0.001/0.001	NO
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)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(g(X:S),Y:S) -> f(X:S,f(g(X:S),Y: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	CleanTRS Processor:
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)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(g(X:S),Y:S) -> f(X:S,f(g(X:S),Y: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	Modular Confluence Combinations Decomposition Processor:
0.001/0.001	It is a CTRS -> No modular confluence
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	CS-TRS Processor:
0.001/0.001	R is a CS-TRS
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)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(g(X:S),Y:S) -> f(X:S,f(g(X:S),Y:S))
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Extended u-Critical Pairs NonLHRV Processor [JLAMP21]:
0.001/0.001	->Extended u-Critical Pair:
0.001/0.001	 Rule 1 (l :-> r) => f(g(x3:S),x4:S) -> f(x3:S,f(g(x3:S),x4:S))
0.001/0.001	 Rule 1 (l' :-> r') => f(g(X:S),Y:S) -> f(X:S,f(g(X:S),Y:S))
0.001/0.001	 Var => x3:S
0.001/0.001	 Pos x3:S in l => [1,1]
0.001/0.001	 Sigma => {x3:S -> f(g(X:S),Y:S)}
0.001/0.001	 s => f(f(g(X:S),Y:S),f(g(f(g(X:S),Y:S)),x4:S))
0.001/0.001	 t => f(g(f(X:S,f(g(X:S),Y:S))),x4:S)
0.001/0.001	 NW => 0
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)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(f 1)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(g 1)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	f(g(X:S),Y:S) -> f(X:S,f(g(X:S),Y:S))
0.001/0.001	)
0.001/0.001	Critical Pairs:
0.001/0.001	<f(f(g(X:S),Y:S),f(g(f(g(X:S),Y:S)),x4:S)),f(g(f(X:S,f(g(X:S),Y:S))),x4:S)>   =>  Not trivial, Not overlay, NW0, N1
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Huet Levy Processor:
0.001/0.001	-> Rules:
0.001/0.001	 f(g(X:S),Y:S) -> f(X:S,f(g(X:S),Y:S))
0.001/0.001	-> Vars:
0.001/0.001	 X, Y
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [X], UV-RActive: [X], UV-LFrozen: [Y], UV-RFrozen: [X, Y])
0.001/0.001	-> FVars:
0.001/0.001	 x3, x4
0.001/0.001	-> PVars:
0.001/0.001	 X: [x3], Y: [x4]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: f(g(x3:S),x4:S) -> f(x3:S,f(g(x3:S),x4:S)), id: 1, possubterms: f(g(x3:S),x4:S)->[], g(x3:S)->[1])
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	<f(f(g(X:S),Y:S),f(g(f(g(X:S),Y:S)),Y:S)),f(g(f(X:S,f(g(X:S),Y:S))),Y:S)>   =>  Not trivial, Not overlay, NW0, N1
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	 Not weakly orthogonal, Not almost orthogonal, Not orthogonal
0.001/0.001	 Not Huet-Levy confluent, Not Newman confluent
0.001/0.001	 R is a CS-TRS, Not left-homogeneous u-replacing variables
0.001/0.001	
0.001/0.001	
0.001/0.001	Problem 1:
0.001/0.001	No Convergence Brute Force Processor:
0.001/0.001	-> Rewritings:
0.001/0.001	s: f(f(g(X:S),Y:S),f(g(f(g(X:S),Y:S)),Y:S))
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('f(f(g(X:S),Y:S),f(g(f(g(X:S),Y:S)),Y:S))', D0)
0.001/0.001	ID: 1 => ('f(f(X:S,f(g(X:S),Y:S)),f(g(f(g(X:S),Y:S)),Y:S))', D1, R1, P[1], S{x3:S -> X:S, x4:S -> Y:S}), NR: 'f(X:S,f(g(X:S),Y:S))'
0.001/0.001	t: f(g(f(X:S,f(g(X:S),Y:S))),Y:S)
0.001/0.001	Nodes: [0,1]
0.001/0.001	Edges: [(0,1)]
0.001/0.001	ID: 0 => ('f(g(f(X:S,f(g(X:S),Y:S))),Y:S)', D0)
0.001/0.001	ID: 1 => ('f(f(X:S,f(g(X:S),Y:S)),f(g(f(X:S,f(g(X:S),Y:S))),Y:S))', D1, R1, P[], S{x3:S -> f(X:S,f(g(X:S),Y:S)), x4:S -> Y:S}), NR: 'f(f(X:S,f(g(X:S),Y:S)),f(g(f(X:S,f(g(X:S),Y:S))),Y:S))'
0.001/0.001	f(f(g(X:S),Y:S),f(g(f(g(X:S),Y:S)),Y:S)) ->* no union *<- f(g(f(X:S,f(g(X:S),Y:S))),Y:S)
0.001/0.001	"Not joinable"
0.001/0.001	
0.001/0.001	The problem is not joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 46%CPU (0avgtext+0avgdata 8652maxresident)k
0.001/0.001	0inputs+0outputs (0major+681minor)pagefaults 0swaps