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 M:S N:S X:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(and 1)
0.001/0.001	(plus 1 2)
0.001/0.001	(x 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	(tt)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	and(tt,X:S) -> X:S
0.001/0.001	plus(N:S,0) -> N:S
0.001/0.001	plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
0.001/0.001	x(N:S,0) -> 0
0.001/0.001	x(N:S,s(M:S)) -> plus(x(N:S,M:S),N: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 M:S N:S X:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(and 1)
0.001/0.001	(plus 1 2)
0.001/0.001	(x 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	(tt)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	and(tt,X:S) -> X:S
0.001/0.001	plus(N:S,0) -> N:S
0.001/0.001	plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
0.001/0.001	x(N:S,0) -> 0
0.001/0.001	x(N:S,s(M:S)) -> plus(x(N:S,M:S),N: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 M:S N:S X:S)
0.001/0.001	(STRATEGY CONTEXTSENSITIVE
0.001/0.001	(and 1)
0.001/0.001	(plus 1 2)
0.001/0.001	(x 1 2)
0.001/0.001	(0)
0.001/0.001	(fSNonEmpty)
0.001/0.001	(s 1)
0.001/0.001	(tt)
0.001/0.001	)
0.001/0.001	(RULES
0.001/0.001	and(tt,X:S) -> X:S
0.001/0.001	plus(N:S,0) -> N:S
0.001/0.001	plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
0.001/0.001	x(N:S,0) -> 0
0.001/0.001	x(N:S,s(M:S)) -> plus(x(N:S,M:S),N: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) -> X:S
0.001/0.001	 plus(N:S,0) -> N:S
0.001/0.001	 plus(N:S,s(M:S)) -> s(plus(N:S,M:S))
0.001/0.001	 x(N:S,0) -> 0
0.001/0.001	 x(N:S,s(M:S)) -> plus(x(N:S,M:S),N:S)
0.001/0.001	-> Vars:
0.001/0.001	 X, N, M, N, N, M, N
0.001/0.001	-> UVars:
0.001/0.001	 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 2, UV-LActive: [N], UV-RActive: [N], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 3, UV-LActive: [M, N], UV-RActive: [M, N], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 4, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	 (UV-RuleId: 5, UV-LActive: [M, N], UV-RActive: [M, N], UV-LFrozen: [], UV-RFrozen: [])
0.001/0.001	-> FVars:
0.001/0.001	 x4, x5, x6, x7, x8, x9, x10
0.001/0.001	-> PVars:
0.001/0.001	 X: [x4], N: [x5, x7, x8, x10], M: [x6, x9]
0.001/0.001	
0.001/0.001	-> Rlps:
0.001/0.001	 (rule: and(tt,x4:S) -> x4:S, id: 1, possubterms: and(tt,x4:S)->[], tt->[1])
0.001/0.001	 (rule: plus(x5:S,0) -> x5:S, id: 2, possubterms: plus(x5:S,0)->[], 0->[2])
0.001/0.001	 (rule: plus(x7:S,s(x6:S)) -> s(plus(x7:S,x6:S)), id: 3, possubterms: plus(x7:S,s(x6:S))->[], s(x6:S)->[2])
0.001/0.001	 (rule: x(x8:S,0) -> 0, id: 4, possubterms: x(x8:S,0)->[], 0->[2])
0.001/0.001	 (rule: x(x10:S,s(x9:S)) -> plus(x(x10:S,x9:S),x10:S), id: 5, possubterms: x(x10:S,s(x9:S))->[], s(x9: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 36%CPU (0avgtext+0avgdata 8516maxresident)k
0.001/0.001	0inputs+0outputs (0major+664minor)pagefaults 0swaps