Certificate for #19825 ⟨a, b | aaa=a, abbb=bab⟩

Completion settings:

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

[1] aaa=a

Axiom: aaa=a.

Defines rule #4.

Referenced by [4].

[2] bab=abbb

Axiom: abbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] baabbb=aabbbbbbb

Overlap of [2] bab=abbb with [2] bab=abbb:

ba b bab

Critical pair: baabbb=abbbab.

Reduce RHS:

[2]	abb(bab)
[2]	⇒ ab(bab)bb
[2]	⇒ a(bab)bbbb
	⇒ aabbbbbbb

Defines rule #3.

Referenced by [4].

[4] abbbbbbbbbbbbbbb=abbbbbbbbb

Overlap of [2] bab=abbb with [3] baabbb=aabbbbbbb:

ba b baabbb

Critical pair: baaabbbbbbb=abbbaabbb.

Reduce LHS:

[1]	b(aaa)bbbbbbb
[2]	⇒ (bab)bbbbbb
	⇒ abbbbbbbbb

Reduce RHS:

[3]	abb(baabbb)
[3]	⇒ ab(baabbb)bbbb
[3]	⇒ a(baabbb)bbbbbbbb
[1]	⇒ (aaa)bbbbbbbbbbbbbbb
	⇒ abbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.