TRS Termination Proof

by unspecified

Input

The rewrite relation of the following TRS is considered.

id(x) x
minus(x,0) x
minus(s(x),s(y)) minus(x,y)
div(0,s(y)) 0
div(s(x),s(y)) s(div(minus(x,y),id(s(y))))

Proof

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
div#(s(x),s(y)) div#(minus(x,y),id(s(y)))
div#(s(x),s(y)) minus#(x,y)
div#(s(x),s(y)) id#(s(y))
minus#(s(x),s(y)) minus#(x,y)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.

Tool configuration

unspecified