Certificate for #1500 ⟨a, b | abaabbabab=1⟩

Back:⟨a, b | abaabbabab=1⟩

Completion settings:

[1] abaabbabab=1

Axiom: abaabbabab=1.

Referenced by [2], [3].

[2] abaabbab=aabbabab

Overlap of [1] abaabbabab=1 with [1] abaabbabab=1:

abaabbab ab abaabbabab

Critical pair: abaabbab=aabbabab.

Referenced by [3], [4].

[3] aabbababab=1

Overlap of [1] abaabbabab=1 with [2] abaabbab=aabbabab:

abaabbabab abaabbab

Critical pair: aabbababab=1.

Defines rule #2.

Referenced by [4], [5].

[4] abaabbaabbabab=aabb

Overlap of [2] abaabbab=aabbabab with [2] abaabbab=aabbabab:

abaabb ab abaabbab

Critical pair: abaabbaabbabab=aabbababaabbab.

Reduce RHS:

[2]aabbab(abaabbab)
[2]⇒ aabb(abaabbab)ab
[3]⇒ aabb(aabbababab)
⇒ aabb

Referenced by [5].

[5] abaabb=aabbab

Overlap of [4] abaabbaabbabab=aabb with [3] aabbababab=1:

abaabb aabbabab aabbababab

Critical pair: abaabb=aabbab.

Defines rule #1.