1.32/1.95	YES
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	(VAR v_NonEmpty:S x1:S)
1.32/1.95	(RULES
1.32/1.95	a(x1:S) -> g(d(x1:S))
1.32/1.95	b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	)
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	Dependency Pairs Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(d(c(x1:S)))
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> A(g(g(x1:S)))
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	SCC Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(d(c(x1:S)))
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> A(g(g(x1:S)))
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Strongly Connected Components:
1.32/1.95	->->Cycle:
1.32/1.95	->->-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(d(c(x1:S)))
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	->->-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	Reduction Pair Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(d(c(x1:S)))
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	-> Usable rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Interpretation type:
1.32/1.95	 Linear
1.32/1.95	->Coefficients:
1.32/1.95	 All rationals
1.32/1.95	->Dimension:
1.32/1.95	 1
1.32/1.95	->Bound:
1.32/1.95	 4
1.32/1.95	->Interpretation:
1.32/1.95	 
1.32/1.95	[a](X) = X + 2/3
1.32/1.95	[b](X) = X + 1
1.32/1.95	[c](X) = X + 4/3
1.32/1.95	[g](X) = X + 2/3
1.32/1.95	[d](X) = X
1.32/1.95	[B](X) = 1/2.X + 3/4
1.32/1.95	[C](X) = 1/2.X + 1
1.32/1.95	[G](X) = 1/2.X + 2/3
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	SCC Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Strongly Connected Components:
1.32/1.95	->->Cycle:
1.32/1.95	->->-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	->->-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	Reduction Pair Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(b(x1:S))) -> C(x1:S)
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	-> Usable rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Interpretation type:
1.32/1.95	 Linear
1.32/1.95	->Coefficients:
1.32/1.95	 All rationals
1.32/1.95	->Dimension:
1.32/1.95	 1
1.32/1.95	->Bound:
1.32/1.95	 4
1.32/1.95	->Interpretation:
1.32/1.95	 
1.32/1.95	[a](X) = X + 1/2
1.32/1.95	[b](X) = X + 3/4
1.32/1.95	[c](X) = X + 1
1.32/1.95	[g](X) = X + 1/2
1.32/1.95	[d](X) = X
1.32/1.95	[B](X) = 2.X + 4/3
1.32/1.95	[C](X) = 2.X + 4
1.32/1.95	[G](X) = 2.X + 4/3
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	SCC Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 C(d(x1:S)) -> G(g(x1:S))
1.32/1.95	 C(d(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Strongly Connected Components:
1.32/1.95	->->Cycle:
1.32/1.95	->->-> Pairs:
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	->->-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	Reduction Pair Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(x1:S)) -> G(g(x1:S))
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	-> Usable rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Interpretation type:
1.32/1.95	 Linear
1.32/1.95	->Coefficients:
1.32/1.95	 All rationals
1.32/1.95	->Dimension:
1.32/1.95	 1
1.32/1.95	->Bound:
1.32/1.95	 4
1.32/1.95	->Interpretation:
1.32/1.95	 
1.32/1.95	[a](X) = X + 1/2
1.32/1.95	[b](X) = X + 3/4
1.32/1.95	[c](X) = X + 1
1.32/1.95	[g](X) = X + 1/2
1.32/1.95	[d](X) = X
1.32/1.95	[B](X) = 2/3.X + 1/2
1.32/1.95	[G](X) = 2/3.X + 1/3
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	SCC Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Strongly Connected Components:
1.32/1.95	->->Cycle:
1.32/1.95	->->-> Pairs:
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	->->-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	Reduction Pair Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 B(b(x1:S)) -> G(x1:S)
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	-> Usable rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Interpretation type:
1.32/1.95	 Linear
1.32/1.95	->Coefficients:
1.32/1.95	 All rationals
1.32/1.95	->Dimension:
1.32/1.95	 1
1.32/1.95	->Bound:
1.32/1.95	 4
1.32/1.95	->Interpretation:
1.32/1.95	 
1.32/1.95	[a](X) = X + 1
1.32/1.95	[b](X) = X + 3/2
1.32/1.95	[c](X) = X + 2
1.32/1.95	[g](X) = X + 1
1.32/1.95	[d](X) = X
1.32/1.95	[B](X) = 3.X + 3/4
1.32/1.95	[G](X) = 3.X + 4
1.32/1.95	
1.32/1.95	Problem 1: 
1.32/1.95	
1.32/1.95	SCC Processor:
1.32/1.95	-> Pairs:
1.32/1.95	 G(g(g(x1:S))) -> B(b(x1:S))
1.32/1.95	 G(g(g(x1:S))) -> B(x1:S)
1.32/1.95	-> Rules:
1.32/1.95	 a(x1:S) -> g(d(x1:S))
1.32/1.95	 b(b(b(x1:S))) -> c(d(c(x1:S)))
1.32/1.95	 b(b(x1:S)) -> a(g(g(x1:S)))
1.32/1.95	 c(d(x1:S)) -> g(g(x1:S))
1.32/1.95	 g(g(g(x1:S))) -> b(b(x1:S))
1.32/1.95	->Strongly Connected Components:
1.32/1.95	 There is no strongly connected component
1.32/1.95	
1.32/1.95	The problem is finite.
1.32/1.96	EOF