Certificate for #4646 ⟨a, b | aabababa=abb⟩

Completion settings:

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

Axiom: aabababa=abb.

Referenced by [3].

Axiom: abb=c.

Defines rule #1.

Referenced by [3], [5], [7].

Simplify [1] aabababa=abb.

Reduce RHS:

Defines rule #2.

Referenced by [4], [5], [6].

Overlap of [3] aabababa=c with [3] aabababa=c:

Critical pair: aabababc=cabababa.

Referenced by [5], [8].

Overlap of [3] aabababa=c with [2] abb=c:

Critical pair: aabababc=cbb.

Reduce LHS:

Defines rule #3.

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

Overlap of [5] cabababa=cbb with [3] aabababa=c:

Critical pair: cabababc=cbbabababa.

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] cabababa=cbb with [2] abb=c:

Critical pair: cabababc=cbbbb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [9].

Simplify [4] aabababc=cabababa.

Reduce RHS:

Defines rule #4.

Referenced by [9].

Overlap of [8] aabababc=cbb with [7] cbbbb=cabababc:

Critical pair: aabababcabababc=cbbbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #7.