0.64/1.34	YES
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	(VAR v_NonEmpty:S x1:S)
0.64/1.34	(RULES
0.64/1.34	a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	c(x1:S) -> a(a(x1:S))
0.64/1.34	d(x1:S) -> c(x1:S)
0.64/1.34	)
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	Dependency Pairs Processor:
0.64/1.34	-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(b(x1:S))
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	SCC Processor:
0.64/1.34	-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(b(x1:S))
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	->Strongly Connected Components:
0.64/1.34	->->Cycle:
0.64/1.34	->->-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(b(x1:S))
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	->->-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	Reduction Pair Processor:
0.64/1.34	-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(b(x1:S))
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	-> Usable rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	->Interpretation type:
0.64/1.34	 Linear
0.64/1.34	->Coefficients:
0.64/1.34	 All rationals
0.64/1.34	->Dimension:
0.64/1.34	 1
0.64/1.34	->Bound:
0.64/1.34	 4
0.64/1.34	->Interpretation:
0.64/1.34	 
0.64/1.34	[a](X) = X + 1/3
0.64/1.34	[b](X) = X + 1/2
0.64/1.34	[c](X) = X + 2/3
0.64/1.34	[d](X) = X + 2/3
0.64/1.34	[A](X) = 1/2.X + 1/3
0.64/1.34	[B](X) = 1/2.X + 1/3
0.64/1.34	[C](X) = 1/2.X + 1/2
0.64/1.34	[D](X) = 1/2.X + 3/4
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	SCC Processor:
0.64/1.34	-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	->Strongly Connected Components:
0.64/1.34	->->Cycle:
0.64/1.34	->->-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	->->-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	Reduction Pair Processor:
0.64/1.34	-> Pairs:
0.64/1.34	 A(a(a(x1:S))) -> B(x1:S)
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	-> Usable rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	->Interpretation type:
0.64/1.34	 Linear
0.64/1.34	->Coefficients:
0.64/1.34	 All rationals
0.64/1.34	->Dimension:
0.64/1.34	 1
0.64/1.34	->Bound:
0.64/1.34	 4
0.64/1.34	->Interpretation:
0.64/1.34	 
0.64/1.34	[a](X) = X + 1/3
0.64/1.34	[b](X) = X + 1/2
0.64/1.34	[c](X) = X + 2/3
0.64/1.34	[d](X) = X + 2/3
0.64/1.34	[A](X) = 4.X + 1/2
0.64/1.34	[B](X) = 4.X + 3
0.64/1.34	[C](X) = 4.X + 3
0.64/1.34	[D](X) = 4.X + 3
0.64/1.34	
0.64/1.34	Problem 1: 
0.64/1.34	
0.64/1.34	SCC Processor:
0.64/1.34	-> Pairs:
0.64/1.34	 B(b(b(x1:S))) -> C(d(x1:S))
0.64/1.34	 B(b(b(x1:S))) -> D(x1:S)
0.64/1.34	 C(x1:S) -> A(a(x1:S))
0.64/1.34	 C(x1:S) -> A(x1:S)
0.64/1.34	 D(x1:S) -> C(x1:S)
0.64/1.34	-> Rules:
0.64/1.34	 a(a(a(x1:S))) -> b(b(x1:S))
0.64/1.34	 b(b(b(x1:S))) -> c(d(x1:S))
0.64/1.34	 c(x1:S) -> a(a(x1:S))
0.64/1.34	 d(x1:S) -> c(x1:S)
0.64/1.34	->Strongly Connected Components:
0.64/1.34	 There is no strongly connected component
0.64/1.34	
0.64/1.34	The problem is finite.
0.64/1.34	EOF