YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(b 1)
(a 1)
(c 1)
(fSNonEmpty)
)
(RULES
b(b(c(a(b(c(x)))))) -> a(b(b(c(b(c(a(x)))))))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

Problem 1: 
Not CS-TRS Procedure:
R is not a CS-TRS

Problem 1: 
Linearity Procedure:
Linear?
YES

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(b 1)
(a 1)
(c 1)
(fSNonEmpty)
)
(RULES
b(b(c(a(b(c(x)))))) -> a(b(b(c(b(c(a(x)))))))
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 b(b(c(a(b(c(x)))))) -> a(b(b(c(b(c(a(x)))))))
-> Vars:
 x

-> Rlps:
 (rule: b(b(c(a(b(c(x)))))) -> a(b(b(c(b(c(a(x))))))), id: 1, possubterms: b(b(c(a(b(c(x))))))->[], b(c(a(b(c(x)))))->[1], c(a(b(c(x))))->[1, 1], a(b(c(x)))->[1, 1, 1], b(c(x))->[1, 1, 1, 1], c(x)->[1, 1, 1, 1, 1])

-> Unifications:


-> Critical pairs info:


-> Problem conclusions:
 Left linear, Right linear, Linear
 Weakly orthogonal, Almost orthogonal, Orthogonal
 Huet-Levy confluent, Not Newman confluent
 R is a TRS 


The problem is confluent.