Certificate for #2348 ⟨a, b | abbaaab=bab⟩

Back:⟨a, b | abbaaab=bab⟩

Completion settings:

[1] abbaaab=bab

Axiom: abbaaab=bab.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [3], [4], [5], [6].

[3] abbaaab=bc

Simplify [1] abbaaab=bab.

Reduce RHS:

[2]b(ab)
⇒ bc

Referenced by [4].

[4] cbaac=bc

Overlap of [3] abbaaab=bc with [2] ab=c:

abbaaab ab

Critical pair: cbaaab=bc.

Reduce LHS:

[2]cbaa(ab)
⇒ cbaac

Defines rule #2.

Referenced by [5], [7].

[5] bbc=cbacc

Overlap of [4] cbaac=bc with [4] cbaac=bc:

cbaa c cbaac

Critical pair: cbaabc=bcbaac.

Reduce LHS:

[2]cba(ab)c
⇒ cbacc

Reduce RHS:

[4]b(cbaac)
⇒ bbc

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

[6] acbacc=cbc

Overlap of [2] ab=c with [5] bbc=cbacc:

a b bbc

Critical pair: acbacc=cbc.

Defines rule #3.

[7] cbacbc=bcbacc

Overlap of [5] bbc=cbacc with [4] cbaac=bc:

bb c cbaac

Critical pair: bbbc=cbaccbaac.

Reduce LHS:

[5]b(bbc)
⇒ bcbacc

Reduce RHS:

[4]cbac(cbaac)
⇒ cbacbc

Flip LHS and RHS.

Defines rule #5.