Certificate for #1864 ⟨a, b, c | aba=bc, acb=1⟩

Completion settings:

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

Axiom: aba=bc.

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

Axiom: acb=1.

Defines rule #4.

Referenced by [4], [6], [8], [9].

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

Critical pair: abbc=bcba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aba=bc with [2] acb=1:

Critical pair: ab=bccb.

Defines rule #3.

Referenced by [5], [7], [10].

Overlap of [1] aba=bc with [4] ab=bccb:

Critical pair: bccba=bc.

Referenced by [6].

Overlap of [2] acb=1 with [5] bccba=bc:

Critical pair: acbc=ccba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Simplify [3] bcba=abbc.

Reduce RHS:

Referenced by [8].

Overlap of [2] acb=1 with [7] bcba=bccbbc:

Critical pair: acbccbbc=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10].

Overlap of [2] acb=1 with [8] cba=ccbbc:

Critical pair: accbbc=a.

Defines rule #5.

Referenced by [11].

Overlap of [8] cba=ccbbc with [4] ab=bccb:

Critical pair: cbbccb=ccbbcb.

Defines rule #2.

Overlap of [6] ccba=c with [9] accbbc=a:

Critical pair: ccba=cccbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.