Certificate for #1555 ⟨a, b | aaaaaabaa=a⟩

Completion settings:

[1] aaaaaabaa=a

Axiom: aaaaaabaa=a.

Referenced by [2], [3], [4], [5], [6].

[2] aaaaabaa=aaaaaaba

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

aaaaaab aa aaaaaabaa

Critical pair: aaaaaaba=aaaaabaa.

Flip LHS and RHS.

Referenced by [3], [4], [5], [6].

[3] aaaabaa=aaaaaba

Overlap of [1] aaaaaabaa=a with [2] aaaaabaa=aaaaaaba:

aaaaaab aa aaaaabaa

Critical pair: aaaaaabaaaaaaba=aaaabaa.

Reduce LHS:

[1](aaaaaabaa)aaaaba
⇒ aaaaaba

Flip LHS and RHS.

Referenced by [5].

[4] aaabaa=aaaaba

Overlap of [2] aaaaabaa=aaaaaaba with [2] aaaaabaa=aaaaaaba:

aaaaab aa aaaaabaa

Critical pair: aaaaabaaaaaaba=aaaaaabaaaabaa.

Reduce LHS:

[2](aaaaabaa)aaaaba
[1]⇒ (aaaaaabaa)aaaba
⇒ aaaaba

Reduce RHS:

[1](aaaaaabaa)aabaa
⇒ aaabaa

Flip LHS and RHS.

Referenced by [5].

[5] abaa=aaba

Overlap of [4] aaabaa=aaaaba with [2] aaaaabaa=aaaaaaba:

aaab aa aaaaabaa

Critical pair: aaabaaaaaaba=aaaabaaaabaa.

Reduce LHS:

[4](aaabaa)aaaaba
[3]⇒ (aaaabaa)aaaba
[2]⇒ (aaaaabaa)aaba
[1]⇒ (aaaaaabaa)aba
⇒ aaba

Reduce RHS:

[3](aaaabaa)aabaa
[2]⇒ (aaaaabaa)abaa
[1]⇒ (aaaaaabaa)baa
⇒ abaa

Flip LHS and RHS.

Defines rule #1.

[6] aaaaaaaba=a

Overlap of [1] aaaaaabaa=a with [2] aaaaabaa=aaaaaaba:

a aaaaabaa aaaaabaa

Critical pair: aaaaaaaba=a.

Defines rule #2.