Certificate for #16342 ⟨a, b | aba=aa, aaab=ba

Completion settings:

[1] aba=aa

Axiom: aba=aa.

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

[2] aaab=ba

Axiom: aaab=ba.

Referenced by [3], [5], [6], [7].

[3] baa=aaaa

Overlap of [2] aaab=ba with [1] aba=aa:

aa ab aba

Critical pair: aaaa=baa.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aaaaa=aaa

Overlap of [1] aba=aa with [3] baa=aaaa:

a ba baa

Critical pair: aaaaa=aaa.

Referenced by [5].

[5] aaaa=aa

Overlap of [3] baa=aaaa with [2] aaab=ba:

ba a aaab

Critical pair: baba=aaaaaab.

Reduce LHS:

[1]b(aba)
[3](baa)
aaaa

Reduce RHS:

[4](aaaaa)ab
[2]a(aaab)
[1](aba)
aa

Defines rule #1.

Referenced by [6].

[6] aab=aa

Overlap of [5] aaaa=aa with [2] aaab=ba:

a aaa aaab

Critical pair: aba=aab.

Reduce LHS:

[1](aba)
aa

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[7] ba=aaa

Overlap of [1] aba=aa with [6] aab=aa:

ab a aab

Critical pair: abaa=aaab.

Reduce LHS:

[1](aba)a
aaa

Reduce RHS:

[2](aaab)
ba

Flip LHS and RHS.

Defines rule #2.