YES

Problem 1: 


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


Problem 1: 

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

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


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
(c)
(f 1)
(h 1, 2)
(a)
(b)
(fSNonEmpty)
)
(RULES
f(f(h(h(f(a),a),c))) -> f(h(f(c),b))
h(f(f(c)),b) -> f(h(h(h(c,h(f(h(c,f(b))),a)),b),c))
h(f(h(f(b),h(h(f(h(c,f(c))),b),a))),h(a,c)) -> c
)
Linear:YES
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Huet Levy Procedure:
-> Rules:
 f(f(h(h(f(a),a),c))) -> f(h(f(c),b))
 h(f(f(c)),b) -> f(h(h(h(c,h(f(h(c,f(b))),a)),b),c))
 h(f(h(f(b),h(h(f(h(c,f(c))),b),a))),h(a,c)) -> c
-> Vars:


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