Certificate for #15901 ⟨a, b | aba=ab, bbbba=a⟩

Back:⟨a, b | aba=ab, bbbba=a⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #4.

Referenced by [3], [4], [6].

[2] bbbba=a

Axiom: bbbba=a.

Defines rule #2.

Referenced by [5].

[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 #5.

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 #6.

[5] aa=abbbb

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

abb a abba

Critical pair: abbabb=abbbba.

Reduce LHS:

[3](abba)bb
⇒ abbbb

Reduce RHS:

[2]a(bbbba)
⇒ aa

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

[6] abbbbb=ab

Overlap of [1] aba=ab with [5] aa=abbbb:

ab a aa

Critical pair: ababbbb=aba.

Reduce LHS:

[1](aba)bbbb
⇒ abbbbb

Reduce RHS:

[1](aba)
⇒ ab

Defines rule #1.