Certificate for #23300 ⟨a, b | aaa=1, baab=abbb

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #1.

Referenced by [3], [4], [6], [9].

[2] baab=abbb

Axiom: baab=abbb.

Defines rule #2.

Referenced by [3], [5], [7], [8], [10].

[3] abbabbb=bbbb

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

baa b baab

Critical pair: baaabbb=abbbaab.

Reduce LHS:

[1]b(aaa)bbb
bbbb

Reduce RHS:

[2]abb(baab)
abbabbb

Flip LHS and RHS.

Referenced by [4], [5], [8].

[4] bbabbb=aabbbb

Overlap of [1] aaa=1 with [3] abbabbb=bbbb:

aa a abbabbb

Critical pair: aabbbb=bbabbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [7], [8].

[5] ababbbbbb=babbbb

Overlap of [2] baab=abbb with [3] abbabbb=bbbb:

ba ab abbabbb

Critical pair: babbbb=abbbbabbb.

Reduce RHS:

[4]abb(bbabbb)
[2]ab(baab)bbb
ababbbbbb

Flip LHS and RHS.

Referenced by [6], [7], [8].

[6] babbbbbb=aababbbb

Overlap of [1] aaa=1 with [5] ababbbbbb=babbbb:

aa a ababbbbbb

Critical pair: aababbbb=babbbbbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

[7] aabbbbbbbbb=bababbbb

Overlap of [2] baab=abbb with [5] ababbbbbb=babbbb:

ba ab ababbbbbb

Critical pair: bababbbb=abbbabbbbbb.

Reduce RHS:

[4]ab(bbabbb)bbb
[2]a(baab)bbbbbb
aabbbbbbbbb

Flip LHS and RHS.

Referenced by [9], [10].

[8] abbbbbbbbbbb=abbbbb

Overlap of [6] babbbbbb=aababbbb with [4] bbabbb=aabbbb:

babbbb bb bbabbb

Critical pair: babbbbaabbbb=aababbbbabbb.

Reduce LHS:

[2]babbb(baab)bbb
[4]bab(bbabbb)bbb
[2]ba(baab)bbbbbb
[2](baab)bbbbbbbb
abbbbbbbbbbb

Reduce RHS:

[4]aababb(bbabbb)
[2]aabab(baab)bbb
[5]aab(ababbbbbb)
[3]a(abbabbb)b
abbbbb

Referenced by [10].

[9] bbbbbbbbb=abababbbb

Overlap of [1] aaa=1 with [7] aabbbbbbbbb=bababbbb:

a aa aabbbbbbbbb

Critical pair: abababbbb=bbbbbbbbb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

[10] bbababbbb=abbbbb

Overlap of [2] baab=abbb with [7] aabbbbbbbbb=bababbbb:

b aab aabbbbbbbbb

Critical pair: bbababbbb=abbbbbbbbbbb.

Reduce RHS:

[8](abbbbbbbbbbb)
abbbbb

Defines rule #5.

[11] babababbbb=abababbbbb

Overlap of [9] bbbbbbbbb=abababbbb with [9] bbbbbbbbb=abababbbb:

b bbbbbbbb bbbbbbbbb

Critical pair: babababbbb=abababbbbb.

Defines rule #7.