YES

Problem 1: 


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


Problem 1: 

CleanTRS Procedure:
R was updated by simple cleaning of the TRS

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


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

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


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

-> 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.