Termination Proof

Input TRS

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

minus(x,0) x
minus(s(x),s(y)) minus(x,y)
divide(x,y) div(x,y,0)
div(0,s(y),z) z
div(s(x),s(y),z) div(minus(s(x),s(y)),s(y),s(z))

Proof

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

divide#(x,y) div#(x,y,0)
div#(s(x),s(y),z) div#(minus(s(x),s(y)),s(y),s(z))
div#(s(x),s(y),z) minus#(s(x),s(y))
minus#(s(x),s(y)) minus#(x,y)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.