Certificate for #12956 ⟨a, b | aba=aab, bbaa=a

Completion settings:

[1] aba=aab

Axiom: aba=aab.

Defines rule #1.

Referenced by [3].

[2] bbaa=a

Axiom: bbaa=a.

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

[3] aabba=aaabb

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

ab a aba

Critical pair: abaab=aabba.

Reduce LHS:

[1](aba)ab
[1]a(aba)b
aaabb

Flip LHS and RHS.

Referenced by [4], [5].

[4] abba=aabb

Overlap of [2] bbaa=a with [3] aabba=aaabb:

bb aa aabba

Critical pair: bbaaabb=abba.

Reduce LHS:

[2](bbaa)abb
aabb

Flip LHS and RHS.

Referenced by [5].

[5] aaabb=aa

Overlap of [4] abba=aabb with [2] bbaa=a:

a bba bbaa

Critical pair: aa=aabba.

Reduce RHS:

[3](aabba)
aaabb

Flip LHS and RHS.

Referenced by [6].

[6] aabb=a

Overlap of [2] bbaa=a with [5] aaabb=aa:

bb aa aaabb

Critical pair: bbaa=aabb.

Reduce LHS:

[2](bbaa)
a

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[7] bba=abb

Overlap of [2] bbaa=a with [6] aabb=a:

bb aa aabb

Critical pair: bba=abb.

Defines rule #2.