Certificate for #20054 ⟨a, b | aab=b, aaaa=bba⟩

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1

[1] aab=b

Axiom: aab=b.

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

[2] aaaa=bba

Axiom: aaaa=bba.

Defines rule #4.

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

[3] bbab=b

Overlap of [2] aaaa=bba with [1] aab=b:

aa aa aab

Critical pair: aab=bbab.

Reduce LHS:

[1]	(aab)
	⇒ b

Flip LHS and RHS.

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

[4] bbaa=abba

Overlap of [2] aaaa=bba with [2] aaaa=bba:

a aaa aaaa

Critical pair: abba=bbaa.

Flip LHS and RHS.

Referenced by [5], [7].

[5] ab=bbb

Overlap of [4] bbaa=abba with [1] aab=b:

bb aa aab

Critical pair: bbb=abbab.

Reduce RHS:

[3]	a(bbab)
	⇒ ab

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

[6] bbbbb=b

Overlap of [2] aaaa=bba with [5] ab=bbb:

aaa a ab

Critical pair: aaabbb=bbab.

Reduce LHS:

[1]	a(aab)bb
[5]	⇒ (ab)bb
	⇒ bbbbb

Reduce RHS:

[3]	(bbab)
	⇒ b

Defines rule #1.

Referenced by [7].

[7] baa=bbba

Overlap of [6] bbbbb=b with [4] bbaa=abba:

bbb bb bbaa

Critical pair: bbbabba=baa.

Reduce LHS:

[3]	b(bbab)ba
	⇒ bbba

Flip LHS and RHS.

Defines rule #3.