1.33/1.34	YES
1.33/1.34	
1.33/1.34	Problem 1: 
1.33/1.34	
1.33/1.34	(VAR v_NonEmpty:S x1:S)
1.33/1.34	(RULES
1.33/1.34	0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.34	0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.34	0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.34	0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.34	1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.34	1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.34	1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.34	q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.34	q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.34	q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.34	q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.34	q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.34	q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.34	q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.34	)
1.33/1.34	
1.33/1.34	Problem 1: 
1.33/1.34	
1.33/1.34	Dependency Pairs Processor:
1.33/1.34	-> Pairs:
1.33/1.34	 0#(q1(1(x1:S))) -> 0#(1'(x1:S))
1.33/1.34	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.34	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.34	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.34	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.34	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.34	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.34	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.34	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.34	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.34	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.34	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.34	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.34	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.34	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.34	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.34	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.34	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.34	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.34	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.34	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.34	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.34	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.34	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.34	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.34	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.34	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.34	-> Rules:
1.33/1.34	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.34	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.34	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.34	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.34	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.34	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.34	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.34	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.34	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.34	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.34	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.34	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.34	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.34	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.34	
1.33/1.34	Problem 1: 
1.33/1.34	
1.33/1.34	SCC Processor:
1.33/1.34	-> Pairs:
1.33/1.34	 0#(q1(1(x1:S))) -> 0#(1'(x1:S))
1.33/1.34	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.34	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.34	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.34	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.34	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.34	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.34	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.34	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.34	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.34	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.34	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.34	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.34	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.34	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.34	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.34	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.34	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.34	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.34	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.34	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.34	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.34	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.34	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.34	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.34	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.34	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.34	-> Rules:
1.33/1.34	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.34	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.34	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.34	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.34	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.34	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.34	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.34	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.34	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.34	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.34	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.34	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.34	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.34	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.34	->Strongly Connected Components:
1.33/1.34	->->Cycle:
1.33/1.34	->->-> Pairs:
1.33/1.34	 0#(q1(1(x1:S))) -> 0#(1'(x1:S))
1.33/1.34	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.34	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.34	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.34	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.34	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.34	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.34	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.34	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.34	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.34	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.34	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.34	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.34	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.34	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.34	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.34	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.34	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.34	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.34	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.34	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.34	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.34	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.34	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.34	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.34	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.34	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.34	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.34	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.34	->->-> Rules:
1.33/1.34	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.34	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.34	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X + 1
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = 2.X + 1
1.33/1.35	[q4](X) = 2.X + 1
1.33/1.35	[0#](X) = 2.X + 2
1.33/1.35	[0'#](X) = 2.X + 2
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X + 2
1.33/1.35	[Q3](X) = 2.X + 1
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 0
1.33/1.35	[0'](X) = 2
1.33/1.35	[1'](X) = 1
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2
1.33/1.35	[q2](X) = X
1.33/1.35	[q3](X) = 2.X + 2
1.33/1.35	[1](X) = X
1.33/1.35	[b](X) = 2.X + 2
1.33/1.35	[q4](X) = 2.X
1.33/1.35	[0#](X) = 2
1.33/1.35	[0'#](X) = 2
1.33/1.35	[1'#](X) = 1
1.33/1.35	[Q0](X) = 2
1.33/1.35	[Q1](X) = 2
1.33/1.35	[Q2](X) = X
1.33/1.35	[Q3](X) = 2
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q1(1(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X + 2
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = X + 2
1.33/1.35	[q4](X) = 2.X + 2
1.33/1.35	[0#](X) = 2.X + 1
1.33/1.35	[0'#](X) = X + 2
1.33/1.35	[1'#](X) = 2.X + 1
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = X + 2
1.33/1.35	[Q3](X) = 2.X + 2
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(0(x1:S))) -> 0#(0(x1:S))
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X + 2
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = X + 1
1.33/1.35	[q4](X) = 2
1.33/1.35	[0#](X) = 2.X + 2
1.33/1.35	[0'#](X) = 2.X + 2
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X + 2
1.33/1.35	[Q3](X) = 2.X + 2
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(0(x1:S))) -> Q2(0(0(x1:S)))
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = 2.X
1.33/1.35	[q4](X) = 2.X
1.33/1.35	[0#](X) = 2.X + 2
1.33/1.35	[0'#](X) = 2.X + 1
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 1
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X + 1
1.33/1.35	[Q3](X) = 2.X + 2
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(1'(x1:S))) -> 0#(1'(x1:S))
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 1
1.33/1.35	[0'](X) = X
1.33/1.35	[1'](X) = 2.X
1.33/1.35	[q0](X) = X
1.33/1.35	[q1](X) = 2.X
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 0
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = 2.X
1.33/1.35	[q4](X) = 0
1.33/1.35	[0#](X) = 2.X + 1
1.33/1.35	[0'#](X) = 2.X + 1
1.33/1.35	[1'#](X) = 2.X + 1
1.33/1.35	[Q0](X) = 2.X + 1
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X + 1
1.33/1.35	[Q3](X) = 2.X + 1
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0#(q2(1'(x1:S))) -> Q2(0(1'(x1:S)))
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = X
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = 2
1.33/1.35	[q4](X) = 2.X + 1
1.33/1.35	[0#](X) = 2.X + 2
1.33/1.35	[0'#](X) = 2.X
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X
1.33/1.35	[Q3](X) = X + 1
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> 0#(q1(x1:S))
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X + 1
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = X + 1
1.33/1.35	[q4](X) = X + 2
1.33/1.35	[0'#](X) = 2.X + 2
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X + 2
1.33/1.35	[Q3](X) = 2.X + 2
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X + 2
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = 2
1.33/1.35	[q4](X) = X + 2
1.33/1.35	[0'#](X) = 2.X + 2
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = 2.X + 2
1.33/1.35	[Q3](X) = 2.X + 2
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q1(1(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 1
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 1
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = 2.X
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = 2.X + 2
1.33/1.35	[q4](X) = 1
1.33/1.35	[0'#](X) = X + 2
1.33/1.35	[1'#](X) = 2.X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = X + 2
1.33/1.35	[Q3](X) = 2.X + 1
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q2(0(x1:S))) -> 0'#(0(x1:S))
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Interpretation type:
1.33/1.35	 Linear
1.33/1.35	->Coefficients:
1.33/1.35	 Natural Numbers
1.33/1.35	->Dimension:
1.33/1.35	 1
1.33/1.35	->Bound:
1.33/1.35	 2
1.33/1.35	->Interpretation:
1.33/1.35	 
1.33/1.35	[0](X) = 2.X + 2
1.33/1.35	[0'](X) = 2.X + 2
1.33/1.35	[1'](X) = 2.X + 2
1.33/1.35	[q0](X) = 2.X + 2
1.33/1.35	[q1](X) = 2.X + 2
1.33/1.35	[q2](X) = 2.X + 2
1.33/1.35	[q3](X) = X
1.33/1.35	[1](X) = 2.X + 2
1.33/1.35	[b](X) = X + 1
1.33/1.35	[q4](X) = X
1.33/1.35	[0'#](X) = X + 2
1.33/1.35	[1'#](X) = X + 2
1.33/1.35	[Q0](X) = 2.X + 2
1.33/1.35	[Q1](X) = 2.X + 2
1.33/1.35	[Q2](X) = X + 2
1.33/1.35	[Q3](X) = X
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	SCC Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	->Strongly Connected Components:
1.33/1.35	->->Cycle:
1.33/1.35	->->-> Pairs:
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	->->-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	
1.33/1.35	Problem 1: 
1.33/1.35	
1.33/1.35	Reduction Pair Processor:
1.33/1.35	-> Pairs:
1.33/1.35	 0'#(q2(0(x1:S))) -> Q2(0'(0(x1:S)))
1.33/1.35	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.35	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.35	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.35	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.35	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.35	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.35	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.35	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.35	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.35	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.35	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.35	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.35	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.35	-> Rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.35	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.35	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.35	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.35	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.35	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.35	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.35	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.35	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.35	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.35	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.35	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.35	-> Usable rules:
1.33/1.35	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X + 1
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 1
1.33/1.36	[q4](X) = 2.X + 2
1.33/1.36	[0'#](X) = 2.X + 2
1.33/1.36	[1'#](X) = 2.X + 2
1.33/1.36	[Q0](X) = 2.X + 2
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = 2.X + 2
1.33/1.36	[Q3](X) = 2.X + 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.36	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.36	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 0'#(q2(1'(x1:S))) -> 0'#(1'(x1:S))
1.33/1.36	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = X
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X + 2
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X + 1
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 2.X + 2
1.33/1.36	[q4](X) = X + 1
1.33/1.36	[0'#](X) = X
1.33/1.36	[1'#](X) = 2.X + 2
1.33/1.36	[Q0](X) = 2.X
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = 2.X + 2
1.33/1.36	[Q3](X) = 2.X + 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 0'#(q2(1'(x1:S))) -> Q2(0'(1'(x1:S)))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X + 1
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X + 1
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = X + 2
1.33/1.36	[q4](X) = 2.X + 2
1.33/1.36	[0'#](X) = X + 2
1.33/1.36	[1'#](X) = 2.X + 2
1.33/1.36	[Q0](X) = 2.X + 1
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = X + 2
1.33/1.36	[Q3](X) = 2.X + 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> 0'#(q1(x1:S))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> 0'#(q0(x1:S))
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X + 1
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X + 1
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X + 1
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 2.X + 2
1.33/1.36	[q4](X) = X + 1
1.33/1.36	[1'#](X) = 2.X + 2
1.33/1.36	[Q0](X) = 2.X + 2
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = 2.X + 2
1.33/1.36	[Q3](X) = 2.X + 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> 1'#(x1:S)
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X + 2
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X + 2
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X + 2
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 2.X + 2
1.33/1.36	[q4](X) = 2.X + 2
1.33/1.36	[1'#](X) = X + 2
1.33/1.36	[Q0](X) = 2.X + 2
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = X + 1
1.33/1.36	[Q3](X) = 2.X + 1
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q1(1(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X + 2
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X + 2
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = X + 2
1.33/1.36	[q4](X) = 2.X + 2
1.33/1.36	[1'#](X) = 2.X + 1
1.33/1.36	[Q0](X) = 2.X + 2
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = 2.X
1.33/1.36	[Q3](X) = 2.X + 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(0(x1:S))) -> 1'#(0(x1:S))
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X + 2
1.33/1.36	[1'](X) = X
1.33/1.36	[q0](X) = 2.X + 2
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X + 1
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 2.X + 2
1.33/1.36	[q4](X) = 2.X
1.33/1.36	[1'#](X) = X
1.33/1.36	[Q0](X) = 2.X + 2
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = 2.X + 2
1.33/1.36	[Q3](X) = 2.X + 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(0(x1:S))) -> Q2(1'(0(x1:S)))
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2
1.33/1.36	[1'](X) = 1
1.33/1.36	[q0](X) = X + 2
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = X
1.33/1.36	[q3](X) = 2.X + 2
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 2
1.33/1.36	[q4](X) = X + 2
1.33/1.36	[1'#](X) = 2
1.33/1.36	[Q0](X) = 2
1.33/1.36	[Q1](X) = 2
1.33/1.36	[Q2](X) = X
1.33/1.36	[Q3](X) = 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(1'(x1:S))) -> 1'#(1'(x1:S))
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X + 2
1.33/1.36	[1'](X) = 2.X + 2
1.33/1.36	[q0](X) = 2.X + 2
1.33/1.36	[q1](X) = 2.X + 2
1.33/1.36	[q2](X) = 2.X + 2
1.33/1.36	[q3](X) = 2.X + 2
1.33/1.36	[1](X) = 2.X + 2
1.33/1.36	[b](X) = 2.X + 2
1.33/1.36	[q4](X) = 2.X
1.33/1.36	[1'#](X) = 2.X + 1
1.33/1.36	[Q0](X) = 2.X + 2
1.33/1.36	[Q1](X) = 2.X + 2
1.33/1.36	[Q2](X) = 2.X + 1
1.33/1.36	[Q3](X) = 2.X + 1
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	Reduction Pair Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 1'#(q2(1'(x1:S))) -> Q2(1'(1'(x1:S)))
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	-> Usable rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Interpretation type:
1.33/1.36	 Linear
1.33/1.36	->Coefficients:
1.33/1.36	 Natural Numbers
1.33/1.36	->Dimension:
1.33/1.36	 1
1.33/1.36	->Bound:
1.33/1.36	 2
1.33/1.36	->Interpretation:
1.33/1.36	 
1.33/1.36	[0](X) = 2.X + 2
1.33/1.36	[0'](X) = 2.X
1.33/1.36	[1'](X) = 1
1.33/1.36	[q0](X) = X
1.33/1.36	[q1](X) = X
1.33/1.36	[q2](X) = X
1.33/1.36	[q3](X) = 2
1.33/1.36	[1](X) = X + 2
1.33/1.36	[b](X) = 0
1.33/1.36	[q4](X) = X + 2
1.33/1.36	[1'#](X) = 2
1.33/1.36	[Q0](X) = 2.X
1.33/1.36	[Q1](X) = 2
1.33/1.36	[Q2](X) = X
1.33/1.36	[Q3](X) = 2
1.33/1.36	
1.33/1.36	Problem 1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 Q0(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q0(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q0(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> 1'#(q1(x1:S))
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q2(0'(x1:S)) -> Q0(x1:S)
1.33/1.36	 Q3(1'(x1:S)) -> 1'#(q3(x1:S))
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->->Cycle:
1.33/1.36	->->-> Pairs:
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	->->-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	
1.33/1.36	
1.33/1.36	The problem is decomposed in 2 subproblems.
1.33/1.36	
1.33/1.36	Problem 1.1: 
1.33/1.36	
1.33/1.36	Subterm Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 Q3(1'(x1:S)) -> Q3(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Projection:
1.33/1.36	 pi(Q3) = 1
1.33/1.36	
1.33/1.36	Problem 1.1: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 Empty
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	 There is no strongly connected component
1.33/1.36	
1.33/1.36	The problem is finite.
1.33/1.36	
1.33/1.36	Problem 1.2: 
1.33/1.36	
1.33/1.36	Subterm Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 Q1(0(x1:S)) -> Q1(x1:S)
1.33/1.36	 Q1(1'(x1:S)) -> Q1(x1:S)
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Projection:
1.33/1.36	 pi(Q1) = 1
1.33/1.36	
1.33/1.36	Problem 1.2: 
1.33/1.36	
1.33/1.36	SCC Processor:
1.33/1.36	-> Pairs:
1.33/1.36	 Empty
1.33/1.36	-> Rules:
1.33/1.36	 0(q1(1(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0(q2(0(x1:S))) -> q2(0(0(x1:S)))
1.33/1.36	 0(q2(1'(x1:S))) -> q2(0(1'(x1:S)))
1.33/1.36	 0'(q1(1(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 0'(q2(0(x1:S))) -> q2(0'(0(x1:S)))
1.33/1.36	 0'(q2(1'(x1:S))) -> q2(0'(1'(x1:S)))
1.33/1.36	 1'(q1(1(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 1'(q2(0(x1:S))) -> q2(1'(0(x1:S)))
1.33/1.36	 1'(q2(1'(x1:S))) -> q2(1'(1'(x1:S)))
1.33/1.36	 q0(0(x1:S)) -> 0'(q1(x1:S))
1.33/1.36	 q0(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q1(0(x1:S)) -> 0(q1(x1:S))
1.33/1.36	 q1(1'(x1:S)) -> 1'(q1(x1:S))
1.33/1.36	 q2(0'(x1:S)) -> 0'(q0(x1:S))
1.33/1.36	 q3(1'(x1:S)) -> 1'(q3(x1:S))
1.33/1.36	 q3(b(x1:S)) -> b(q4(x1:S))
1.33/1.36	->Strongly Connected Components:
1.33/1.36	 There is no strongly connected component
1.33/1.36	
1.33/1.36	The problem is finite.
1.33/1.36	EOF