Certificate for #5274 ⟨a, b | aba=bb, aaaa=a

Completion settings:

[1] aba=bb

Axiom: aba=bb.

Defines rule #5.

Referenced by [3], [4], [5], [6], [7], [8], [11].

[2] aaaa=a

Axiom: aaaa=a.

Defines rule #11.

Referenced by [4], [5].

[3] bbba=abbb

Overlap of [1] aba=bb with [1] aba=bb:

ab a aba

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

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

[4] bbaaa=bb

Overlap of [1] aba=bb with [2] aaaa=a:

ab a aaaa

Critical pair: aba=bbaaa.

Reduce LHS:

[1](aba)
bb

Flip LHS and RHS.

Defines rule #10.

[5] aaabb=bb

Overlap of [2] aaaa=a with [1] aba=bb:

aaa a aba

Critical pair: aaabb=aba.

Reduce RHS:

[1](aba)
bb

Defines rule #9.

Referenced by [6], [7], [11].

[6] bbaabb=abbb

Overlap of [1] aba=bb with [5] aaabb=bb:

ab a aaabb

Critical pair: abbb=bbaabb.

Flip LHS and RHS.

Defines rule #8.

Referenced by [8], [10].

[7] aabbbbb=babbb

Overlap of [5] aaabb=bb with [3] bbba=abbb:

aaab b bbba

Critical pair: aaababbb=bbbba.

Reduce LHS:

[1]aa(aba)bbb
aabbbbb

Reduce RHS:

[3]b(bbba)
babbb

Referenced by [9], [12].

[8] abbabbb=bbabbbbb

Overlap of [6] bbaabb=abbb with [3] bbba=abbb:

bbaab b bbba

Critical pair: bbaababbb=abbbbba.

Reduce LHS:

[1]bba(aba)bbb
bbabbbbb

Reduce RHS:

[3]abb(bbba)
abbabbb

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10].

[9] baabbb=bbabbbbbbb

Overlap of [7] aabbbbb=babbb with [3] bbba=abbb:

aabb bbb bbba

Critical pair: aabbabbb=babbba.

Reduce LHS:

[8]a(abbabbb)
[8](abbabbb)bb
bbabbbbbbb

Reduce RHS:

[3]ba(bbba)
baabbb

Flip LHS and RHS.

Defines rule #7.

[10] aabbbb=babbbbbbbb

Overlap of [8] abbabbb=bbabbbbb with [3] bbba=abbb:

abba bbb bbba

Critical pair: abbaabbb=bbabbbbba.

Reduce LHS:

[6]a(bbaabb)b
aabbbb

Reduce RHS:

[3]bbabb(bbba)
[8]bb(abbabbb)
[3]b(bbba)bbbbb
babbbbbbbb

Defines rule #4.

Referenced by [11], [12].

[11] bbbbbbbbbb=bbbb

Overlap of [5] aaabb=bb with [10] aabbbb=babbbbbbbb:

a aabb aabbbb

Critical pair: ababbbbbbbb=bbbb.

Reduce LHS:

[1](aba)bbbbbbbb
bbbbbbbbbb

Defines rule #1.

[12] babbbbbbbbb=babbb

Overlap of [7] aabbbbb=babbb with [10] aabbbb=babbbbbbbb:

aabbbbb aabbbb

Critical pair: babbbbbbbbb=babbb.

Defines rule #2.