Certificate for #12238 ⟨a, b | aaab=aa, bbba=a

Completion settings:

[1] aaab=aa

Axiom: aaab=aa.

Referenced by [3], [4], [5], [6], [7].

[2] bbba=a

Axiom: bbba=a.

Defines rule #3.

Referenced by [3].

[3] aabba=aaaa

Overlap of [1] aaab=aa with [2] bbba=a:

aaa b bbba

Critical pair: aaaa=aabba.

Flip LHS and RHS.

Referenced by [4].

[4] aaba=aaaaa

Overlap of [1] aaab=aa with [3] aabba=aaaa:

a aab aabba

Critical pair: aaaaa=aaba.

Flip LHS and RHS.

Referenced by [5].

[5] aaaaaa=aaa

Overlap of [1] aaab=aa with [4] aaba=aaaaa:

a aab aaba

Critical pair: aaaaaa=aaa.

Referenced by [6].

[6] aaaaa=aa

Overlap of [5] aaaaaa=aaa with [1] aaab=aa:

aaa aaa aaab

Critical pair: aaaaa=aaab.

Reduce RHS:

[1](aaab)
aa

Defines rule #1.

Referenced by [7].

[7] aab=aaaa

Overlap of [6] aaaaa=aa with [1] aaab=aa:

aa aaa aaab

Critical pair: aaaa=aab.

Flip LHS and RHS.

Defines rule #2.