Certificate for #953 ⟨a, b | aabbaba=ab⟩

Completion settings:

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

Axiom: aabbaba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

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

Overlap of [1] aabbaba=ab with [2] abb=c:

Critical pair: acaba=ab.

Defines rule #1.

Referenced by [4], [5], [6], [7].

Overlap of [3] acaba=ab with [2] abb=c:

Critical pair: acabc=abbb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7], [8], [9], [11], [12], [13].

Overlap of [3] acaba=ab with [3] acaba=ab:

Critical pair: acabab=abcaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [10].

Overlap of [3] acaba=ab with [4] acabc=cb:

Critical pair: acabcb=abcabc.

Reduce LHS:

Defines rule #6.

Overlap of [3] acaba=ab with [5] abcaba=c:

Critical pair: acabc=abbcaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [4] acabc=cb with [5] abcaba=c:

Critical pair: acc=cbaba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Overlap of [5] abcaba=c with [4] acabc=cb:

Critical pair: abcabcb=ccabc.

Defines rule #10.

Overlap of [5] abcaba=c with [5] abcaba=c:

Critical pair: abcabc=cbcaba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [13].

Overlap of [7] ccaba=cb with [4] acabc=cb:

Critical pair: ccabcb=cbcabc.

Defines rule #9.

Overlap of [8] cbaba=acc with [4] acabc=cb:

Critical pair: cbabcb=acccabc.

Defines rule #11.

Overlap of [10] cbcaba=abcabc with [4] acabc=cb:

Critical pair: cbcabcb=abcabccabc.

Defines rule #12.