Certificate for #22821 ⟨a, b | aaa=1, abbbb=bab

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #4.

Referenced by [4].

[2] bab=abbbb

Axiom: abbbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] baabbbb=aabbbbbbbbbbbbb

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

ba b bab

Critical pair: baabbbb=abbbbab.

Reduce RHS:

[2]abbb(bab)
[2]abb(bab)bbb
[2]ab(bab)bbbbbb
[2]a(bab)bbbbbbbbb
aabbbbbbbbbbbbb

Defines rule #3.

Referenced by [4].

[4] bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbbbbbbbbbbbb

Overlap of [2] bab=abbbb with [3] baabbbb=aabbbbbbbbbbbbb:

ba b baabbbb

Critical pair: baaabbbbbbbbbbbbb=abbbbaabbbb.

Reduce LHS:

[1]b(aaa)bbbbbbbbbbbbb
bbbbbbbbbbbbbb

Reduce RHS:

[3]abbb(baabbbb)
[3]abb(baabbbb)bbbbbbbbb
[3]ab(baabbbb)bbbbbbbbbbbbbbbbbb
[3]a(baabbbb)bbbbbbbbbbbbbbbbbbbbbbbbbbb
[1](aaa)bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.