NO

Problem 1: 


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(a 1)
(b 1)
(c 1)
(d 1)
(fSNonEmpty)
)
(RULES
a(x) -> a(b(x))
a(x) -> b(c(x))
b(x) -> c(d(x))
c(x) -> b(d(x))
d(x) -> c(b(x))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::


Problem 1: 

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

Problem 1: 
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(a 1)
(b 1)
(c 1)
(d 1)
(fSNonEmpty)
)
(RULES
a(x) -> a(b(x))
a(x) -> b(c(x))
b(x) -> c(d(x))
c(x) -> b(d(x))
d(x) -> c(b(x))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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

-> Rlps:
 (rule: a(x) -> a(b(x)), id: 1, possubterms: a(x)->[])
 (rule: a(x) -> b(c(x)), id: 2, possubterms: a(x)->[])
 (rule: b(x) -> c(d(x)), id: 3, possubterms: b(x)->[])
 (rule: c(x) -> b(d(x)), id: 4, possubterms: c(x)->[])
 (rule: d(x) -> c(b(x)), id: 5, possubterms: d(x)->[])

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

-> Critical pairs info:
<a(b(x')),b(c(x'))>   =>  Not trivial, 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:
(VAR x x')
(REPLACEMENT-MAP
(a 1)
(b 1)
(c 1)
(d 1)
(fSNonEmpty)
)
(RULES
a(x) -> a(b(x))
a(x) -> b(c(x))
b(x) -> c(d(x))
c(x) -> b(d(x))
d(x) -> c(b(x))
)
Critical Pairs:
<a(b(x')),b(c(x'))>   =>  Not trivial, Overlay, Proper, NW0, N1
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

No Convergence InfChecker Procedure:
Infeasible convergence?
YES

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty x x1 vNonEmpty z0)
(STRATEGY CONTEXTSENSITIVE
(a 1)
(b 1)
(c 1)
(d 1)
(c_x1)
(fSNonEmpty)
)
(RULES
a(x) -> a(b(x))
a(x) -> b(c(x))
b(x) -> c(d(x))
c(x) -> b(d(x))
d(x) -> c(b(x))
)]
Infeasibility Conditions:
a(b(c_x1)) ->* z0, b(c(c_x1)) ->* z0

Problem 1: 

Obtaining a model using AGES:

 -> Theory (Usable Rules):
a(x) -> a(b(x))
a(x) -> b(c(x))
b(x) -> c(d(x))
c(x) -> b(d(x))
d(x) -> c(b(x))

 -> AGES Output:




The problem is infeasible.


The problem is not confluent.