YES

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty)
(REPLACEMENT-MAP
(f 1)
(h 1, 2)
(a)
(b)
(c)
(fSNonEmpty)
)
(RULES
f(h(a,h(c,a))) -> c
h(c,b) -> f(a)
h(c,c) -> h(b,f(b))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


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)
(REPLACEMENT-MAP
(f 1)
(h 1, 2)
(a)
(b)
(c)
(fSNonEmpty)
)
(RULES
f(h(a,h(c,a))) -> c
h(c,b) -> f(a)
h(c,c) -> h(b,f(b))
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Huet Levy Procedure:
-> Rules:
 f(h(a,h(c,a))) -> c
 h(c,b) -> f(a)
 h(c,c) -> h(b,f(b))
-> Vars:


-> Rlps:
 (rule: f(h(a,h(c,a))) -> c, id: 1, possubterms: f(h(a,h(c,a)))->[], h(a,h(c,a))->[1], a->[1, 1], h(c,a)->[1, 2], c->[1, 2, 1], a->[1, 2, 2])
 (rule: h(c,b) -> f(a), id: 2, possubterms: h(c,b)->[], c->[1], b->[2])
 (rule: h(c,c) -> h(b,f(b)), id: 3, possubterms: h(c,c)->[], c->[1], c->[2])

-> 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.