Certification Problem

Input (TPDB TRS_Standard/Transformed_CSR_04/Ex6_9_Luc02c_Z)

The rewrite relation of the following TRS is considered.

2nd(cons1(X,cons(Y,Z)))	→	Y	(1)
2nd(cons(X,X1))	→	2nd(cons1(X,activate(X1)))	(2)
from(X)	→	cons(X,n__from(s(X)))	(3)
from(X)	→	n__from(X)	(4)
activate(n__from(X))	→	from(X)	(5)
activate(X)	→	X	(6)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

2nd^#(cons(X,X1))	→	2nd^#(cons1(X,activate(X1)))	(7)
2nd^#(cons(X,X1))	→	activate^#(X1)	(8)
activate^#(n__from(X))	→	from^#(X)	(9)

1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.