YES

Problem 1: 


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


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(c) -> b
h(f(f(f(h(c,h(b,c))))),h(f(f(b)),b)) -> f(h(b,f(a)))
)
Linear:YES
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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


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