Certificate for #1175 ⟨a, b | aaaba=baba⟩

Completion settings:

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

Axiom: aaaba=baba.

Referenced by [3].

Axiom: baba=c.

Defines rule #2.

Referenced by [3], [4], [6], [7].

Simplify [1] aaaba=baba.

Reduce RHS:

Defines rule #9.

Referenced by [5], [6], [7], [8], [9], [11].

Overlap of [2] baba=c with [2] baba=c:

Critical pair: bac=cba.

Defines rule #1.

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

Critical pair: aaabc=caaba.

Referenced by [8], [10].

Overlap of [3] aaaba=c with [2] baba=c:

Critical pair: aaac=cba.

Defines rule #6.

Referenced by [8].

Overlap of [2] baba=c with [3] aaaba=c:

Critical pair: babc=caaba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [10], [12].

Overlap of [3] aaaba=c with [6] aaac=cba:

Critical pair: aaabcba=caac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [7] caaba=babc with [3] aaaba=c:

Critical pair: caabc=babcaaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Simplify [5] aaabc=caaba.

Reduce RHS:

Defines rule #7.

Referenced by [11], [12].

Overlap of [3] aaaba=c with [10] aaabc=babc:

Critical pair: aaabbabc=caabc.

Defines rule #10.

Overlap of [7] caaba=babc with [10] aaabc=babc:

Critical pair: caabbabc=babcaabc.

Defines rule #8.