Certificate for #1991 ⟨a, b | aabbaabb=ba

Completion settings:

[1] aabbaabb=ba

Axiom: aabbaabb=ba.

Referenced by [4].

[2] abb=c

Axiom: abb=c.

Defines rule #10.

Referenced by [4], [6], [7], [12].

[3] ac=d

Axiom: ac=d.

Defines rule #5.

Referenced by [4], [5].

[4] ba=dd

Overlap of [1] aabbaabb=ba with [2] abb=c:

a abbaabb abb

Critical pair: acaabb=ba.

Reduce LHS:

[3](ac)aabb
[2]da(abb)
[3]d(ac)
dd

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6], [7], [9].

[5] bd=ddc

Overlap of [4] ba=dd with [3] ac=d:

b a ac

Critical pair: bd=ddc.

Defines rule #1.

Referenced by [6], [8], [9], [10], [13].

[6] addcd=ca

Overlap of [2] abb=c with [4] ba=dd:

ab b ba

Critical pair: abdd=ca.

Reduce LHS:

[5]a(bd)d
addcd

Defines rule #6.

Referenced by [11].

[7] ddbb=bc

Overlap of [4] ba=dd with [2] abb=c:

b a abb

Critical pair: bc=ddbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9], [10], [11], [13].

[8] bbc=ddcdbb

Overlap of [5] bd=ddc with [7] ddbb=bc:

b d ddbb

Critical pair: bbc=ddcdbb.

Defines rule #9.

Referenced by [13].

[9] bca=ddddcd

Overlap of [7] ddbb=bc with [4] ba=dd:

ddb b ba

Critical pair: ddbdd=bca.

Reduce LHS:

[5]dd(bd)d
ddddcd

Flip LHS and RHS.

Defines rule #8.

Referenced by [12].

[10] bcd=ddddcdc

Overlap of [7] ddbb=bc with [5] bd=ddc:

ddb b bd

Critical pair: ddbddc=bcd.

Reduce LHS:

[5]dd(bd)dc
ddddcdc

Flip LHS and RHS.

Defines rule #2.

[11] addcbc=cadbb

Overlap of [6] addcd=ca with [7] ddbb=bc:

addc d ddbb

Critical pair: addcbc=cadbb.

Defines rule #12.

[12] bcc=ddddcdbb

Overlap of [9] bca=ddddcd with [2] abb=c:

bc a abb

Critical pair: bcc=ddddcdbb.

Defines rule #7.

[13] bcbc=ddddcdcdbb

Overlap of [7] ddbb=bc with [8] bbc=ddcdbb:

ddb b bbc

Critical pair: ddbddcdbb=bcbc.

Reduce LHS:

[5]dd(bd)dcdbb
ddddcdcdbb

Flip LHS and RHS.

Defines rule #11.