20.01/20.30	NO
20.01/20.30	
20.01/20.30	Problem 1: 
20.01/20.30	
20.01/20.30	(VAR v_NonEmpty:S)
20.01/20.30	(RULES
20.01/20.30	a -> b
20.01/20.30	a -> c
20.01/20.30	b -> c | b ->* c
20.01/20.30	)
20.01/20.30	
20.01/20.30	Problem 1: 
20.01/20.30	Valid CTRS Processor:
20.01/20.30	-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	 b -> c | b ->* c
20.01/20.30	-> The system is a deterministic 3-CTRS.
20.01/20.30	
20.01/20.30	Problem 1: 
20.01/20.30	
20.01/20.30	Dependency Pairs Processor:
20.01/20.30	
20.01/20.30	Conditional Termination Problem 1:
20.01/20.30	-> Pairs:
20.01/20.30	 A -> B
20.01/20.30	-> QPairs:
20.01/20.30	 Empty
20.01/20.30	-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	 b -> c | b ->* c
20.01/20.30	
20.01/20.30	Conditional Termination Problem 2:
20.01/20.30	-> Pairs:
20.01/20.30	 B -> B
20.01/20.30	-> QPairs:
20.01/20.30	 Empty
20.01/20.30	-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	 b -> c | b ->* c
20.01/20.30	
20.01/20.30	Problem 1: 
20.01/20.30	
20.01/20.30	SCC Processor:
20.01/20.30	-> Pairs:
20.01/20.30	 B -> B
20.01/20.30	-> QPairs:
20.01/20.30	 Empty
20.01/20.30	-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	 b -> c | b ->* c
20.01/20.30	->Strongly Connected Components:
20.01/20.30	->->Cycle:
20.01/20.30	->->-> Pairs:
20.01/20.30	 B -> B
20.01/20.30	-> QPairs:
20.01/20.30	 Empty
20.01/20.30	->->-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	 b -> c | b ->* c
20.01/20.30	
20.01/20.30	Problem 1: 
20.01/20.30	
20.01/20.30	Unsatisfiable Rule Processor:
20.01/20.30	-> Pairs:
20.01/20.30	 B -> B
20.01/20.30	-> QPairs:
20.01/20.30	 Empty
20.01/20.30	-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	 b -> c | b ->* c
20.01/20.30	->AGES Output:
20.01/20.30	 
20.01/20.30	Model Results
20.01/20.30	
20.01/20.30	System:
20.01/20.30	mod InTheory is
20.01/20.30	  sorts S Bool .
20.01/20.30	
20.01/20.30	op _->*_ : S S -> Bool .
20.01/20.30	op _->_ : S S -> Bool .
20.01/20.30	op a :  -> S .
20.01/20.30	op b :  -> S .
20.01/20.30	op c :  -> S .
20.01/20.30	op fSNonEmpty :  -> S .
20.01/20.30	op gtrsim : S S -> Bool .
20.01/20.30	op sqsupset : S S -> Bool .
20.01/20.30	
20.01/20.30	endm
20.01/20.30	
20.01/20.30	
20.01/20.30	Property:
20.01/20.30	x:S ->R* x:S
20.01/20.30	x:S ->R y:S /\ y:S ->R* z:S => x:S ->R* z:S
20.01/20.30	gtrsim(x:S,y:S) /\ sqsupset(y:S,z:S) => sqsupset(x:S,z:S)
20.01/20.30	a ->R b
20.01/20.30	a ->R c
20.01/20.30	b ->R* c => b ->R c
20.01/20.30	x:S ->R y:S => gtrsim(x:S,y:S)
20.01/20.30	sqsupset(c,b)
20.01/20.30	
20.01/20.30	Results:
20.01/20.30	
20.01/20.30	
20.01/20.30	Domains:
20.01/20.30	S: -|N
20.01/20.30	
20.01/20.30	Function Interpretations:
20.01/20.30	|[a]| =  - 1
20.01/20.30	|[b]| = 0
20.01/20.30	|[c]| =  - 1
20.01/20.30	|[fSNonEmpty]| =  - 1
20.01/20.30	
20.01/20.30	Predicate Interpretations:
20.01/20.30	 x_1_1:S ->* x_2_1:S <=> ((1 >= x_1_1:S) /\ (x_2_1:S >= x_1_1:S))
20.01/20.30	 x_1_1:S -> x_2_1:S <=> ((x_2_1:S >= x_1_1:S) /\ (1 + x_2_1:S >= 0))
20.01/20.30	gtrsim(x_1_1:S,x_2_1:S) <=> ((1+3.x_2_1:S >= 2.x_1_1:S) /\ (1 + x_2_1:S >= 0))
20.01/20.30	sqsupset(x_1_1:S,x_2_1:S) <=> (4.x_2_1:S >= 4+4.x_1_1:S)
20.01/20.30	
20.01/20.30	Problem 1: 
20.01/20.30	
20.01/20.30	Infinite Processor:
20.01/20.30	-> Pairs:
20.01/20.30	 B -> B
20.01/20.30	-> QPairs:
20.01/20.30	 Empty
20.01/20.30	-> Rules:
20.01/20.30	 a -> b
20.01/20.30	 a -> c
20.01/20.30	-> Pairs in cycle:
20.01/20.30	 B -> B
20.01/20.30	
20.01/20.30	The problem is infinite.
20.27/20.31	EOF