Certificate for #20240 ⟨a, b | aba=a, babb=bba⟩

Back:⟨a, b | aba=a, babb=bba⟩

Completion settings:

[1] aba=a

Axiom: aba=a.

Defines rule #3.

Referenced by [3], [4].

[2] bba=babb

Axiom: babb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] babbbb=babb

Overlap of [2] bba=babb with [1] aba=a:

bb a aba

Critical pair: bba=babbba.

Reduce LHS:

[2](bba)
⇒ babb

Reduce RHS:

[2]bab(bba)
[2]⇒ ba(bba)bb
[1]⇒ b(aba)bbbb
⇒ babbbb

Flip LHS and RHS.

Referenced by [4].

[4] abbbb=abb

Overlap of [1] aba=a with [3] babbbb=babb:

a ba babbbb

Critical pair: ababb=abbbb.

Reduce LHS:

[1](aba)bb
⇒ abb

Flip LHS and RHS.

Defines rule #1.