Certificate for #15904 ⟨a, b | aba=ab, bbbbb=b⟩

Back:⟨a, b | aba=ab, bbbbb=b⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [4].

[2] bbbbb=b

Axiom: bbbbb=b.

Defines rule #4.

[3] abba=abb

Overlap of [1] aba=ab with [1] aba=ab:

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] abbba=abbb

Overlap of [1] aba=ab with [3] abba=abb:

ab a abba

Critical pair: ababb=abbba.

Reduce LHS:

[1](aba)bb
⇒ abbb

Flip LHS and RHS.

Defines rule #3.

[5] abbbba=abbbb

Overlap of [3] abba=abb with [3] abba=abb:

abb a abba

Critical pair: abbabb=abbbba.

Reduce LHS:

[3](abba)bb
⇒ abbbb

Flip LHS and RHS.

Defines rule #5.