0.001/0.001	YES
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S y:S z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(add 1 2)
0.001/0.001	(quad 1)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	add(x:S,0) -> x:S
0.001/0.001	add(x:S,s(y:S)) -> s(add(x:S,y:S))
0.001/0.001	quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	
0.001/0.001	Inlining of Conditions Processor [STERN17]:
0.001/0.001	
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S y:S z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(add 1 2)
0.001/0.001	(quad 1)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	add(x:S,0) -> x:S
0.001/0.001	add(x:S,s(y:S)) -> s(add(x:S,y:S))
0.001/0.001	quad(x:S) -> add(add(x:S,x:S),add(x:S,x:S))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	Confluence Problem:
0.001/0.001	(VAR vNonEmpty:S x:S y:S z:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(add 1 2)
0.001/0.001	(quad 1)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	add(x:S,0) -> x:S
0.001/0.001	add(x:S,s(y:S)) -> s(add(x:S,y:S))
0.001/0.001	quad(x:S) -> add(add(x:S,x:S),add(x:S,x:S))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Critical Pairs Processor:
0.001/0.001	-> Rules:
0.001/0.001	add(x:S,0) -> x:S
0.001/0.001	add(x:S,s(y:S)) -> s(add(x:S,y:S))
0.001/0.001	quad(x:S) -> add(add(x:S,x:S),add(x:S,x:S))
0.001/0.001	-> Vars:
0.001/0.001	"x", "x", "y", "x"
0.001/0.001	-> FVars:
0.001/0.001	"x4", "x5", "x6", "x7"
0.001/0.001	-> PVars:
0.001/0.001	"x": ["x4", "x5", "x7"], "y": ["x6"]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	crule: add(x4:S,0) -> x4:S, id: 1, possubterms: add(x4:S,0)-> [], 0-> [2]
0.001/0.001	crule: add(x5:S,s(x6:S)) -> s(add(x5:S,x6:S)), id: 2, possubterms: add(x5:S,s(x6:S))-> [], s(x6:S)-> [2]
0.001/0.001	crule: quad(x7:S) -> add(add(x7:S,x7:S),add(x7:S,x7:S)), id: 3, possubterms: quad(x7:S)-> []
0.001/0.001	
0.001/0.001	-> Unifications:
0.001/0.001	
0.001/0.001	
0.001/0.001	-> Critical pairs info:
0.001/0.001	
0.001/0.001	
0.001/0.001	-> Problem conclusions:
0.001/0.001	 Left linear, Not right linear, Not linear
0.001/0.001	 Weakly orthogonal, Almost orthogonal, Orthogonal
0.001/0.001	 CTRS Type: 1
0.001/0.001	 Deterministic, Strongly deterministic
0.001/0.001	 Oriented CTRS, Properly oriented CTRS, Join CTRS
0.001/0.001	 Maybe right-stable CTRS, Overlay CTRS
0.001/0.001	 Normal CTRS, Almost normal CTRS
0.001/0.001	 Maybe terminating CTRS, Joinable CCPs
0.001/0.001	 Level confluent
0.001/0.001	 Confluent
0.001/0.001	
0.001/0.001	The problem is joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 36%CPU (0avgtext+0avgdata 8272maxresident)k
0.001/0.001	0inputs+0outputs (0major+649minor)pagefaults 0swaps