Certificate for #1948 ⟨a, b | aabaabaa=ab⟩

Back:⟨a, b | aabaabaa=ab⟩

Completion settings:

[1] aabaabaa=ab

Axiom: aabaabaa=ab.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Defines rule #3.

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

[3] aabaabaa=c

Simplify [1] aabaabaa=ab.

Reduce RHS:

[2](ab)
⇒ c

Referenced by [4].

[4] acacaa=c

Overlap of [3] aabaabaa=c with [2] ab=c:

a abaabaa ab

Critical pair: acaabaa=c.

Reduce LHS:

[2]aca(ab)aa
⇒ acacaa

Defines rule #1.

Referenced by [5], [6].

[5] cb=acacac

Overlap of [4] acacaa=c with [2] ab=c:

acaca a ab

Critical pair: acacac=cb.

Flip LHS and RHS.

Defines rule #4.

[6] ccacaa=acacac

Overlap of [4] acacaa=c with [4] acacaa=c:

acaca a acacaa

Critical pair: acacac=ccacaa.

Flip LHS and RHS.

Defines rule #2.