Certificate for #10729 ⟨a, b | aaab=baa, abab=1⟩

Back:⟨a, b | aaab=baa, abab=1⟩

Completion settings:

[1] aaab=baa

Axiom: aaab=baa.

Referenced by [3], [6].

[2] abab=1

Axiom: abab=1.

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

[3] bbaa=aa

Overlap of [1] aaab=baa with [2] abab=1:

aa ab abab

Critical pair: aa=baaab.

Reduce RHS:

[1]b(aaab)
⇒ bbaa

Flip LHS and RHS.

Referenced by [4].

[4] bba=a

Overlap of [3] bbaa=aa with [2] abab=1:

bba a abab

Critical pair: bba=aabab.

Reduce RHS:

[2]a(abab)
⇒ a

Referenced by [5].

[5] bb=1

Overlap of [4] bba=a with [2] abab=1:

bb a abab

Critical pair: bb=abab.

Reduce RHS:

[2](abab)
⇒ 1

Defines rule #1.

Referenced by [6], [7].

[6] aaa=baab

Overlap of [1] aaab=baa with [5] bb=1:

aaa b bb

Critical pair: aaa=baab.

Defines rule #3.

[7] aba=b

Overlap of [2] abab=1 with [5] bb=1:

aba b bb

Critical pair: aba=b.

Defines rule #2.