Properties of a Automatic Group

Subsections

• Automatic Group Predicates

Automatic Group Predicates

IsConfluent(G) : GrpAtc -> BoolElt

Returns true if G is confluent, false otherwise.

Example GrpAtc_IsConfluent (H31E7)

> FG<a,b> := FreeGroup(2);
> Q := quo< FG | a^5=1, b^5=1, b*a*b^-1*b^-1*a^-1*a^-1=1>;
> G := AutomaticGroup(Q);
Running Knuth-Bendix with the following parameter values
MaxRelations  = 200
MaxStates     = 0
TidyInt       = 20
MaxWdiffs     = 512
HaltingFactor = 100
MinTime       = 5
#System is confluent.
#Halting with 63 equations.
#First word-difference machine with 45 states computed.
#Second word-difference machine with 49 states computed.
#System is confluent, or halting factor condition holds.
#Word-acceptor with 18 states computed.
#General multiplier with 128 states computed.
#Multiplier incorrect with generator number 4.
#General multiplier with 130 states computed.
#Validity test on general multiplier succeeded.
#General length-2 multiplier with 324 states computed.
#Checking inverse and short relations.
#Checking relation:  _1^3 = _2^2
#Checking relation:  _3^3 = _4^2
#Checking relation:  _3*_1*_4 = _1^2*_3
#Axiom checking succeeded.
> IsConfluent(G);
true