4.05/4.84	YES
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	(VAR v_NonEmpty:S x1:S)
4.05/4.84	(RULES
4.05/4.84	b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	c(x1:S) -> g(x1:S)
4.05/4.84	d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	f(x1:S) -> a(g(x1:S))
4.05/4.84	g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	)
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Dependency Pairs Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 B(b(x1:S)) -> C(d(x1:S))
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	 G(x1:S) -> D(a(b(x1:S)))
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 B(b(x1:S)) -> C(d(x1:S))
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	 G(x1:S) -> D(a(b(x1:S)))
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	->->Cycle:
4.05/4.84	->->-> Pairs:
4.05/4.84	 B(b(x1:S)) -> C(d(x1:S))
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	->->-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Reduction Pair Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 B(b(x1:S)) -> C(d(x1:S))
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	-> Usable rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Interpretation type:
4.05/4.84	 Linear
4.05/4.84	->Coefficients:
4.05/4.84	 All rationals
4.05/4.84	->Dimension:
4.05/4.84	 1
4.05/4.84	->Bound:
4.05/4.84	 4
4.05/4.84	->Interpretation:
4.05/4.84	 
4.05/4.84	[b](X) = X + 1
4.05/4.84	[c](X) = X + 1
4.05/4.84	[d](X) = X + 2/3
4.05/4.84	[f](X) = X
4.05/4.84	[g](X) = X + 1
4.05/4.84	[a](X) = 0
4.05/4.84	[B](X) = 1/2.X + 2/3
4.05/4.84	[C](X) = 1/2.X + 3/4
4.05/4.84	[D](X) = 1/2.X + 1/2
4.05/4.84	[F](X) = 1/2.X + 3/4
4.05/4.84	[G](X) = 1/2.X + 2/3
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	->->Cycle:
4.05/4.84	->->-> Pairs:
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	->->-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Reduction Pair Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 B(b(x1:S)) -> D(x1:S)
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	-> Usable rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Interpretation type:
4.05/4.84	 Linear
4.05/4.84	->Coefficients:
4.05/4.84	 All rationals
4.05/4.84	->Dimension:
4.05/4.84	 1
4.05/4.84	->Bound:
4.05/4.84	 4
4.05/4.84	->Interpretation:
4.05/4.84	 
4.05/4.84	[b](X) = X + 1
4.05/4.84	[c](X) = X + 1
4.05/4.84	[d](X) = X + 2/3
4.05/4.84	[f](X) = 3/4.X
4.05/4.84	[g](X) = X + 1
4.05/4.84	[a](X) = 0
4.05/4.84	[B](X) = 4.X + 4/3
4.05/4.84	[C](X) = 4.X + 3
4.05/4.84	[D](X) = 4.X + 1/3
4.05/4.84	[F](X) = 4.X + 3/2
4.05/4.84	[G](X) = 4.X + 4/3
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> B(c(x1:S))
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	 G(x1:S) -> B(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	->->Cycle:
4.05/4.84	->->-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	->->-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Reduction Pair Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(d(d(x1:S)))
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	-> Usable rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Interpretation type:
4.05/4.84	 Linear
4.05/4.84	->Coefficients:
4.05/4.84	 All rationals
4.05/4.84	->Dimension:
4.05/4.84	 1
4.05/4.84	->Bound:
4.05/4.84	 4
4.05/4.84	->Interpretation:
4.05/4.84	 
4.05/4.84	[b](X) = X + 2
4.05/4.84	[c](X) = X + 2
4.05/4.84	[d](X) = X + 4/3
4.05/4.84	[f](X) = 1/2
4.05/4.84	[g](X) = X + 2
4.05/4.84	[a](X) = 1/4
4.05/4.84	[C](X) = 4.X + 4
4.05/4.84	[D](X) = 4.X + 2/3
4.05/4.84	[F](X) = 4.X + 3
4.05/4.84	[G](X) = 4.X + 1/2
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	->->Cycle:
4.05/4.84	->->-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	->->-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Reduction Pair Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(d(x1:S))
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	-> Usable rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Interpretation type:
4.05/4.84	 Linear
4.05/4.84	->Coefficients:
4.05/4.84	 All rationals
4.05/4.84	->Dimension:
4.05/4.84	 1
4.05/4.84	->Bound:
4.05/4.84	 4
4.05/4.84	->Interpretation:
4.05/4.84	 
4.05/4.84	[b](X) = X + 3/4
4.05/4.84	[c](X) = X + 3/4
4.05/4.84	[d](X) = X + 1/2
4.05/4.84	[f](X) = 0
4.05/4.84	[g](X) = X + 3/4
4.05/4.84	[a](X) = 0
4.05/4.84	[C](X) = 1/4.X + 1/3
4.05/4.84	[D](X) = 1/4.X + 1/3
4.05/4.84	[F](X) = 1/4.X + 1/4
4.05/4.84	[G](X) = 1/4.X + 1/4
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	->->Cycle:
4.05/4.84	->->-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	->->-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Reduction Pair Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(c(x1:S)) -> D(x1:S)
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	-> Usable rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Interpretation type:
4.05/4.84	 Linear
4.05/4.84	->Coefficients:
4.05/4.84	 All rationals
4.05/4.84	->Dimension:
4.05/4.84	 1
4.05/4.84	->Bound:
4.05/4.84	 4
4.05/4.84	->Interpretation:
4.05/4.84	 
4.05/4.84	[b](X) = X + 2
4.05/4.84	[c](X) = X + 2
4.05/4.84	[d](X) = X + 4/3
4.05/4.84	[f](X) = X
4.05/4.84	[g](X) = X + 2
4.05/4.84	[a](X) = 0
4.05/4.84	[C](X) = 1/3.X
4.05/4.84	[D](X) = 1/3.X + 1/3
4.05/4.84	[F](X) = 1/3.X + 1/4
4.05/4.84	[G](X) = 1/3.X
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> C(x1:S)
4.05/4.84	 D(d(d(x1:S))) -> G(c(x1:S))
4.05/4.84	 D(d(x1:S)) -> C(f(x1:S))
4.05/4.84	 D(d(x1:S)) -> F(x1:S)
4.05/4.84	 F(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	->->Cycle:
4.05/4.84	->->-> Pairs:
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	->->-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	Subterm Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	 G(g(x1:S)) -> C(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Projection:
4.05/4.84	 pi(C) = 1
4.05/4.84	 pi(G) = 1
4.05/4.84	
4.05/4.84	Problem 1: 
4.05/4.84	
4.05/4.84	SCC Processor:
4.05/4.84	-> Pairs:
4.05/4.84	 C(x1:S) -> G(x1:S)
4.05/4.84	-> Rules:
4.05/4.84	 b(b(x1:S)) -> c(d(x1:S))
4.05/4.84	 c(c(x1:S)) -> d(d(d(x1:S)))
4.05/4.84	 c(x1:S) -> g(x1:S)
4.05/4.84	 d(d(d(x1:S))) -> g(c(x1:S))
4.05/4.84	 d(d(x1:S)) -> c(f(x1:S))
4.05/4.84	 f(x1:S) -> a(g(x1:S))
4.05/4.84	 g(g(x1:S)) -> b(c(x1:S))
4.05/4.84	 g(x1:S) -> d(a(b(x1:S)))
4.05/4.84	->Strongly Connected Components:
4.05/4.84	 There is no strongly connected component
4.05/4.84	
4.05/4.84	The problem is finite.
4.05/4.84	EOF