Certificate for #21786 ⟨a, b | aaa=1, bbabbbb=a

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #3.

Referenced by [4], [5], [12], [13], [14].

[2] bbabbbb=a

Axiom: bbabbbb=a.

Referenced by [3], [6], [8], [9].

[3] aabbbb=bbabba

Overlap of [2] bbabbbb=a with [2] bbabbbb=a:

bbabb bb bbabbbb

Critical pair: bbabba=aabbbb.

Flip LHS and RHS.

Referenced by [4], [10], [12].

[4] abbabba=bbbb

Overlap of [1] aaa=1 with [3] aabbbb=bbabba:

a aa aabbbb

Critical pair: abbabba=bbbb.

Referenced by [5], [6], [7].

[5] abbabb=bbbbaa

Overlap of [4] abbabba=bbbb with [1] aaa=1:

abbabb a aaa

Critical pair: abbabb=bbbbaa.

Referenced by [8], [12].

[6] abbaa=bbbbbbbb

Overlap of [4] abbabba=bbbb with [2] bbabbbb=a:

abba bba bbabbbb

Critical pair: abbaa=bbbbbbbb.

Referenced by [12], [13].

[7] abbbbbb=bbbbbba

Overlap of [4] abbabba=bbbb with [4] abbabba=bbbb:

abb abba abbabba

Critical pair: abbbbbb=bbbbbba.

Referenced by [11].

[8] bbbbaabb=aa

Overlap of [5] abbabb=bbbbaa with [2] bbabbbb=a:

a bbabb bbabbbb

Critical pair: aa=bbbbaabb.

Flip LHS and RHS.

Referenced by [9], [10], [14].

[9] abaabb=bbabaa

Overlap of [2] bbabbbb=a with [8] bbbbaabb=aa:

bbab bbb bbbbaabb

Critical pair: bbabaa=abaabb.

Flip LHS and RHS.

Referenced by [11].

[10] aabb=bbbbbbabba

Overlap of [8] bbbbaabb=aa with [3] aabbbb=bbabba:

bbbb aabb aabbbb

Critical pair: bbbbbbabba=aabb.

Flip LHS and RHS.

Referenced by [11], [12].

[11] bbbbbbababba=bbabaa

Simplify [9] abaabb=bbabaa.

Reduce LHS:

[10]ab(aabb)
[7](abbbbbb)babba
bbbbbbababba

Referenced by [12].

[12] bbbbbbbabba=bbbbbbbbbbbbbbbaa

Overlap of [3] aabbbb=bbabba with [11] bbbbbbababba=bbabaa:

aa bbbb bbbbbbababba

Critical pair: aabbabaa=bbabbabbababba.

Reduce LHS:

[10](aabb)abaa
[6]bbbbbb(abbaa)baa
bbbbbbbbbbbbbbbaa

Reduce RHS:

[5]bb(abbabb)ababba
[1]bbbbbb(aaa)babba
bbbbbbbabba

Flip LHS and RHS.

Referenced by [14].

[13] abb=bbbbbbbba

Overlap of [6] abbaa=bbbbbbbb with [1] aaa=1:

abb aa aaa

Critical pair: abb=bbbbbbbba.

Defines rule #2.

Referenced by [14].

[14] bbbbbbbbbbbbbbbbbb=1

Overlap of [13] abb=bbbbbbbba with [8] bbbbaabb=aa:

a bb bbbbaabb

Critical pair: aaa=bbbbbbbbabbaabb.

Reduce LHS:

[1](aaa)
⇒ 1

Reduce RHS:

[12]b(bbbbbbbabba)abb
[1]bbbbbbbbbbbbbbbb(aaa)bb
bbbbbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.