Certificate for #4156 ⟨a, b | aabbaaaba=ab⟩

Completion settings:

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

Axiom: aabbaaaba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #4.

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

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

Critical pair: acaaaba=ab.

Defines rule #1.

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

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

Critical pair: acaaabc=abbb.

Reduce RHS:

Defines rule #2.

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

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

Critical pair: acaaabab=abcaaaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [3] acaaaba=ab with [4] acaaabc=cb:

Critical pair: acaaabcb=abcaaabc.

Reduce LHS:

Defines rule #6.

Overlap of [3] acaaaba=ab with [5] abcaaaba=c:

Critical pair: acaaabc=abbcaaaba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [4] acaaabc=cb with [5] abcaaaba=c:

Critical pair: acaac=cbaaaba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Overlap of [5] abcaaaba=c with [4] acaaabc=cb:

Critical pair: abcaaabcb=ccaaabc.

Defines rule #10.

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

Critical pair: abcaaabc=cbcaaaba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [13].

Overlap of [7] ccaaaba=cb with [4] acaaabc=cb:

Critical pair: ccaaabcb=cbcaaabc.

Defines rule #9.

Overlap of [8] cbaaaba=acaac with [4] acaaabc=cb:

Critical pair: cbaaabcb=acaaccaaabc.

Defines rule #11.

Overlap of [10] cbcaaaba=abcaaabc with [4] acaaabc=cb:

Critical pair: cbcaaabcb=abcaaabccaaabc.

Defines rule #12.