81.83/82.14	YES
81.83/82.14	
81.83/82.14	Problem 1: 
81.83/82.14	
81.83/82.14	(VAR v_NonEmpty:S x:S y:S)
81.83/82.14	(RULES
81.83/82.14	if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	le(0,y:S) -> ttrue
81.83/82.14	le(s(x:S),0) -> ffalse
81.83/82.14	le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	minus(x:S,0) -> x:S
81.83/82.14	mod(0,y:S) -> 0
81.83/82.14	mod(s(x:S),0) -> 0
81.83/82.14	mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	) 
81.83/82.14	(STRATEGY INNERMOST)
81.83/82.14	
81.83/82.14	Problem 1: 
81.83/82.14	
81.83/82.14	Dependency Pairs Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MINUS(x:S,y:S)
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S)
81.83/82.14	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
81.83/82.14	 MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S)
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	 MOD(s(x:S),s(y:S)) -> LE(y:S,x:S)
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	
81.83/82.14	Problem 1: 
81.83/82.14	
81.83/82.14	SCC Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MINUS(x:S,y:S)
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S)
81.83/82.14	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
81.83/82.14	 MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S)
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	 MOD(s(x:S),s(y:S)) -> LE(y:S,x:S)
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Strongly Connected Components:
81.83/82.14	->->Cycle:
81.83/82.14	->->-> Pairs:
81.83/82.14	 MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S)
81.83/82.14	->->-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->->Cycle:
81.83/82.14	->->-> Pairs:
81.83/82.14	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
81.83/82.14	->->-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->->Cycle:
81.83/82.14	->->-> Pairs:
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S)
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->->-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	
81.83/82.14	
81.83/82.14	The problem is decomposed in 3 subproblems.
81.83/82.14	
81.83/82.14	Problem 1.1: 
81.83/82.14	
81.83/82.14	Subterm Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S)
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Projection:
81.83/82.14	 pi(MINUS) = 1
81.83/82.14	
81.83/82.14	Problem 1.1: 
81.83/82.14	
81.83/82.14	SCC Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 Empty
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Strongly Connected Components:
81.83/82.14	 There is no strongly connected component
81.83/82.14	
81.83/82.14	The problem is finite.
81.83/82.14	
81.83/82.14	Problem 1.2: 
81.83/82.14	
81.83/82.14	Subterm Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Projection:
81.83/82.14	 pi(LE) = 1
81.83/82.14	
81.83/82.14	Problem 1.2: 
81.83/82.14	
81.83/82.14	SCC Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 Empty
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Strongly Connected Components:
81.83/82.14	 There is no strongly connected component
81.83/82.14	
81.83/82.14	The problem is finite.
81.83/82.14	
81.83/82.14	Problem 1.3: 
81.83/82.14	
81.83/82.14	Instantiation Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S)
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Instantiated Pairs:
81.83/82.14	->->Original Pair:
81.83/82.14	 IF_MOD(ttrue,x:S,y:S) -> MOD(minus(x:S,y:S),y:S)
81.83/82.14	->-> Instantiated pairs:
81.83/82.14	 IF_MOD(ttrue,s(x7:S),s(x8:S)) -> MOD(minus(s(x7:S),s(x8:S)),s(x8:S))
81.83/82.14	
81.83/82.14	Problem 1.3: 
81.83/82.14	
81.83/82.14	SCC Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 IF_MOD(ttrue,s(x7:S),s(x8:S)) -> MOD(minus(s(x7:S),s(x8:S)),s(x8:S))
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Strongly Connected Components:
81.83/82.14	->->Cycle:
81.83/82.14	->->-> Pairs:
81.83/82.14	 IF_MOD(ttrue,s(x7:S),s(x8:S)) -> MOD(minus(s(x7:S),s(x8:S)),s(x8:S))
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->->-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	
81.83/82.14	Problem 1.3: 
81.83/82.14	
81.83/82.14	Narrowing Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 IF_MOD(ttrue,s(x7:S),s(x8:S)) -> MOD(minus(s(x7:S),s(x8:S)),s(x8:S))
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->Narrowed Pairs:
81.83/82.14	->->Original Pair:
81.83/82.14	 IF_MOD(ttrue,s(x7:S),s(x8:S)) -> MOD(minus(s(x7:S),s(x8:S)),s(x8:S))
81.83/82.14	->-> Narrowed pairs:
81.83/82.14	 IF_MOD(ttrue,s(x:S),s(y:S)) -> MOD(minus(x:S,y:S),s(y:S))
81.83/82.14	->->Original Pair:
81.83/82.14	 MOD(s(x:S),s(y:S)) -> IF_MOD(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.14	->-> Narrowed pairs:
81.83/82.14	 MOD(s(0),s(s(x:S))) -> IF_MOD(ffalse,s(0),s(s(x:S)))
81.83/82.14	 MOD(s(s(y:S)),s(s(x:S))) -> IF_MOD(le(x:S,y:S),s(s(y:S)),s(s(x:S)))
81.83/82.14	 MOD(s(y:S),s(0)) -> IF_MOD(ttrue,s(y:S),s(0))
81.83/82.14	
81.83/82.14	Problem 1.3: 
81.83/82.14	
81.83/82.14	SCC Processor:
81.83/82.14	-> Pairs:
81.83/82.14	 IF_MOD(ttrue,s(x:S),s(y:S)) -> MOD(minus(x:S,y:S),s(y:S))
81.83/82.14	 MOD(s(0),s(s(x:S))) -> IF_MOD(ffalse,s(0),s(s(x:S)))
81.83/82.14	 MOD(s(s(y:S)),s(s(x:S))) -> IF_MOD(le(x:S,y:S),s(s(y:S)),s(s(x:S)))
81.83/82.14	 MOD(s(y:S),s(0)) -> IF_MOD(ttrue,s(y:S),s(0))
81.83/82.14	-> Rules:
81.83/82.14	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.14	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.14	 le(0,y:S) -> ttrue
81.83/82.14	 le(s(x:S),0) -> ffalse
81.83/82.14	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.14	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.14	 minus(x:S,0) -> x:S
81.83/82.14	 mod(0,y:S) -> 0
81.83/82.14	 mod(s(x:S),0) -> 0
81.83/82.14	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.16	->Strongly Connected Components:
81.83/82.16	->->Cycle:
81.83/82.16	->->-> Pairs:
81.83/82.16	 IF_MOD(ttrue,s(x:S),s(y:S)) -> MOD(minus(x:S,y:S),s(y:S))
81.83/82.16	 MOD(s(s(y:S)),s(s(x:S))) -> IF_MOD(le(x:S,y:S),s(s(y:S)),s(s(x:S)))
81.83/82.16	 MOD(s(y:S),s(0)) -> IF_MOD(ttrue,s(y:S),s(0))
81.83/82.16	->->-> Rules:
81.83/82.16	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.16	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.16	 le(0,y:S) -> ttrue
81.83/82.16	 le(s(x:S),0) -> ffalse
81.83/82.16	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.16	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.16	 minus(x:S,0) -> x:S
81.83/82.16	 mod(0,y:S) -> 0
81.83/82.16	 mod(s(x:S),0) -> 0
81.83/82.16	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.16	
81.83/82.16	Problem 1.3: 
81.83/82.16	
81.83/82.16	Reduction Pairs Processor:
81.83/82.16	-> Pairs:
81.83/82.16	 IF_MOD(ttrue,s(x:S),s(y:S)) -> MOD(minus(x:S,y:S),s(y:S))
81.83/82.16	 MOD(s(s(y:S)),s(s(x:S))) -> IF_MOD(le(x:S,y:S),s(s(y:S)),s(s(x:S)))
81.83/82.16	 MOD(s(y:S),s(0)) -> IF_MOD(ttrue,s(y:S),s(0))
81.83/82.16	-> Rules:
81.83/82.16	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.16	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.16	 le(0,y:S) -> ttrue
81.83/82.16	 le(s(x:S),0) -> ffalse
81.83/82.16	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.16	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.16	 minus(x:S,0) -> x:S
81.83/82.16	 mod(0,y:S) -> 0
81.83/82.16	 mod(s(x:S),0) -> 0
81.83/82.16	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.16	-> Usable rules:
81.83/82.16	 le(0,y:S) -> ttrue
81.83/82.16	 le(s(x:S),0) -> ffalse
81.83/82.16	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.16	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.16	 minus(x:S,0) -> x:S
81.83/82.16	->Interpretation type:
81.83/82.16	 Linear
81.83/82.16	->Coefficients:
81.83/82.16	 Natural Numbers
81.83/82.16	->Dimension:
81.83/82.16	 1
81.83/82.16	->Bound:
81.83/82.16	 2
81.83/82.16	->Interpretation:
81.83/82.16	 
81.83/82.16	[if_mod](X1,X2,X3) = 0
81.83/82.16	[le](X1,X2) = 0
81.83/82.16	[minus](X1,X2) = 2.X1 + 1
81.83/82.16	[mod](X1,X2) = 0
81.83/82.16	[0] = 2
81.83/82.16	[fSNonEmpty] = 0
81.83/82.16	[false] = 0
81.83/82.16	[s](X) = 2.X + 2
81.83/82.16	[true] = 0
81.83/82.16	[IF_MOD](X1,X2,X3) = 2.X1 + 2.X2
81.83/82.16	[LE](X1,X2) = 0
81.83/82.16	[MINUS](X1,X2) = 0
81.83/82.16	[MOD](X1,X2) = 2.X1
81.83/82.16	
81.83/82.16	Problem 1.3: 
81.83/82.16	
81.83/82.16	SCC Processor:
81.83/82.16	-> Pairs:
81.83/82.16	 MOD(s(s(y:S)),s(s(x:S))) -> IF_MOD(le(x:S,y:S),s(s(y:S)),s(s(x:S)))
81.83/82.16	 MOD(s(y:S),s(0)) -> IF_MOD(ttrue,s(y:S),s(0))
81.83/82.16	-> Rules:
81.83/82.16	 if_mod(ffalse,s(x:S),s(y:S)) -> s(x:S)
81.83/82.16	 if_mod(ttrue,x:S,y:S) -> mod(minus(x:S,y:S),y:S)
81.83/82.16	 le(0,y:S) -> ttrue
81.83/82.16	 le(s(x:S),0) -> ffalse
81.83/82.16	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
81.83/82.16	 minus(s(x:S),s(y:S)) -> minus(x:S,y:S)
81.83/82.16	 minus(x:S,0) -> x:S
81.83/82.16	 mod(0,y:S) -> 0
81.83/82.16	 mod(s(x:S),0) -> 0
81.83/82.16	 mod(s(x:S),s(y:S)) -> if_mod(le(y:S,x:S),s(x:S),s(y:S))
81.83/82.16	->Strongly Connected Components:
81.83/82.16	 There is no strongly connected component
81.83/82.16	
81.83/82.16	The problem is finite.
81.83/82.16	EOF