Certificate for #349 ⟨a, b | aaaabaa=a⟩

Back:⟨a, b | aaaabaa=a⟩

Completion settings:

[1] aaaabaa=a

Axiom: aaaabaa=a.

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

[2] aaabaa=aaaaba

Overlap of [1] aaaabaa=a with [1] aaaabaa=a:

aaaab aa aaaabaa

Critical pair: aaaaba=aaabaa.

Flip LHS and RHS.

Referenced by [3], [4].

[3] abaa=aaba

Overlap of [2] aaabaa=aaaaba with [2] aaabaa=aaaaba:

aaab aa aaabaa

Critical pair: aaabaaaaba=aaaabaabaa.

Reduce LHS:

[2](aaabaa)aaba
[1]⇒ (aaaabaa)aba
⇒ aaba

Reduce RHS:

[1](aaaabaa)baa
⇒ abaa

Flip LHS and RHS.

Defines rule #1.

[4] aaaaaba=a

Overlap of [1] aaaabaa=a with [2] aaabaa=aaaaba:

a aaabaa aaabaa

Critical pair: aaaaaba=a.

Defines rule #2.