Certificate for #1601 ⟨a, b | aaa=bb, aab=b⟩

Back:⟨a, b | aaa=bb, aab=b⟩

Completion settings:

[1] aaa=bb

Axiom: aaa=bb.

Defines rule #2.

Referenced by [3], [4].

[2] aab=b

Axiom: aab=b.

Defines rule #3.

Referenced by [4], [6].

[3] bba=abb

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

a aa aaa

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [6].

[4] bbb=ab

Overlap of [1] aaa=bb with [2] aab=b:

a aa aab

Critical pair: ab=bbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6].

[5] bab=abb

Overlap of [4] bbb=ab with [4] bbb=ab:

b bb bbb

Critical pair: bab=abb.

Referenced by [6].

[6] ba=ab

Overlap of [5] bab=abb with [3] bba=abb:

ba b bba

Critical pair: baabb=abbba.

Reduce LHS:

[2]b(aab)b
[4]⇒ (bbb)
⇒ ab

Reduce RHS:

[4]a(bbb)a
[2]⇒ (aab)a
⇒ ba

Flip LHS and RHS.

Defines rule #1.