The Problem

We are designing this program to work with the exact presentation:

  G = < a , b ; abaBAB , AAbbb >

where lower case letters are generators and uppercase letters are their inverses. This presentation is known to be trivial. That is, it is known to be exactly:

  F = < a , b ; >

We are given 12 transformations. Each transformation specifies a way to rewrite the two relators. If the first relator is called x, its inverse is X, the second relator is called y, and its inverse is Y then we have the Andrews-Curtis Transformations: T1: x -> xy ; y -> y

• T2: x -> X ; y -> y
• T3: x -> axA ; y -> y
• T4: x -> x ; y -> yx
• T5: x -> x ; y -> Y
• T6: x -> x ; y -> ayA
• T7: x -> bxB ; y -> y
• T8: x -> x ; y -> byB
• T9: x -> Axa ; y -> y
• T10: x -> x ; y -> Aya
• T11: x -> Bxb ; y -> y
• T12: x -> x ; y -> Byb