Certificate for #4685 ⟨a, b | aaab=b, abbb=a⟩

Back:⟨a, b | aaab=b, abbb=a⟩

Completion settings:

[1] aaab=b

Axiom: aaab=b.

Defines rule #3.

Referenced by [3], [4].

[2] abbb=a

Axiom: abbb=a.

Referenced by [3], [5].

[3] bbb=aaa

Overlap of [1] aaab=b with [2] abbb=a:

aa ab abbb

Critical pair: aaa=bbb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] baaa=b

Overlap of [3] bbb=aaa with [3] bbb=aaa:

b bb bbb

Critical pair: baaa=aaab.

Reduce RHS:

[1](aaab)
⇒ b

Defines rule #4.

Referenced by [5].

[5] aaaa=a

Overlap of [2] abbb=a with [4] baaa=b:

abb b baaa

Critical pair: abbb=aaaa.

Reduce LHS:

[2](abbb)
⇒ a

Flip LHS and RHS.

Defines rule #2.