NO

Problem 1: 


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


Problem 1: 

Problem 1: 

Modular Confluence Combinations Decomposition Procedure:
TRS combination:
{b -> f(h(a,a))
 f(a) -> b
 h(a,b) -> a}
{c -> a}
Not disjoint
Constructor-sharing
Not composable
Left linear
Not layer-preserving
TRS1
Just (STRATEGY CONTEXTSENSITIVE
(b)
(f 1)
(h 1 2)
(a)
)
(RULES
b -> f(h(a,a))
f(a) -> b
h(a,b) -> a
)

TRS2
Just (STRATEGY CONTEXTSENSITIVE
(c)
(a)
)
(RULES
c -> a
)

Problem 1: 


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


Problem 1: 

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

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

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


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

-> Unifications:
(R3 unifies with R1 at p: [2], l: h(a,b), lp: b, sig: {}, l': b, r: a, r': f(h(a,a)))

-> Critical pairs info:
<h(a,f(h(a,a))),a>   =>  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: 
No Convergence Brute Force Procedure:
-> Rewritings:
s: h(a,f(h(a,a)))
Nodes: [0]
Edges: []
ID: 0 => ('h(a,f(h(a,a)))', D0)
t: a
Nodes: [0]
Edges: []
ID: 0 => ('a', D0)
h(a,f(h(a,a))) ->* no union *<- a
"Not joinable"

The problem is not confluent.