Certificate for #2000 ⟨a, b | aabbbaab=aa⟩

Back:⟨a, b | aabbbaab=aa⟩

Completion settings:

[1] aabbbaab=aa

Axiom: aabbbaab=aa.

Defines rule #4.

Referenced by [2], [3], [4].

[2] aabbaab=aabbbaa

Overlap of [1] aabbbaab=aa with [1] aabbbaab=aa:

aabbb aab aabbbaab

Critical pair: aabbbaa=aabbaab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] aabaab=aabbaa

Overlap of [1] aabbbaab=aa with [2] aabbaab=aabbbaa:

aabbb aab aabbaab

Critical pair: aabbbaabbbaa=aabaab.

Reduce LHS:

[1](aabbbaab)bbaa
⇒ aabbaa

Flip LHS and RHS.

Defines rule #2.

[4] aaaab=aabaa

Overlap of [2] aabbaab=aabbbaa with [2] aabbaab=aabbbaa:

aabb aab aabbaab

Critical pair: aabbaabbbaa=aabbbaabaab.

Reduce LHS:

[2](aabbaab)bbaa
[1]⇒ (aabbbaab)baa
⇒ aabaa

Reduce RHS:

[1](aabbbaab)aab
⇒ aaaab

Flip LHS and RHS.

Defines rule #1.