Certificate for #19507 ⟨a, b | aab=b, aaaaa=bb⟩

Back:⟨a, b | aab=b, aaaaa=bb⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [3], [6].

[2] aaaaa=bb

Axiom: aaaaa=bb.

Defines rule #4.

Referenced by [3], [4].

[3] bbb=ab

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

aaa aa aab

Critical pair: aaab=bbb.

Reduce LHS:

[1]a(aab)
⇒ ab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

[4] bba=abb

Overlap of [2] aaaaa=bb with [2] aaaaa=bb:

a aaaa aaaaa

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [6].

[5] bab=abb

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

b bb bbb

Critical pair: bab=abb.

Referenced by [6].

[6] ba=ab

Overlap of [5] bab=abb with [4] bba=abb:

ba b bba

Critical pair: baabb=abbba.

Reduce LHS:

[1]b(aab)b
[3]⇒ (bbb)
⇒ ab

Reduce RHS:

[3]a(bbb)a
[1]⇒ (aab)a
⇒ ba

Flip LHS and RHS.

Defines rule #1.