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 v_NonEmpty:S:S M:S:S N:S:S X:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(and 1)
0.001/0.001	(plus 2)
0.001/0.001	(x 2)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	(tt)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	and(tt,X:S:S) -> X:S:S
0.001/0.001	plus(N:S:S,num0) -> N:S:S
0.001/0.001	plus(N:S:S,s(M:S:S)) -> s(plus(N:S:S,M:S:S))
0.001/0.001	x(N:S:S,num0) -> num0
0.001/0.001	x(N:S:S,s(M:S:S)) -> plus(x(N:S:S,M:S:S),N:S: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 v_NonEmpty:S:S M:S:S N:S:S X:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(and 1)
0.001/0.001	(plus 2)
0.001/0.001	(x 2)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	(tt)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	and(tt,X:S:S) -> X:S:S
0.001/0.001	plus(N:S:S,num0) -> N:S:S
0.001/0.001	plus(N:S:S,s(M:S:S)) -> s(plus(N:S:S,M:S:S))
0.001/0.001	x(N:S:S,num0) -> num0
0.001/0.001	x(N:S:S,s(M:S:S)) -> plus(x(N:S:S,M:S:S),N:S: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	Left-Homogeneous u-Replacing Variables Processor:
0.001/0.001	R satisfies LHRV condition
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 v_NonEmpty:S:S M:S:S N:S:S X:S:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(and 1)
0.001/0.001	(plus 2)
0.001/0.001	(x 2)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(num0)
0.001/0.001	(s)
0.001/0.001	(tt)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	and(tt,X:S:S) -> X:S:S
0.001/0.001	plus(N:S:S,num0) -> N:S:S
0.001/0.001	plus(N:S:S,s(M:S:S)) -> s(plus(N:S:S,M:S:S))
0.001/0.001	x(N:S:S,num0) -> num0
0.001/0.001	x(N:S:S,s(M:S:S)) -> plus(x(N:S:S,M:S:S),N:S:S)
0.001/0.001	)
0.001/0.001	:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
0.001/0.001	
0.001/0.001	Huet Levy Processor:
0.001/0.001	-> Rules:
0.001/0.001	 and(tt,X:S:S) -> X:S:S
0.001/0.001	 plus(N:S:S,num0) -> N:S:S
0.001/0.001	 plus(N:S:S,s(M:S:S)) -> s(plus(N:S:S,M:S:S))
0.001/0.001	 x(N:S:S,num0) -> num0
0.001/0.001	 x(N:S:S,s(M:S:S)) -> plus(x(N:S:S,M:S:S),N:S:S)
0.001/0.001	-> Vars:
0.001/0.001	 X:S, N:S, M:S, N:S, N:S, M:S, N:S
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S])
0.001/0.001	-> FVars:
0.001/0.001	 x5, x6, x7, x8, x9, x10, x11
0.001/0.001	-> PVars:
0.001/0.001	 X:S: [x5], N:S: [x6, x8, x9, x11], M:S: [x7, x10]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: and(tt,x5:S) -> x5:S, id: 1, possubterms: and(tt,x5:S)->[], tt->[1])
0.001/0.001	 (rule: plus(x6:S,num0) -> x6:S, id: 2, possubterms: plus(x6:S,num0)->[], num0->[2])
0.001/0.001	 (rule: plus(x8:S,s(x7:S)) -> s(plus(x8:S,x7:S)), id: 3, possubterms: plus(x8:S,s(x7:S))->[], s(x7:S)->[2])
0.001/0.001	 (rule: x(x9:S,num0) -> num0, id: 4, possubterms: x(x9:S,num0)->[], num0->[2])
0.001/0.001	 (rule: x(x11:S,s(x10:S)) -> plus(x(x11:S,x10:S),x11:S), id: 5, possubterms: x(x11:S,s(x10:S))->[], s(x10:S)->[2])
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	 Huet-Levy confluent, Not Newman confluent
0.001/0.001	 R is a CS-TRS, Left-homogeneous u-replacing variables
0.001/0.001	
0.001/0.001	
0.001/0.001	The problem is joinable.
0.001/0.001	0.00user 0.00system 0:00.01elapsed 33%CPU (0avgtext+0avgdata 8236maxresident)k
0.001/0.001	8inputs+0outputs (0major+657minor)pagefaults 0swaps