Certificate for #19840 ⟨a, b | aaa=a, babb=bba⟩

Back:⟨a, b | aaa=a, babb=bba⟩

Completion settings:

[1] aaa=a

Axiom: aaa=a.

Defines rule #3.

Referenced by [3].

[2] bba=babb

Axiom: babb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] babababb=babb

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

bb a aaa

Critical pair: bba=babbaa.

Reduce LHS:

[2](bba)
⇒ babb

Reduce RHS:

[2]ba(bba)a
[2]⇒ baba(bba)
⇒ babababb

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] babbbbbbbbbb=babbbb

Overlap of [2] bba=babb with [3] babababb=babb:

b ba babababb

Critical pair: bbabb=babbbababb.

Reduce LHS:

[2](bba)bb
⇒ babbbb

Reduce RHS:

[2]bab(bba)babb
[2]⇒ ba(bba)bbbabb
[2]⇒ bababbb(bba)bb
[2]⇒ bababb(bba)bbbb
[2]⇒ babab(bba)bbbbbb
[2]⇒ baba(bba)bbbbbbbb
[3]⇒ (babababb)bbbbbbbb
⇒ babbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.