Certificate for #27129 ⟨a, b | aa=1, ababbbb=bb

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [11].

[2] ababbbb=bb

Axiom: ababbbb=bb.

Referenced by [3], [4], [7], [9].

[3] babbbb=abb

Overlap of [1] aa=1 with [2] ababbbb=bb:

a a ababbbb

Critical pair: abb=babbbb.

Flip LHS and RHS.

Referenced by [4], [5], [6], [7], [8], [10].

[4] ababbbabb=babb

Overlap of [2] ababbbb=bb with [3] babbbb=abb:

ababbb b babbbb

Critical pair: ababbbabb=bbabbbb.

Reduce RHS:

[3]b(babbbb)
babb

Referenced by [10].

[5] babbbabb=ababb

Overlap of [3] babbbb=abb with [3] babbbb=abb:

babbb b babbbb

Critical pair: babbbabb=abbabbbb.

Reduce RHS:

[3]ab(babbbb)
ababb

Referenced by [6], [7], [8], [9], [10].

[6] babbbababb=abababb

Overlap of [3] babbbb=abb with [5] babbbabb=ababb:

babbb b babbbabb

Critical pair: babbbababb=abbabbbabb.

Reduce RHS:

[5]ab(babbbabb)
abababb

Referenced by [8].

[7] babbabb=bb

Overlap of [5] babbbabb=ababb with [3] babbbb=abb:

babb babb babbbb

Critical pair: babbabb=ababbbb.

Reduce RHS:

[2](ababbbb)
bb

Referenced by [8], [9].

[8] abababb=abbbb

Overlap of [5] babbbabb=ababb with [3] babbbb=abb:

babbbab b babbbb

Critical pair: babbbababb=ababbabbbb.

Reduce LHS:

[6](babbbababb)
abababb

Reduce RHS:

[7]a(babbabb)bb
abbbb

Referenced by [9].

[9] abbbabb=bb

Overlap of [5] babbbabb=ababb with [5] babbbabb=ababb:

babbbab b babbbabb

Critical pair: babbbabababb=ababbabbbabb.

Reduce LHS:

[8]babbb(abababb)
[5](babbbabb)bb
[2](ababbbb)
bb

Reduce RHS:

[7]a(babbabb)babb
abbbabb

Flip LHS and RHS.

Referenced by [10], [11].

[10] babb=abbb

Overlap of [5] babbbabb=ababb with [9] abbbabb=bb:

babbb abb abbbabb

Critical pair: babbbbb=ababbbabb.

Reduce LHS:

[3](babbbb)b
abbb

Reduce RHS:

[4](ababbbabb)
babb

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

[11] bbbbb=bb

Overlap of [10] babb=abbb with [10] babb=abbb:

bab b babb

Critical pair: bababbb=abbbabb.

Reduce LHS:

[10]ba(babb)b
[1]b(aa)bbbb
bbbbb

Reduce RHS:

[9](abbbabb)
bb

Defines rule #3.