Certificate for #4649 ⟨a, b | aabababa=bba⟩

Completion settings:

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

Axiom: aabababa=bba.

Referenced by [3].

Axiom: bba=c.

Defines rule #1.

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

Simplify [1] aabababa=bba.

Reduce RHS:

Defines rule #2.

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

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

Critical pair: aabababc=cabababa.

Flip LHS and RHS.

Referenced by [5], [8].

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

Critical pair: bbc=cabababa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8], [9].

Overlap of [3] aabababa=c with [5] aabababc=bbc:

Critical pair: aabababbbc=cabababc.

Defines rule #6.

Overlap of [2] bba=c with [5] aabababc=bbc:

Critical pair: bbbbc=cabababc.

Defines rule #5.

Simplify [4] cabababa=aabababc.

Reduce RHS:

Defines rule #4.

Referenced by [9].

Overlap of [8] cabababa=bbc with [5] aabababc=bbc:

Critical pair: cabababbbc=bbcabababc.

Defines rule #7.