Certificate for #27160 ⟨a, b | aa=1, abbbbab=bb

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [5], [8], [9], [10].

[2] abbbbab=bb

Axiom: abbbbab=bb.

Referenced by [3], [4], [5].

[3] bbbbab=abb

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

a a abbbbab

Critical pair: abb=bbbbab.

Flip LHS and RHS.

Referenced by [4], [6], [7], [9].

[4] babb=abbbbbb

Overlap of [2] abbbbab=bb with [2] abbbbab=bb:

abbbb ab abbbbab

Critical pair: abbbbbb=bbbbbab.

Reduce RHS:

[3]b(bbbbab)
babb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6], [9].

[5] bbbbbbbbbbbbbbbbbb=bbb

Overlap of [2] abbbbab=bb with [4] babb=abbbbbb:

abbb bab babb

Critical pair: abbbabbbbbb=bbb.

Reduce LHS:

[4]abb(babb)bbbb
[4]ab(babb)bbbbbbbb
[4]a(babb)bbbbbbbbbbbb
[1](aa)bbbbbbbbbbbbbbbbbb
bbbbbbbbbbbbbbbbbb

Referenced by [6], [7].

[6] bbbab=abbbbbbbbbbbbb

Overlap of [5] bbbbbbbbbbbbbbbbbb=bbb with [3] bbbbab=abb:

bbbbbbbbbbbbbb bbbb bbbbab

Critical pair: bbbbbbbbbbbbbbabb=bbbab.

Reduce LHS:

[3]bbbbbbbbbb(bbbbab)b
[3]bbbbbb(bbbbab)bb
[3]bb(bbbbab)bbb
[4]b(babb)bbb
[4](babb)bbbbbbb
abbbbbbbbbbbbb

Flip LHS and RHS.

Referenced by [7].

[7] abbbbbbbbbbbbbbbbb=abb

Overlap of [5] bbbbbbbbbbbbbbbbbb=bbb with [6] bbbab=abbbbbbbbbbbbb:

bbbbbbbbbbbbbbbb bb bbbab

Critical pair: bbbbbbbbbbbbbbbbabbbbbbbbbbbbb=bbbbab.

Reduce LHS:

[3]bbbbbbbbbbbb(bbbbab)bbbbbbbbbbbb
[3]bbbbbbbb(bbbbab)bbbbbbbbbbbbb
[3]bbbb(bbbbab)bbbbbbbbbbbbbb
[3](bbbbab)bbbbbbbbbbbbbbb
abbbbbbbbbbbbbbbbb

Reduce RHS:

[3](bbbbab)
abb

Referenced by [8], [9].

[8] bbbbbbbbbbbbbbbbb=bb

Overlap of [1] aa=1 with [7] abbbbbbbbbbbbbbbbb=abb:

a a abbbbbbbbbbbbbbbbb

Critical pair: aabb=bbbbbbbbbbbbbbbbb.

Reduce LHS:

[1](aa)bb
bb

Flip LHS and RHS.

Defines rule #1.

[9] abbab=bbbbbbbbb

Overlap of [7] abbbbbbbbbbbbbbbbb=abb with [3] bbbbab=abb:

abbbbbbbbbbbbb bbbb bbbbab

Critical pair: abbbbbbbbbbbbbabb=abbab.

Reduce LHS:

[3]abbbbbbbbb(bbbbab)b
[3]abbbbb(bbbbab)bb
[3]ab(bbbbab)bbb
[4]a(babb)bbb
[1](aa)bbbbbbbbb
bbbbbbbbb

Flip LHS and RHS.

Referenced by [10].

[10] bbab=abbbbbbbbb

Overlap of [1] aa=1 with [9] abbab=bbbbbbbbb:

a a abbab

Critical pair: abbbbbbbbb=bbab.

Flip LHS and RHS.

Defines rule #3.