Certificate for #3911 ⟨a, b | aabb=ba, baba=1⟩

Completion settings:

[1] aabb=ba

Axiom: aabb=ba.

Defines rule #1.

Referenced by [3], [4], [6], [10], [11], [12].

[2] baba=1

Axiom: baba=1.

Defines rule #5.

Referenced by [3], [4], [5], [6], [7], [9].

[3] baaba=aab

Overlap of [1] aabb=ba with [2] baba=1:

aab b baba

Critical pair: aab=baaba.

Flip LHS and RHS.

Referenced by [5], [7].

[4] babba=abb

Overlap of [2] baba=1 with [1] aabb=ba:

bab a aabb

Critical pair: babba=abb.

Defines rule #9.

[5] baaab=aba

Overlap of [2] baba=1 with [3] baaba=aab:

ba ba baaba

Critical pair: baaab=aba.

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

[6] abab=1

Overlap of [5] baaab=aba with [1] aabb=ba:

ba aab aabb

Critical pair: baba=abab.

Reduce LHS:

[2](baba)
⇒ 1

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[7] baaa=aaab

Overlap of [5] baaab=aba with [2] baba=1:

baaa b baba

Critical pair: baaa=abaaba.

Reduce RHS:

[3]a(baaba)
aaab

Defines rule #3.

[8] abaab=baa

Overlap of [5] baaab=aba with [6] abab=1:

baa ab abab

Critical pair: baa=abaab.

Flip LHS and RHS.

Referenced by [9], [10].

[9] bbaa=ab

Overlap of [2] baba=1 with [8] abaab=baa:

b aba abaab

Critical pair: bbaa=ab.

Defines rule #6.

Referenced by [11].

[10] baab=abba

Overlap of [8] abaab=baa with [1] aabb=ba:

ab aab aabb

Critical pair: abba=baab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [12].

[11] bbba=abbb

Overlap of [9] bbaa=ab with [1] aabb=ba:

bb aa aabb

Critical pair: bbba=abbb.

Defines rule #7.

[12] abbab=bba

Overlap of [10] baab=abba with [1] aabb=ba:

b aab aabb

Critical pair: bba=abbab.

Flip LHS and RHS.

Defines rule #8.