72.14/72.29	YES
72.14/72.29	
72.14/72.29	Problem 1: 
72.14/72.29	
72.14/72.29	(VAR v_NonEmpty:S X:S)
72.14/72.29	(RULES
72.14/72.29	active(g(X:S)) -> mark(h(X:S))
72.14/72.29	active(h(d)) -> mark(g(c))
72.14/72.29	active(c) -> mark(d)
72.14/72.29	g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	proper(c) -> ok(c)
72.14/72.29	proper(d) -> ok(d)
72.14/72.29	top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	top(ok(X:S)) -> top(active(X:S))
72.14/72.29	) 
72.14/72.29	(STRATEGY INNERMOST)
72.14/72.29	
72.14/72.29	Problem 1: 
72.14/72.29	
72.14/72.29	Dependency Pairs Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 ACTIVE(g(X:S)) -> H(X:S)
72.14/72.29	 G(ok(X:S)) -> G(X:S)
72.14/72.29	 H(ok(X:S)) -> H(X:S)
72.14/72.29	 PROPER(g(X:S)) -> G(proper(X:S))
72.14/72.29	 PROPER(g(X:S)) -> PROPER(X:S)
72.14/72.29	 PROPER(h(X:S)) -> H(proper(X:S))
72.14/72.29	 PROPER(h(X:S)) -> PROPER(X:S)
72.14/72.29	 TOP(mark(X:S)) -> PROPER(X:S)
72.14/72.29	 TOP(mark(X:S)) -> TOP(proper(X:S))
72.14/72.29	 TOP(ok(X:S)) -> ACTIVE(X:S)
72.14/72.29	 TOP(ok(X:S)) -> TOP(active(X:S))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	
72.14/72.29	Problem 1: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 ACTIVE(g(X:S)) -> H(X:S)
72.14/72.29	 G(ok(X:S)) -> G(X:S)
72.14/72.29	 H(ok(X:S)) -> H(X:S)
72.14/72.29	 PROPER(g(X:S)) -> G(proper(X:S))
72.14/72.29	 PROPER(g(X:S)) -> PROPER(X:S)
72.14/72.29	 PROPER(h(X:S)) -> H(proper(X:S))
72.14/72.29	 PROPER(h(X:S)) -> PROPER(X:S)
72.14/72.29	 TOP(mark(X:S)) -> PROPER(X:S)
72.14/72.29	 TOP(mark(X:S)) -> TOP(proper(X:S))
72.14/72.29	 TOP(ok(X:S)) -> ACTIVE(X:S)
72.14/72.29	 TOP(ok(X:S)) -> TOP(active(X:S))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	->->Cycle:
72.14/72.29	->->-> Pairs:
72.14/72.29	 H(ok(X:S)) -> H(X:S)
72.14/72.29	->->-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->->Cycle:
72.14/72.29	->->-> Pairs:
72.14/72.29	 G(ok(X:S)) -> G(X:S)
72.14/72.29	->->-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->->Cycle:
72.14/72.29	->->-> Pairs:
72.14/72.29	 PROPER(g(X:S)) -> PROPER(X:S)
72.14/72.29	 PROPER(h(X:S)) -> PROPER(X:S)
72.14/72.29	->->-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->->Cycle:
72.14/72.29	->->-> Pairs:
72.14/72.29	 TOP(mark(X:S)) -> TOP(proper(X:S))
72.14/72.29	 TOP(ok(X:S)) -> TOP(active(X:S))
72.14/72.29	->->-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	
72.14/72.29	
72.14/72.29	The problem is decomposed in 4 subproblems.
72.14/72.29	
72.14/72.29	Problem 1.1: 
72.14/72.29	
72.14/72.29	Subterm Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 H(ok(X:S)) -> H(X:S)
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Projection:
72.14/72.29	 pi(H) = 1
72.14/72.29	
72.14/72.29	Problem 1.1: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 Empty
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	 There is no strongly connected component
72.14/72.29	
72.14/72.29	The problem is finite.
72.14/72.29	
72.14/72.29	Problem 1.2: 
72.14/72.29	
72.14/72.29	Subterm Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 G(ok(X:S)) -> G(X:S)
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Projection:
72.14/72.29	 pi(G) = 1
72.14/72.29	
72.14/72.29	Problem 1.2: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 Empty
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	 There is no strongly connected component
72.14/72.29	
72.14/72.29	The problem is finite.
72.14/72.29	
72.14/72.29	Problem 1.3: 
72.14/72.29	
72.14/72.29	Subterm Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 PROPER(g(X:S)) -> PROPER(X:S)
72.14/72.29	 PROPER(h(X:S)) -> PROPER(X:S)
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Projection:
72.14/72.29	 pi(PROPER) = 1
72.14/72.29	
72.14/72.29	Problem 1.3: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 Empty
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	 There is no strongly connected component
72.14/72.29	
72.14/72.29	The problem is finite.
72.14/72.29	
72.14/72.29	Problem 1.4: 
72.14/72.29	
72.14/72.29	Narrowing Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 TOP(mark(X:S)) -> TOP(proper(X:S))
72.14/72.29	 TOP(ok(X:S)) -> TOP(active(X:S))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Narrowed Pairs:
72.14/72.29	->->Original Pair:
72.14/72.29	 TOP(mark(X:S)) -> TOP(proper(X:S))
72.14/72.29	->-> Narrowed pairs:
72.14/72.29	 TOP(mark(g(X:S))) -> TOP(g(proper(X:S)))
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(mark(c)) -> TOP(ok(c))
72.14/72.29	 TOP(mark(d)) -> TOP(ok(d))
72.14/72.29	->->Original Pair:
72.14/72.29	 TOP(ok(X:S)) -> TOP(active(X:S))
72.14/72.29	->-> Narrowed pairs:
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	 TOP(ok(h(d))) -> TOP(mark(g(c)))
72.14/72.29	 TOP(ok(c)) -> TOP(mark(d))
72.14/72.29	
72.14/72.29	Problem 1.4: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 TOP(mark(g(X:S))) -> TOP(g(proper(X:S)))
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(mark(c)) -> TOP(ok(c))
72.14/72.29	 TOP(mark(d)) -> TOP(ok(d))
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	 TOP(ok(h(d))) -> TOP(mark(g(c)))
72.14/72.29	 TOP(ok(c)) -> TOP(mark(d))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	->->Cycle:
72.14/72.29	->->-> Pairs:
72.14/72.29	 TOP(mark(g(X:S))) -> TOP(g(proper(X:S)))
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	 TOP(ok(h(d))) -> TOP(mark(g(c)))
72.14/72.29	->->-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	
72.14/72.29	Problem 1.4: 
72.14/72.29	
72.14/72.29	Reduction Pairs Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 TOP(mark(g(X:S))) -> TOP(g(proper(X:S)))
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	 TOP(ok(h(d))) -> TOP(mark(g(c)))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	-> Usable rules:
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	->Interpretation type:
72.14/72.29	 Linear
72.14/72.29	->Coefficients:
72.14/72.29	 Natural Numbers
72.14/72.29	->Dimension:
72.14/72.29	 1
72.14/72.29	->Bound:
72.14/72.29	 2
72.14/72.29	->Interpretation:
72.14/72.29	 
72.14/72.29	[active](X) = 0
72.14/72.29	[g](X) = 2.X + 2
72.14/72.29	[h](X) = 2.X + 1
72.14/72.29	[proper](X) = X
72.14/72.29	[top](X) = 0
72.14/72.29	[c] = 0
72.14/72.29	[d] = 2
72.14/72.29	[fSNonEmpty] = 0
72.14/72.29	[mark](X) = X + 1
72.14/72.29	[ok](X) = X
72.14/72.29	[ACTIVE](X) = 0
72.14/72.29	[G](X) = 0
72.14/72.29	[H](X) = 0
72.14/72.29	[PROPER](X) = 0
72.14/72.29	[TOP](X) = 2.X
72.14/72.29	
72.14/72.29	Problem 1.4: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	 TOP(ok(h(d))) -> TOP(mark(g(c)))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	->->Cycle:
72.14/72.29	->->-> Pairs:
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	->->-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	
72.14/72.29	Problem 1.4: 
72.14/72.29	
72.14/72.29	Reduction Pairs Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 TOP(mark(h(X:S))) -> TOP(h(proper(X:S)))
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	-> Usable rules:
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	->Interpretation type:
72.14/72.29	 Linear
72.14/72.29	->Coefficients:
72.14/72.29	 Natural Numbers
72.14/72.29	->Dimension:
72.14/72.29	 1
72.14/72.29	->Bound:
72.14/72.29	 2
72.14/72.29	->Interpretation:
72.14/72.29	 
72.14/72.29	[active](X) = 0
72.14/72.29	[g](X) = 2.X + 1
72.14/72.29	[h](X) = 0
72.14/72.29	[proper](X) = X
72.14/72.29	[top](X) = 0
72.14/72.29	[c] = 2
72.14/72.29	[d] = 2
72.14/72.29	[fSNonEmpty] = 0
72.14/72.29	[mark](X) = 2.X + 1
72.14/72.29	[ok](X) = X
72.14/72.29	[ACTIVE](X) = 0
72.14/72.29	[G](X) = 0
72.14/72.29	[H](X) = 0
72.14/72.29	[PROPER](X) = 0
72.14/72.29	[TOP](X) = X
72.14/72.29	
72.14/72.29	Problem 1.4: 
72.14/72.29	
72.14/72.29	SCC Processor:
72.14/72.29	-> Pairs:
72.14/72.29	 TOP(ok(g(X:S))) -> TOP(mark(h(X:S)))
72.14/72.29	-> Rules:
72.14/72.29	 active(g(X:S)) -> mark(h(X:S))
72.14/72.29	 active(h(d)) -> mark(g(c))
72.14/72.29	 active(c) -> mark(d)
72.14/72.29	 g(ok(X:S)) -> ok(g(X:S))
72.14/72.29	 h(ok(X:S)) -> ok(h(X:S))
72.14/72.29	 proper(g(X:S)) -> g(proper(X:S))
72.14/72.29	 proper(h(X:S)) -> h(proper(X:S))
72.14/72.29	 proper(c) -> ok(c)
72.14/72.29	 proper(d) -> ok(d)
72.14/72.29	 top(mark(X:S)) -> top(proper(X:S))
72.14/72.29	 top(ok(X:S)) -> top(active(X:S))
72.14/72.29	->Strongly Connected Components:
72.14/72.29	 There is no strongly connected component
72.14/72.29	
72.14/72.29	The problem is finite.
72.14/72.29	EOF