Certificate for #4331 ⟨a, b | abbaaabba=bb⟩

Completion settings:

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

Axiom: abbaaabba=bb.

Referenced by [3].

Axiom: aabba=c.

Referenced by [3], [4], [5], [10].

Overlap of [1] abbaaabba=bb with [2] aabba=c:

Critical pair: abbac=bb.

Referenced by [5], [6].

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

Critical pair: aabbc=cabba.

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] aabba=c with [3] abbac=bb:

Critical pair: abb=cc.

Referenced by [6], [7], [9], [10].

Overlap of [3] abbac=bb with [5] abb=cc:

Critical pair: ccac=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8].

Overlap of [5] abb=cc with [6] bb=ccac:

Critical pair: abccac=ccb.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] bb=ccac with [6] bb=ccac:

Critical pair: bccac=ccacb.

Flip LHS and RHS.

Defines rule #4.

Simplify [4] cabba=aabbc.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [2] aabba=c with [5] abb=cc:

Critical pair: acca=c.

Defines rule #1.