Termination Proof

Input TRS

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

cond(true,x,y) cond(gr(x,y),p(x),s(y))
gr(0,x) false
gr(s(x),s(y)) gr(x,y)
gr(s(x),0) true
p(s(x)) x
p(0) 0

Proof

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

cond#(true,x,y) cond#(gr(x,y),p(x),s(y))
cond#(true,x,y) gr#(x,y)
cond#(true,x,y) p#(x)
gr#(s(x),s(y)) gr#(x,y)

1.1 Dependency Graph Processor

The dependency pairs are split into 2 components.