Certificate for #4176 ⟨a, b | aabbababa=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: aabbababa=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #1.

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

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

Critical pair: acababa=ab.

Defines rule #2.

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

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

Critical pair: acababc=abbb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7], [8], [9], [11], [13], [18].

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

Critical pair: acababab=abcababa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [10], [12], [14].

Overlap of [3] acababa=ab with [4] acababc=cb:

Critical pair: acababcb=abcababc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [9], [10], [13], [14], [15], [16], [17].

Overlap of [3] acababa=ab with [5] abcababa=c:

Critical pair: acababc=abbcababa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [11], [12], [16].

Overlap of [4] acababc=cb with [5] abcababa=c:

Critical pair: acabc=cbababa.

Flip LHS and RHS.

Defines rule #8.

Referenced by [18].

Overlap of [5] abcababa=c with [4] acababc=cb:

Critical pair: abcababcb=ccababc.

Reduce LHS:

Defines rule #7.

Referenced by [17].

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

Critical pair: abcababc=cbcababa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [17].

Overlap of [7] ccababa=cb with [4] acababc=cb:

Critical pair: ccababcb=cbcababc.

Defines rule #11.

Referenced by [16].

Overlap of [7] ccababa=cb with [5] abcababa=c:

Critical pair: ccababc=cbbcababa.

Flip LHS and RHS.

Defines rule #14.

Overlap of [4] acababc=cb with [6] abcababc=cbb:

Critical pair: acabcbb=cbababc.

Defines rule #10.

Overlap of [6] abcababc=cbb with [5] abcababa=c:

Critical pair: abcabc=cbbababa.

Flip LHS and RHS.

Defines rule #12.

Overlap of [6] abcababc=cbb with [6] abcababc=cbb:

Critical pair: abcabcbb=cbbababc.

Flip LHS and RHS.

Defines rule #13.

Overlap of [7] ccababa=cb with [6] abcababc=cbb:

Critical pair: ccababcbb=cbbcababc.

Reduce LHS:

Defines rule #16.

Referenced by [17].

Overlap of [10] cbcababa=cbb with [6] abcababc=cbb:

Critical pair: cbcababcbb=cbbbcababc.

Reduce LHS:

Reduce RHS:

Defines rule #17.

Overlap of [8] cbababa=acabc with [4] acababc=cb:

Critical pair: cbababcb=acabccababc.

Defines rule #15.