Certificate for #22264 ⟨a, b | aaa=1, ababab=bb

Completion settings:

[1] aaa=1

Axiom: aaa=1.

Defines rule #6.

Referenced by [3], [9], [11].

[2] ababab=bb

Axiom: ababab=bb.

Referenced by [3], [4], [10].

[3] babab=aabb

Overlap of [1] aaa=1 with [2] ababab=bb:

aa a ababab

Critical pair: aabb=babab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6].

[4] bbab=abbb

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

ab abab ababab

Critical pair: abbb=bbab.

Flip LHS and RHS.

Defines rule #3.

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

[5] babaabbb=aababbb

Overlap of [3] babab=aabb with [4] bbab=abbb:

baba b bbab

Critical pair: babaabbb=aabbbab.

Reduce RHS:

[4]aab(bbab)
aababbb

Referenced by [8].

[6] baabb=ababbb

Overlap of [4] bbab=abbb with [3] babab=aabb:

b bab babab

Critical pair: baabb=abbbab.

Reduce RHS:

[4]ab(bbab)
ababbb

Defines rule #4.

Referenced by [7], [8].

[7] baababbb=aababbbbbb

Overlap of [6] baabb=ababbb with [4] bbab=abbb:

baab b bbab

Critical pair: baababbb=ababbbbab.

Reduce RHS:

[4]ababb(bbab)
[4]aba(bbab)bb
[6]a(baabb)bbb
aababbbbbb

Defines rule #7.

Referenced by [8].

[8] aababbbbbbb=aababbb

Simplify [5] babaabbb=aababbb.

Reduce LHS:

[6]ba(baabb)b
[7](baababbb)b
aababbbbbbb

Referenced by [9], [10].

[9] babbbbbbb=babbb

Overlap of [1] aaa=1 with [8] aababbbbbbb=aababbb:

a aa aababbbbbbb

Critical pair: aaababbb=babbbbbbb.

Reduce LHS:

[1](aaa)babbb
babbb

Flip LHS and RHS.

Defines rule #2.

[10] abbbbbbbb=abbbb

Overlap of [8] aababbbbbbb=aababbb with [4] bbab=abbb:

aababbbbb bb bbab

Critical pair: aababbbbbabbb=aababbbab.

Reduce LHS:

[4]aababbb(bbab)bb
[4]aabab(bbab)bbbb
[2]a(ababab)bbbbbb
abbbbbbbb

Reduce RHS:

[4]aabab(bbab)
[2]a(ababab)bb
abbbb

Referenced by [11].

[11] bbbbbbbb=bbbb

Overlap of [1] aaa=1 with [10] abbbbbbbb=abbbb:

aa a abbbbbbbb

Critical pair: aaabbbb=bbbbbbbb.

Reduce LHS:

[1](aaa)bbbb
bbbb

Flip LHS and RHS.

Defines rule #1.