YES
(ignored inputs)COMMENT from the collection of \cite{AT2012}
Rewrite Rules:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T,
     and3(?x,?y,?z) -> and3(?y,?z,?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ F = and3(?y,F,?x),
     T = and3(T,T,T) ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ and3(?y,F,?x) = F,
     and3(T,T,T) = T,
     F = and3(?y,F,?x),
     T = and3(T,T,T) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <and3(?y_1,F,?x_1), F> by Rules <2, 0> preceded by []
 joinable by a reduction of rules <[([],2),([],2),([],0)], []>
Critical Pair <and3(T,T,T), T> by Rules <2, 1> preceded by []
 joinable by a reduction of rules <[([],1)], []>
unknown Diagram Decreasing
check Non-Confluence...
obtain 13 rules by 3 steps unfolding
strenghten and3(?x_6,F,?z_6) and F
strenghten and3(?x_8,?y_8,F) and F
strenghten and3(F,?x_5,?y_5) and F
strenghten and3(T,T,T) and T
strenghten and3(?y_10,?z_10,?x_10) and and3(?x_10,?y_10,?z_10)
obtain 6 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Root-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
unknown Huet (modulo AC)
check by Reduction-Preserving Completion...
STEP: 1 (parallel)
S:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T ]
P:
   [ and3(?x,?y,?z) -> and3(?y,?z,?x) ]
S: terminating
CP(S,S):
PCP_in(symP,S):
CP(S,symP):
<F, and3(?y,F,?x)> --> <F, and3(?y,F,?x)> => no
<F, and3(F,?x,?y)> --> <F, and3(F,?x,?y)> => no
<T, and3(T,T,T)> --> <T, T> => yes
<T, and3(T,T,T)> --> <T, T> => yes
check joinability condition:
check modulo reachablity from F to and3(?y,F,?x): maybe not reachable
check modulo reachablity from F to and3(F,?x,?y): maybe not reachable
failed
failure(Step 1)
   [ and3(?y,F,?x) -> F,
     and3(F,?x,?y) -> F ]
Added S-Rules:
   [ and3(?y,F,?x) -> F,
     and3(F,?x,?y) -> F ]
Added P-Rules:
   [ ]
STEP: 2 (linear)
S:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T ]
P:
   [ and3(?x,?y,?z) -> and3(?y,?z,?x) ]
S: terminating
CP(S,S):
CP_in(symP,S):
CP(S,symP):
<F, and3(?y,F,?x)> --> <F, and3(?y,F,?x)> => no
<F, and3(F,?x,?y)> --> <F, and3(F,?x,?y)> => no
<T, and3(T,T,T)> --> <T, T> => yes
<T, and3(T,T,T)> --> <T, T> => yes
check joinability condition:
check modulo reachablity from F to and3(?y,F,?x): maybe not reachable
check modulo reachablity from F to and3(F,?x,?y): maybe not reachable
failed
failure(Step 2)
   [ and3(?y,F,?x) -> F,
     and3(F,?x,?y) -> F ]
Added S-Rules:
   [ and3(?y,F,?x) -> F,
     and3(F,?x,?y) -> F ]
Added P-Rules:
   [ ]
STEP: 3 (relative)
S:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T ]
P:
   [ and3(?x,?y,?z) -> and3(?y,?z,?x) ]
Check relative termination:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T ]
   [ and3(?x,?y,?z) -> and3(?y,?z,?x) ]
Polynomial Interpretation:
  F:= 0
  T:= 0
  and3:= (4)+(1)*x1+(7)*x1*x1+(14)*x1*x2*x3+(1)*x2+(7)*x2*x2+(1)*x3+(7)*x3*x3
relatively terminating
S/P: relatively terminating
check CP condition:
failed
failure(Step 3)
STEP: 4 (parallel)
S:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T,
     and3(?y,F,?x) -> F,
     and3(F,?x,?y) -> F ]
P:
   [ and3(?x,?y,?z) -> and3(?y,?z,?x) ]
S: terminating
CP(S,S):
<F, F> --> <F, F> => yes
<F, F> --> <F, F> => yes
<F, F> --> <F, F> => yes
PCP_in(symP,S):
CP(S,symP):
<F, and3(?y,F,?x)> --> <F, F> => yes
<F, and3(F,?x,?y)> --> <F, F> => yes
<T, and3(T,T,T)> --> <T, T> => yes
<T, and3(T,T,T)> --> <T, T> => yes
<F, and3(F,?x,?y)> --> <F, F> => yes
<F, and3(?x,?y,F)> --> <F, F> => yes
<F, and3(?x,?y,F)> --> <F, F> => yes
<F, and3(?y,F,?x)> --> <F, F> => yes
S:
   [ and3(?x,?y,F) -> F,
     and3(T,T,T) -> T,
     and3(?y,F,?x) -> F,
     and3(F,?x,?y) -> F ]
P:
   [ and3(?x,?y,?z) -> and3(?y,?z,?x) ]
Success
Reduction-Preserving Completion
Direct Methods: CR

Final result: CR
130.trs: Success(CR)
(138 msec.)