Certificate for #1607 ⟨a, b | aaa=bb, bab=b⟩

Completion settings:

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

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

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

[2] bab=b

Axiom: bab=b.

Defines rule #5.

Referenced by [4], [5].

[3] aaab=baaa

Overlap of [1] bb=aaa with [1] bb=aaa:

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [4], [8].

[4] abaaa=aaa

Overlap of [1] bb=aaa with [2] bab=b:

b b bab

Critical pair: bb=aaaab.

Reduce LHS:

[1]	(bb)
	⇒ aaa

Reduce RHS:

[3]	a(aaab)
	⇒ abaaa

Flip LHS and RHS.

Referenced by [7].

[5] baaaa=aaa

Overlap of [2] bab=b with [1] bb=aaa:

ba b bb

Critical pair: baaaa=bb.

Reduce RHS:

[1]	(bb)
	⇒ aaa

Referenced by [6].

[6] baaa=aaaaaaa

Overlap of [1] bb=aaa with [5] baaaa=aaa:

b b baaaa

Critical pair: baaa=aaaaaaa.

Defines rule #2.

Referenced by [7], [8].

[7] aaaaaaaa=aaa

Simplify [4] abaaa=aaa.

Reduce LHS:

[6]	a(baaa)
	⇒ aaaaaaaa

Defines rule #1.

[8] aaab=aaaaaaa

Simplify [3] aaab=baaa.

Reduce RHS:

[6]	(baaa)
	⇒ aaaaaaa

Defines rule #3.