Certificate for #4206 ⟨a, b | aabbbbaab=aa⟩

Back:⟨a, b | aabbbbaab=aa⟩

Completion settings:

[1] aabbbbaab=aa

Axiom: aabbbbaab=aa.

Defines rule #5.

Referenced by [2], [3], [4], [5].

[2] aabbbaab=aabbbbaa

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

aabbbb aab aabbbbaab

Critical pair: aabbbbaa=aabbbaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] aabbaab=aabbbaa

Overlap of [1] aabbbbaab=aa with [2] aabbbaab=aabbbbaa:

aabbbb aab aabbbaab

Critical pair: aabbbbaabbbbaa=aabbaab.

Reduce LHS:

[1](aabbbbaab)bbbaa
⇒ aabbbaa

Flip LHS and RHS.

Defines rule #3.

[4] aabaab=aabbaa

Overlap of [2] aabbbaab=aabbbbaa with [2] aabbbaab=aabbbbaa:

aabbb aab aabbbaab

Critical pair: aabbbaabbbbaa=aabbbbaabbaab.

Reduce LHS:

[2](aabbbaab)bbbaa
[1]⇒ (aabbbbaab)bbaa
⇒ aabbaa

Reduce RHS:

[1](aabbbbaab)baab
⇒ aabaab

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] aaaab=aabaa

Overlap of [1] aabbbbaab=aa with [4] aabaab=aabbaa:

aabbbb aab aabaab

Critical pair: aabbbbaabbaa=aaaab.

Reduce LHS:

[1](aabbbbaab)baa
⇒ aabaa

Flip LHS and RHS.

Defines rule #1.