Certificate for #4821 ⟨a, b | abababab=aba⟩

Completion settings:

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

Axiom: abababab=aba.

Referenced by [3].

Axiom: aba=c.

Defines rule #5.

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

Simplify [1] abababab=aba.

Reduce RHS:

Referenced by [4].

Overlap of [3] abababab=c with [2] aba=c:

Critical pair: cbabab=c.

Reduce LHS:

Referenced by [6], [7], [8].

Overlap of [2] aba=c with [2] aba=c:

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Overlap of [4] cbcb=c with [4] cbcb=c:

Critical pair: cbc=ccb.

Defines rule #1.

Referenced by [7], [8].

Overlap of [4] cbcb=c with [6] cbc=ccb:

Critical pair: ccbb=c.

Defines rule #2.

Overlap of [4] cbcb=c with [5] cba=abc:

Critical pair: cbabc=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.