Certificate for #1646 ⟨a, b | aab=bb, aba=a⟩

Back:⟨a, b | aab=bb, aba=a⟩

Completion settings:

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3].

[2] aba=a

Axiom: aba=a.

Defines rule #3.

Referenced by [4], [5].

[3] baab=aaaab

Overlap of [1] bb=aab with [1] bb=aab:

b b bb

Critical pair: baab=aabb.

Reduce RHS:

[1]aa(bb)
⇒ aaaab

Referenced by [4].

[4] baa=aaaa

Overlap of [3] baab=aaaab with [2] aba=a:

ba ab aba

Critical pair: baa=aaaaba.

Reduce RHS:

[2]aaa(aba)
⇒ aaaa

Defines rule #2.

Referenced by [5].

[5] aaaaa=aa

Overlap of [2] aba=a with [4] baa=aaaa:

a ba baa

Critical pair: aaaaa=aa.

Defines rule #1.