Certificate for #14514 ⟨a, b | aaab=b, babaa=b

Completion settings:

[1] aaab=b

Axiom: aaab=b.

Defines rule #2.

Referenced by [3], [4], [7], [8].

[2] babaa=b

Axiom: babaa=b.

Referenced by [3], [4], [5], [6], [7], [8], [10].

[3] babb=bab

Overlap of [2] babaa=b with [1] aaab=b:

bab aa aaab

Critical pair: babb=bab.

Referenced by [5], [8].

[4] babab=baab

Overlap of [2] babaa=b with [1] aaab=b:

baba a aaab

Critical pair: babab=baab.

Referenced by [5], [6].

[5] baabaa=bab

Overlap of [3] babb=bab with [2] babaa=b:

bab b babaa

Critical pair: babb=bababaa.

Reduce LHS:

[3](babb)
bab

Reduce RHS:

[4](babab)aa
baabaa

Flip LHS and RHS.

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

[6] baab=bbaa

Overlap of [2] babaa=b with [5] baabaa=bab:

ba baa baabaa

Critical pair: babab=bbaa.

Reduce LHS:

[4](babab)
baab

Referenced by [7], [8], [9], [11].

[7] bbb=bb

Overlap of [5] baabaa=bab with [1] aaab=b:

baaba a aaab

Critical pair: baabab=babaab.

Reduce LHS:

[6](baab)ab
[1]bb(aaab)
bbb

Reduce RHS:

[2](babaa)b
bb

Referenced by [8].

[8] bb=b

Overlap of [5] baabaa=bab with [5] baabaa=bab:

baa baa baabaa

Critical pair: baabab=babbaa.

Reduce LHS:

[6](baab)ab
[1]bb(aaab)
[7](bbb)
bb

Reduce RHS:

[3](babb)aa
[2](babaa)
b

Defines rule #3.

Referenced by [9], [11].

[9] bab=baaaa

Overlap of [8] bb=b with [5] baabaa=bab:

b b baabaa

Critical pair: bbab=baabaa.

Reduce LHS:

[8](bb)ab
bab

Reduce RHS:

[6](baab)aa
[8](bb)aaaa
baaaa

Defines rule #4.

Referenced by [10].

[10] baaaaaa=b

Overlap of [2] babaa=b with [9] bab=baaaa:

babaa bab

Critical pair: baaaaaa=b.

Defines rule #1.

[11] baab=baa

Simplify [6] baab=bbaa.

Reduce RHS:

[8](bb)aa
baa

Defines rule #5.