Certificate for #15848 ⟨a, b | aba=ab, aaabb=b

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Referenced by [3].

[2] aaabb=b

Axiom: aaabb=b.

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

[3] abba=abb

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

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
abb

Flip LHS and RHS.

Referenced by [4].

[4] ba=b

Overlap of [2] aaabb=b with [3] abba=abb:

aa abb abba

Critical pair: aaabb=ba.

Reduce LHS:

[2](aaabb)
b

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

[5] bbb=bb

Overlap of [4] ba=b with [2] aaabb=b:

b a aaabb

Critical pair: bb=baabb.

Reduce RHS:

[4](ba)abb
[4](ba)bb
bbb

Flip LHS and RHS.

Referenced by [6].

[6] bb=b

Overlap of [2] aaabb=b with [5] bbb=bb:

aaa bb bbb

Critical pair: aaabb=bb.

Reduce LHS:

[2](aaabb)
b

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] aaab=b

Overlap of [2] aaabb=b with [6] bb=b:

aaa bb bb

Critical pair: aaab=b.

Defines rule #3.