Certificate for #28284 ⟨a, b | aa=1, bbabb=babb

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

[2] bbabb=babb

Axiom: bbabb=babb.

Referenced by [4].

[3] bb=c

Axiom: bb=c.

Defines rule #3.

Referenced by [4], [5], [6], [7].

[4] bbabb=bac

Simplify [2] bbabb=babb.

Reduce RHS:

[3]ba(bb)
bac

Referenced by [5].

[5] bac=cac

Overlap of [4] bbabb=bac with [3] bb=c:

bbabb bb

Critical pair: cabb=bac.

Reduce LHS:

[3]ca(bb)
cac

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

[6] bc=cb

Overlap of [3] bb=c with [3] bb=c:

b b bb

Critical pair: bc=cb.

Defines rule #2.

Referenced by [7].

[7] ccac=cac

Overlap of [3] bb=c with [5] bac=cac:

b b bac

Critical pair: bcac=cac.

Reduce LHS:

[6](bc)ac
[5]c(bac)
ccac

Defines rule #5.