Certificate for #1897 ⟨a, b, c | aba=cc, bbc=1⟩

Completion settings:

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

Axiom: aba=cc.

Flip LHS and RHS.

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

Axiom: bbc=1.

Referenced by [4], [7].

Overlap of [1] cc=aba with [1] cc=aba:

Critical pair: caba=abac.

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] bbc=1 with [1] cc=aba:

Critical pair: bbaba=c.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6], [7].

Simplify [3] abac=caba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [1] cc=aba with [4] c=bbaba:

Critical pair: bbabac=aba.

Reduce LHS:

Defines rule #3.

Overlap of [2] bbc=1 with [4] c=bbaba:

Critical pair: bbbbaba=1.

Defines rule #1.