NO
Problem 1:
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Confluence Problem:
(VAR vNonEmpty x)
(REPLACEMENT-MAP
(a 1)
(b 1)
(fSNonEmpty)
)
(RULES
a(b(a(x))) -> a(b(a(a(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)
(fSNonEmpty)
)
(RULES
a(b(a(x))) -> a(b(a(a(b(x)))))
)
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Huet Levy Ordered by Num of Vars and Symbs Procedure:
-> Rules:
a(b(a(x))) -> a(b(a(a(b(x)))))
-> Vars:
x
-> Rlps:
(rule: a(b(a(x))) -> a(b(a(a(b(x))))), id: 1, possubterms: a(b(a(x)))->[], b(a(x))->[1], a(x)->[1, 1])
-> Unifications:
(R1 unifies with R1 at p: [1,1], l: a(b(a(x))), lp: a(x), sig: {x -> b(a(x'))}, l': a(b(a(x'))), r: a(b(a(a(b(x))))), r': a(b(a(a(b(x'))))))
-> Critical pairs info:
=> 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:
(VAR x x')
(REPLACEMENT-MAP
(a 1)
(b 1)
(fSNonEmpty)
)
(RULES
a(b(a(x))) -> a(b(a(a(b(x)))))
)
Critical Pairs:
=> Not trivial, Not 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_x1)
(fSNonEmpty)
)
(RULES
a(b(a(x))) -> a(b(a(a(b(x)))))
)]
Infeasibility Conditions:
a(b(a(b(a(a(b(c_x1))))))) ->* z0, a(b(a(a(b(b(a(c_x1))))))) ->* z0
Problem 1:
Obtaining a model using AGES:
-> Theory (Usable Rules):
a(b(a(x))) -> a(b(a(a(b(x)))))
-> AGES Output:
The problem is infeasible.
The problem is not confluent.