Certificate for #4024 ⟨a, b | aaabbabaa=ba⟩

Completion settings:

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

Axiom: aaabbabaa=ba.

Referenced by [3].

Axiom: ba=c.

Defines rule #1.

Referenced by [3], [4], [5], [7].

Simplify [1] aaabbabaa=ba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabbabaa=c with [2] ba=c:

Critical pair: aaabcbaa=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6], [8], [9].

Overlap of [2] ba=c with [4] aaabcca=c:

Critical pair: bc=caabcca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [9], [10], [11].

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

Critical pair: aaabccc=caabcca.

Reduce RHS:

Defines rule #3.

Referenced by [7], [8], [11].

Overlap of [2] ba=c with [6] aaabccc=bc:

Critical pair: bbc=caabccc.

Defines rule #5.

Overlap of [4] aaabcca=c with [6] aaabccc=bc:

Critical pair: aaabccbc=caabccc.

Defines rule #7.

Overlap of [4] aaabcca=c with [5] caabcca=bc:

Critical pair: aaabcbc=cabcca.

Defines rule #6.

Overlap of [5] caabcca=bc with [5] caabcca=bc:

Critical pair: caabcbc=bcabcca.

Defines rule #8.

Overlap of [5] caabcca=bc with [6] aaabccc=bc:

Critical pair: caabccbc=bcaabccc.

Defines rule #9.