	->Coefficients:
1.15/1.19	 Natural Numbers
1.15/1.19	->Dimension:
1.15/1.19	 1
1.15/1.19	->Bound:
1.15/1.19	 2
1.15/1.19	->Interpretation:
1.15/1.19	 
1.15/1.19	[0](X) = 2.X
1.15/1.19	[3](X) = 0
1.15/1.19	[1](X) = 2
1.15/1.19	[2](X) = 2
1.15/1.19	[4](X) = 0
1.15/1.19	[5](X) = 0
1.15/1.19	[0#](X) = 2.X + 1
1.15/1.19	[3#](X) = 2
1.15/1.19	
1.15/1.19	Problem 1: 
1.15/1.19	
1.15/1.19	SCC Processor:
1.15/1.19	-> Pairs:
1.15/1.19	 3#(0(1(3(2(x1:S))))) -> 0#(3(2(x1:S)))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 0#(3(x1:S))
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.19	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.19	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.19	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.19	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.19	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.19	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.19	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.19	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.19	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.19	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.19	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.19	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.19	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.19	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.19	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.19	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.19	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.19	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.19	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.19	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.19	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.19	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.19	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.19	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.19	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.19	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.19	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.19	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.19	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.19	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.19	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.19	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.19	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.19	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.19	->Strongly Connected Components:
1.15/1.19	->->Cycle:
1.15/1.19	->->-> Pairs:
1.15/1.19	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.19	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.19	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.19	->->-> Rules:
1.15/1.19	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.19	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.20	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.20	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.20	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.20	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.20	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.20	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.20	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.20	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.20	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.20	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.20	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.20	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.20	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.20	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.20	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.20	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.20	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.20	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.20	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.20	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.20	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.20	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.20	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.20	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.20	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.20	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.20	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.20	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.20	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.20	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.20	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.20	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.20	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.20	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.20	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.20	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.20	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.20	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.20	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.20	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.20	
1.15/1.20	Problem 1: 
1.15/1.20	
1.15/1.20	Subterm Processor:
1.15/1.20	-> Pairs:
1.15/1.20	 3#(0(4(0(2(x1:S))))) -> 3#(x1:S)
1.15/1.20	 3#(4(0(1(4(x1:S))))) -> 3#(4(x1:S))
1.15/1.20	 3#(4(0(1(5(x1:S))))) -> 3#(x1:S)
1.15/1.20	 3#(4(1(2(4(x1:S))))) -> 3#(x1:S)
1.15/1.20	-> Rules:
1.15/1.20	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.20	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.20	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.20	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.20	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.20	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.20	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.20	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.20	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.20	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.20	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.20	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.20	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.20	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.20	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.20	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.20	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.20	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.20	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.20	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.20	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.20	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.20	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.20	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.20	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.20	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.20	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.20	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.20	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.20	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.20	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.20	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.20	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.20	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.20	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.20	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.20	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.20	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.20	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.20	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.20	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.20	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.20	->Projection:
1.15/1.20	 pi(3#) = 1
1.15/1.20	
1.15/1.20	Problem 1: 
1.15/1.20	
1.15/1.20	SCC Processor:
1.15/1.20	-> Pairs:
1.15/1.20	 Empty
1.15/1.20	-> Rules:
1.15/1.20	 0(0(1(4(5(x1:S))))) -> 0(4(1(0(3(5(x1:S))))))
1.15/1.20	 0(1(0(2(4(x1:S))))) -> 2(0(0(4(1(1(x1:S))))))
1.15/1.20	 0(1(0(2(x1:S)))) -> 0(0(3(1(2(x1:S)))))
1.15/1.20	 0(1(3(3(4(x1:S))))) -> 0(0(3(1(3(4(x1:S))))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(0(3(x1:S)))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(3(1(x1:S)))))
1.15/1.20	 0(1(3(4(x1:S)))) -> 0(4(1(1(3(x1:S)))))
1.15/1.20	 0(1(2(3(4(x1:S))))) -> 2(0(4(1(0(3(x1:S))))))
1.15/1.20	 0(1(4(0(2(x1:S))))) -> 0(4(1(5(0(2(x1:S))))))
1.15/1.20	 0(1(4(3(4(x1:S))))) -> 0(4(0(3(1(4(x1:S))))))
1.15/1.20	 0(1(4(3(4(x1:S))))) -> 3(0(4(1(5(4(x1:S))))))
1.15/1.20	 0(1(4(3(5(x1:S))))) -> 5(4(5(0(3(1(x1:S))))))
1.15/1.20	 0(1(4(1(5(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
1.15/1.20	 0(1(5(0(2(x1:S))))) -> 0(0(4(1(2(5(x1:S))))))
1.15/1.20	 0(1(5(1(4(x1:S))))) -> 4(5(0(3(1(1(x1:S))))))
1.15/1.20	 0(2(1(4(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.20	 0(2(1(4(5(x1:S))))) -> 0(4(1(2(5(2(x1:S))))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 0(4(1(3(2(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 0(4(1(2(3(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 2(0(4(1(4(x1:S)))))
1.15/1.20	 0(2(1(4(x1:S)))) -> 5(5(0(4(1(2(x1:S))))))
1.15/1.20	 0(2(1(5(4(x1:S))))) -> 5(0(2(0(4(1(x1:S))))))
1.15/1.20	 0(2(1(5(x1:S)))) -> 5(0(4(1(2(x1:S)))))
1.15/1.20	 0(2(2(4(x1:S)))) -> 0(4(2(2(5(x1:S)))))
1.15/1.20	 0(2(2(4(x1:S)))) -> 0(4(2(5(2(x1:S)))))
1.15/1.20	 0(2(4(3(5(x1:S))))) -> 0(4(5(2(5(3(x1:S))))))
1.15/1.20	 0(2(4(1(5(x1:S))))) -> 5(0(4(1(5(2(x1:S))))))
1.15/1.20	 0(2(5(1(4(x1:S))))) -> 0(0(5(4(1(2(x1:S))))))
1.15/1.20	 3(0(1(3(2(x1:S))))) -> 0(3(1(0(3(2(x1:S))))))
1.15/1.20	 3(0(2(1(4(x1:S))))) -> 4(0(4(1(3(2(x1:S))))))
1.15/1.20	 3(0(2(1(5(x1:S))))) -> 5(3(2(0(4(1(x1:S))))))
1.15/1.20	 3(0(4(0(2(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.20	 3(0(4(0(2(x1:S))))) -> 0(4(1(2(0(3(x1:S))))))
1.15/1.20	 3(0(5(1(4(x1:S))))) -> 3(0(4(1(1(5(x1:S))))))
1.15/1.20	 3(0(5(1(5(x1:S))))) -> 0(4(1(3(5(5(x1:S))))))
1.15/1.20	 3(2(4(1(2(x1:S))))) -> 3(1(2(2(5(4(x1:S))))))
1.15/1.20	 3(2(4(1(5(x1:S))))) -> 3(1(4(5(2(5(x1:S))))))
1.15/1.20	 3(4(0(1(2(x1:S))))) -> 0(4(2(0(3(1(x1:S))))))
1.15/1.20	 3(4(0(1(4(x1:S))))) -> 0(4(1(5(3(4(x1:S))))))
1.15/1.20	 3(4(0(1(5(x1:S))))) -> 0(4(1(5(5(3(x1:S))))))
1.15/1.20	 3(4(0(2(4(x1:S))))) -> 0(3(4(0(4(2(x1:S))))))
1.15/1.20	 3(4(0(2(x1:S)))) -> 3(0(4(5(2(x1:S)))))
1.15/1.20	 3(4(0(2(x1:S)))) -> 3(5(0(4(2(x1:S)))))
1.15/1.20	 3(4(3(0(2(x1:S))))) -> 3(3(0(4(1(2(x1:S))))))
1.15/1.20	 3(4(1(3(5(x1:S))))) -> 4(3(0(3(1(5(x1:S))))))
1.15/1.20	 3(4(1(2(4(x1:S))))) -> 0(4(1(2(4(3(x1:S))))))
1.15/1.20	 3(4(5(0(2(x1:S))))) -> 0(3(0(4(2(5(x1:S))))))
1.15/1.20	 3(5(0(2(2(x1:S))))) -> 0(3(2(5(2(5(x1:S))))))
1.15/1.20	 3(5(2(1(4(x1:S))))) -> 3(5(1(0(4(2(x1:S))))))
1.15/1.20	->Strongly Connected Components:
1.15/1.20	 There is no strongly connected component
1.15/1.20	
1.15/1.20	The problem is finite.
1.15/1.20	EOF