Certificate for #25196 ⟨a, b | aa=a, ababb=bba⟩

Completion settings:

Reduction order:
- Left-to-right shortlex with a < b

[1] aa=a

Axiom: aa=a.

Defines rule #1.

Referenced by [3], [4].

[2] ababb=bba

Axiom: ababb=bba.

Defines rule #3.

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

[3] abba=bba

Overlap of [1] aa=a with [2] ababb=bba:

a a ababb

Critical pair: abba=ababb.

Reduce RHS:

[2]	(ababb)
	⇒ bba

Defines rule #2.

Referenced by [4], [7].

[4] abbba=bba

Overlap of [2] ababb=bba with [3] abba=bba:

ab abb abba

Critical pair: abbba=bbaa.

Reduce RHS:

[1]	bb(aa)
	⇒ bba

Defines rule #4.

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

[5] bbaba=bba

Overlap of [2] ababb=bba with [4] abbba=bba:

ab abb abbba

Critical pair: abbba=bbaba.

Reduce LHS:

[4]	(abbba)
	⇒ bba

Flip LHS and RHS.

Defines rule #5.

Referenced by [6].

[6] abbbbba=bbabb

Overlap of [4] abbba=bba with [2] ababb=bba:

abbb a ababb

Critical pair: abbbbba=bbababb.

Reduce RHS:

[5]	(bbaba)bb
	⇒ bbabb

Referenced by [7].

[7] bbbba=bbabb

Overlap of [4] abbba=bba with [3] abba=bba:

abbb a abba

Critical pair: abbbbba=bbabba.

Reduce LHS:

[6]	(abbbbba)
	⇒ bbabb

Reduce RHS:

[3]	bb(abba)
	⇒ bbbba

Flip LHS and RHS.

Defines rule #6.