0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR v_NonEmpty:S X:S)
0.00/0.01	(RULES
0.00/0.01	active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	f(active(X:S)) -> f(X:S)
0.00/0.01	f(mark(X:S)) -> f(X:S)
0.00/0.01	g(active(X:S)) -> g(X:S)
0.00/0.01	g(mark(X:S)) -> g(X:S)
0.00/0.01	h(active(X:S)) -> h(X:S)
0.00/0.01	h(mark(X:S)) -> h(X:S)
0.00/0.01	mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	mark(g(X:S)) -> active(g(X:S))
0.00/0.01	mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	) 
0.00/0.01	(STRATEGY INNERMOST)
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Dependency Pairs Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 ACTIVE(f(X:S)) -> G(h(f(X:S)))
0.00/0.01	 ACTIVE(f(X:S)) -> H(f(X:S))
0.00/0.01	 ACTIVE(f(X:S)) -> MARK(g(h(f(X:S))))
0.00/0.01	 F(active(X:S)) -> F(X:S)
0.00/0.01	 F(mark(X:S)) -> F(X:S)
0.00/0.01	 G(active(X:S)) -> G(X:S)
0.00/0.01	 G(mark(X:S)) -> G(X:S)
0.00/0.01	 H(active(X:S)) -> H(X:S)
0.00/0.01	 H(mark(X:S)) -> H(X:S)
0.00/0.01	 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
0.00/0.01	 MARK(f(X:S)) -> F(mark(X:S))
0.00/0.01	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.01	 MARK(g(X:S)) -> ACTIVE(g(X:S))
0.00/0.01	 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
0.00/0.01	 MARK(h(X:S)) -> H(mark(X:S))
0.00/0.01	 MARK(h(X:S)) -> MARK(X:S)
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 ACTIVE(f(X:S)) -> G(h(f(X:S)))
0.00/0.01	 ACTIVE(f(X:S)) -> H(f(X:S))
0.00/0.01	 ACTIVE(f(X:S)) -> MARK(g(h(f(X:S))))
0.00/0.01	 F(active(X:S)) -> F(X:S)
0.00/0.01	 F(mark(X:S)) -> F(X:S)
0.00/0.01	 G(active(X:S)) -> G(X:S)
0.00/0.01	 G(mark(X:S)) -> G(X:S)
0.00/0.01	 H(active(X:S)) -> H(X:S)
0.00/0.01	 H(mark(X:S)) -> H(X:S)
0.00/0.01	 MARK(f(X:S)) -> ACTIVE(f(mark(X:S)))
0.00/0.01	 MARK(f(X:S)) -> F(mark(X:S))
0.00/0.01	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.01	 MARK(g(X:S)) -> ACTIVE(g(X:S))
0.00/0.01	 MARK(h(X:S)) -> ACTIVE(h(mark(X:S)))
0.00/0.01	 MARK(h(X:S)) -> H(mark(X:S))
0.00/0.01	 MARK(h(X:S)) -> MARK(X:S)
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 H(active(X:S)) -> H(X:S)
0.00/0.01	 H(mark(X:S)) -> H(X:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 G(active(X:S)) -> G(X:S)
0.00/0.01	 G(mark(X:S)) -> G(X:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 F(active(X:S)) -> F(X:S)
0.00/0.01	 F(mark(X:S)) -> F(X:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.01	 MARK(h(X:S)) -> MARK(X:S)
0.00/0.01	->->-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	
0.00/0.01	
0.00/0.01	The problem is decomposed in 4 subproblems.
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 H(active(X:S)) -> H(X:S)
0.00/0.01	 H(mark(X:S)) -> H(X:S)
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Projection:
0.00/0.01	 pi(H) = 1
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 G(active(X:S)) -> G(X:S)
0.00/0.01	 G(mark(X:S)) -> G(X:S)
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Projection:
0.00/0.01	 pi(G) = 1
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.3: 
0.00/0.01	
0.00/0.01	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 F(active(X:S)) -> F(X:S)
0.00/0.01	 F(mark(X:S)) -> F(X:S)
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Projection:
0.00/0.01	 pi(F) = 1
0.00/0.01	
0.00/0.01	Problem 1.3: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.4: 
0.00/0.01	
0.00/0.01	Subterm Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 MARK(f(X:S)) -> MARK(X:S)
0.00/0.01	 MARK(h(X:S)) -> MARK(X:S)
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Projection:
0.00/0.01	 pi(MARK) = 1
0.00/0.01	
0.00/0.01	Problem 1.4: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 active(f(X:S)) -> mark(g(h(f(X:S))))
0.00/0.01	 f(active(X:S)) -> f(X:S)
0.00/0.01	 f(mark(X:S)) -> f(X:S)
0.00/0.01	 g(active(X:S)) -> g(X:S)
0.00/0.01	 g(mark(X:S)) -> g(X:S)
0.00/0.01	 h(active(X:S)) -> h(X:S)
0.00/0.01	 h(mark(X:S)) -> h(X:S)
0.00/0.01	 mark(f(X:S)) -> active(f(mark(X:S)))
0.00/0.01	 mark(g(X:S)) -> active(g(X:S))
0.00/0.01	 mark(h(X:S)) -> active(h(mark(X:S)))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.02	EOF