Certificate for #16055 ⟨a, b | aaa=bb, aaba=bb⟩

Back:⟨a, b | aaa=bb, aaba=bb⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [2], [3], [5].

[2] aaba=aaa

Axiom: aaba=bb.

Reduce RHS:

[1](bb)
⇒ aaa

Defines rule #3.

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

[3] baaa=aaab

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

b b bb

Critical pair: baaa=aaab.

Defines rule #4.

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

[4] aaaaab=aaaaa

Overlap of [2] aaba=aaa with [3] baaa=aaab:

aa ba baaa

Critical pair: aaaaab=aaaaa.

Referenced by [6].

[5] aaaaaaa=aaaa

Overlap of [3] baaa=aaab with [2] aaba=aaa:

ba aa aaba

Critical pair: baaaa=aaabba.

Reduce LHS:

[3](baaa)a
[2]⇒ a(aaba)
⇒ aaaa

Reduce RHS:

[1]aaa(bb)a
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [6].

[6] aaaab=aaaa

Overlap of [3] baaa=aaab with [4] aaaaab=aaaaa:

baa a aaaaab

Critical pair: baaaaaaa=aaabaaaab.

Reduce LHS:

[3](baaa)aaaa
[2]⇒ a(aaba)aaa
[5]⇒ (aaaaaaa)
⇒ aaaa

Reduce RHS:

[2]a(aaba)aaab
[5]⇒ (aaaaaaa)b
⇒ aaaab

Flip LHS and RHS.

Defines rule #2.