Certificate for #8073 ⟨a, b | aaa=1, abbb=bab⟩

Back:⟨a, b | aaa=1, abbb=bab⟩

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #4.

Referenced by [4].

[2] bab=abbb

Axiom: abbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] baabbb=aabbbbbbb

Overlap of [2] bab=abbb with [2] bab=abbb:

ba b bab

Critical pair: baabbb=abbbab.

Reduce RHS:

[2]abb(bab)
[2]⇒ ab(bab)bb
[2]⇒ a(bab)bbbb
⇒ aabbbbbbb

Defines rule #3.

Referenced by [4].

[4] bbbbbbbbbbbbbbb=bbbbbbbb

Overlap of [2] bab=abbb with [3] baabbb=aabbbbbbb:

ba b baabbb

Critical pair: baaabbbbbbb=abbbaabbb.

Reduce LHS:

[1]b(aaa)bbbbbbb
⇒ bbbbbbbb

Reduce RHS:

[3]abb(baabbb)
[3]⇒ ab(baabbb)bbbb
[3]⇒ a(baabbb)bbbbbbbb
[1]⇒ (aaa)bbbbbbbbbbbbbbb
⇒ bbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.