Certificate for #4647 ⟨a, b, c | aa=a, bbbcb=1⟩

Back:⟨a, b, c | aa=a, bbbcb=1⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

[2] bbbcb=1

Axiom: bbbcb=1.

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

[3] bbcb=bbbc

Overlap of [2] bbbcb=1 with [2] bbbcb=1:

bbbc b bbbcb

Critical pair: bbbc=bbcb.

Flip LHS and RHS.

Referenced by [4], [5].

[4] cb=bc

Overlap of [3] bbcb=bbbc with [3] bbcb=bbbc:

bbc b bbcb

Critical pair: bbcbbbc=bbbcbcb.

Reduce LHS:

[3](bbcb)bbc
[2]⇒ (bbbcb)bc
⇒ bc

Reduce RHS:

[2](bbbcb)cb
⇒ cb

Flip LHS and RHS.

Defines rule #2.

[5] bbbbc=1

Overlap of [2] bbbcb=1 with [3] bbcb=bbbc:

b bbcb bbcb

Critical pair: bbbbc=1.

Defines rule #3.