Certificate for #1573 ⟨a, b, c | aaa=bb, bac=1⟩

Completion settings:

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

Axiom: aaa=bb.

Flip LHS and RHS.

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

Axiom: bac=1.

Referenced by [4], [6].

Overlap of [1] bb=aaa with [1] bb=aaa:

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] bb=aaa with [2] bac=1:

Critical pair: b=aaaac.

Defines rule #4.

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

Overlap of [1] bb=aaa with [4] b=aaaac:

Critical pair: aaaacb=aaa.

Reduce LHS:

Defines rule #3.

Overlap of [2] bac=1 with [4] b=aaaac:

Critical pair: aaaacac=1.

Defines rule #1.

Simplify [3] aaab=baaa.

Reduce LHS:

Reduce RHS:

Defines rule #2.