20.01/20.20	NO
20.01/20.20	
20.01/20.20	Problem 1: 
20.01/20.20	
20.01/20.20	(VAR v_NonEmpty:S)
20.01/20.20	(RULES
20.01/20.20	a -> b | a ->* b
20.01/20.20	)
20.01/20.20	
20.01/20.20	Problem 1: 
20.01/20.20	Valid CTRS Processor:
20.01/20.20	-> Rules:
20.01/20.20	 a -> b | a ->* b
20.01/20.20	-> The system is a deterministic 3-CTRS.
20.01/20.20	
20.01/20.20	Problem 1: 
20.01/20.20	
20.01/20.20	Dependency Pairs Processor:
20.01/20.20	
20.01/20.20	Conditional Termination Problem 1:
20.01/20.20	-> Pairs:
20.01/20.20	 Empty
20.01/20.20	-> QPairs:
20.01/20.20	 Empty
20.01/20.20	-> Rules:
20.01/20.20	 a -> b | a ->* b
20.01/20.20	
20.01/20.20	Conditional Termination Problem 2:
20.01/20.20	-> Pairs:
20.01/20.20	 A -> A
20.01/20.20	-> QPairs:
20.01/20.20	 Empty
20.01/20.20	-> Rules:
20.01/20.20	 a -> b | a ->* b
20.01/20.20	
20.01/20.20	Problem 1: 
20.01/20.20	
20.01/20.20	SCC Processor:
20.01/20.20	-> Pairs:
20.01/20.20	 A -> A
20.01/20.20	-> QPairs:
20.01/20.20	 Empty
20.01/20.20	-> Rules:
20.01/20.20	 a -> b | a ->* b
20.01/20.20	->Strongly Connected Components:
20.01/20.20	->->Cycle:
20.01/20.20	->->-> Pairs:
20.01/20.20	 A -> A
20.01/20.20	-> QPairs:
20.01/20.20	 Empty
20.01/20.20	->->-> Rules:
20.01/20.20	 a -> b | a ->* b
20.01/20.20	
20.01/20.20	Problem 1: 
20.01/20.20	
20.01/20.20	Unsatisfiable Rule Processor:
20.01/20.20	-> Pairs:
20.01/20.20	 A -> A
20.01/20.20	-> QPairs:
20.01/20.20	 Empty
20.01/20.20	-> Rules:
20.01/20.20	 a -> b | a ->* b
20.01/20.20	->AGES Output:
20.01/20.20	 
20.01/20.20	Model Results
20.01/20.20	
20.01/20.20	System:
20.01/20.20	mod InTheory is
20.01/20.20	  sorts S Bool .
20.01/20.20	
20.01/20.20	op _->*_ : S S -> Bool .
20.01/20.20	op _->_ : S S -> Bool .
20.01/20.20	op a :  -> S .
20.01/20.20	op b :  -> S .
20.01/20.20	op fSNonEmpty :  -> S .
20.01/20.20	op gtrsim : S S -> Bool .
20.01/20.20	op sqsupset : S S -> Bool .
20.01/20.20	
20.01/20.20	endm
20.01/20.20	
20.01/20.20	
20.01/20.20	Property:
20.01/20.20	x:S ->R* x:S
20.01/20.20	x:S ->R y:S /\ y:S ->R* z:S => x:S ->R* z:S
20.01/20.20	gtrsim(x:S,y:S) /\ sqsupset(y:S,z:S) => sqsupset(x:S,z:S)
20.01/20.20	a ->R* b => a ->R b
20.01/20.20	x:S ->R y:S => gtrsim(x:S,y:S)
20.01/20.20	sqsupset(b,a)
20.01/20.20	
20.01/20.20	Results:
20.01/20.20	
20.01/20.20	
20.01/20.20	Domains:
20.01/20.20	S: -|N U {1}
20.01/20.20	
20.01/20.20	Function Interpretations:
20.01/20.20	|[a]| = 1
20.01/20.20	|[b]| = 0
20.01/20.20	|[fSNonEmpty]| = 1
20.01/20.20	
20.01/20.20	Predicate Interpretations:
20.01/20.20	 x_1_1:S ->* x_2_1:S <=> ((x_2_1:S >= x_1_1:S) /\ (1 + x_2_1:S >= x_1_1:S))
20.01/20.20	 x_1_1:S -> x_2_1:S <=> (1 + x_1_1:S + x_2_1:S >= 0)
20.01/20.20	gtrsim(x_1_1:S,x_2_1:S) <=> ((0 >= 22+2.x_1_1:S) /\ (10+3.x_2_1:S >= x_1_1:S))
20.01/20.20	sqsupset(x_1_1:S,x_2_1:S) <=> (5.x_2_1:S >= 5+5.x_1_1:S)
20.01/20.20	
20.01/20.20	Problem 1: 
20.01/20.20	
20.01/20.20	Infinite Processor:
20.01/20.20	-> Pairs:
20.01/20.20	 A -> A
20.01/20.20	-> QPairs:
20.01/20.20	 Empty
20.01/20.20	-> Rules:
20.01/20.20	 Empty
20.01/20.20	-> Pairs in cycle:
20.01/20.20	 A -> A
20.01/20.20	
20.01/20.20	The problem is infinite.
20.01/20.20	EOF