NO

Problem 1: 


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


Problem 1: 

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

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

Huet Levy Ordered by Num of Vars and Symbs Procedure:
-> Rules:
 b -> h(h(c,f(b)),a)
 f(b) -> b
-> Vars:


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

-> Unifications:
(R2 unifies with R1 at p: [1], l: f(b), lp: b, sig: {}, l': b, r: b, r': h(h(c,f(b)),a))

-> Critical pairs info:
<f(h(h(c,f(b)),a)),b>   =>  Not trivial, Not overlay, Proper, NW0, N1

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


Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(REPLACEMENT-MAP
(b)
(f 1)
(a)
(c)
(fSNonEmpty)
(h 1, 2)
)
(RULES
b -> h(h(c,f(b)),a)
f(b) -> b
)
Critical Pairs:
<f(h(h(c,f(b)),a)),b>   =>  Not trivial, Not overlay, Proper, NW0, N1
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

No Convergence InfChecker Procedure:
Infeasible convergence?
YES

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty vNonEmpty z0)
(STRATEGY CONTEXTSENSITIVE
(b)
(f 1)
(a)
(c)
(fSNonEmpty)
(h 1 2)
)
(RULES
b -> h(h(c,f(b)),a)
f(b) -> b
)]
Infeasibility Conditions:
f(h(h(c,f(b)),a)) ->* z0, b ->* z0

Problem 1: 

Obtaining a model using AGES:

 -> Theory (Usable Rules):
b -> h(h(c,f(b)),a)
f(b) -> b

 -> AGES Output:




The problem is infeasible.


The problem is not confluent.