Certificate for #1557 ⟨a, b, c | aaa=ab, bcb=1⟩

Completion settings:

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

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

Axiom: bcb=1.

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

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

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

Overlap of [1] ab=aaa with [2] bcb=1:

Critical pair: a=aaacb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] bcb=1 with [3] cb=bc:

Critical pair: bbc=1.

Defines rule #4.