Termination Proof

Input TRS

Termination of the rewrite relation of the following TRS is considered.

a(plus(0),y) y

Proof

1 Uncurrying

We uncurry the binary symbol a in combination with the following symbol map which also determines the applicative arities of these symbols.

plus(x1) is mapped to plus(x1), plus2(x1, x2)
0 is mapped to new_0

No rules have to be added for the eta-expansion.

Uncurrying the rules and adding the uncurrying rules yields the new set of rules

plus2(new_0,y) y
a(plus(x),y) plus2(x,y)

1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

a#(plus(x),y) plus2#(x,y)

1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.