0.00/0.02	YES
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	(VAR v_NonEmpty:S x:S y:S)
0.00/0.02	(RULES
0.00/0.02	le(0,s(x:S)) -> ttrue
0.00/0.02	le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	le(x:S,0) -> ffalse
0.00/0.02	m -> s(s(s(s(0))))
0.00/0.02	pop(empty) -> empty
0.00/0.02	pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	size(empty) -> 0
0.00/0.02	size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	top(empty) -> eentry
0.00/0.02	top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	)
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	Valid CTRS Processor:
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	-> The system is a deterministic 3-CTRS.
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	Dependency Pairs Processor:
0.00/0.02	
0.00/0.02	Conditional Termination Problem 1:
0.00/0.02	-> Pairs:
0.00/0.02	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.02	 SIZE(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	
0.00/0.02	Conditional Termination Problem 2:
0.00/0.02	-> Pairs:
0.00/0.02	 POP(push(x:S,y:S)) -> LE(size(x:S),m)
0.00/0.02	 POP(push(x:S,y:S)) -> M
0.00/0.02	 POP(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	 TOP(push(x:S,y:S)) -> LE(size(x:S),m)
0.00/0.02	 TOP(push(x:S,y:S)) -> M
0.00/0.02	 TOP(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.02	 SIZE(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	
0.00/0.02	
0.00/0.02	The problem is decomposed in 2 subproblems.
0.00/0.02	
0.00/0.02	Problem 1.1: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.02	 SIZE(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	->->Cycle:
0.00/0.02	->->-> Pairs:
0.00/0.02	 SIZE(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	->->-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->->Cycle:
0.00/0.02	->->-> Pairs:
0.00/0.02	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	->->-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	
0.00/0.02	
0.00/0.02	The problem is decomposed in 2 subproblems.
0.00/0.02	
0.00/0.02	Problem 1.1.1: 
0.00/0.02	
0.00/0.02	Conditional Subterm Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 SIZE(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->Projection:
0.00/0.02	 pi(SIZE) = 1
0.00/0.02	
0.00/0.02	Problem 1.1.1: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	
0.00/0.02	Problem 1.1.2: 
0.00/0.02	
0.00/0.02	Conditional Subterm Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->Projection:
0.00/0.02	 pi(LE) = 1
0.00/0.02	
0.00/0.02	Problem 1.1.2: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	
0.00/0.02	Problem 1.2: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 POP(push(x:S,y:S)) -> LE(size(x:S),m)
0.00/0.02	 POP(push(x:S,y:S)) -> M
0.00/0.02	 POP(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	 TOP(push(x:S,y:S)) -> LE(size(x:S),m)
0.00/0.02	 TOP(push(x:S,y:S)) -> M
0.00/0.02	 TOP(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 LE(s(x:S),s(y:S)) -> LE(x:S,y:S)
0.00/0.02	 SIZE(push(x:S,y:S)) -> SIZE(x:S)
0.00/0.02	-> Rules:
0.00/0.02	 le(0,s(x:S)) -> ttrue
0.00/0.02	 le(s(x:S),s(y:S)) -> le(x:S,y:S)
0.00/0.02	 le(x:S,0) -> ffalse
0.00/0.02	 m -> s(s(s(s(0))))
0.00/0.02	 pop(empty) -> empty
0.00/0.02	 pop(push(x:S,y:S)) -> x:S | le(size(x:S),m) ->* ttrue
0.00/0.02	 size(empty) -> 0
0.00/0.02	 size(push(x:S,y:S)) -> s(size(x:S))
0.00/0.02	 top(empty) -> eentry
0.00/0.02	 top(push(x:S,y:S)) -> y:S | le(size(x:S),m) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	EOF