(VAR X XS N Y YS) (STRATEGY CONTEXTSENSITIVE (pairNs) (cons 1) (0) (incr 1) (oddNs) (s 1) (take 1 2) (nil) (zip 1 2) (pair 1 2) (tail 1) (repItems 1) ) (RULES pairNs -> cons(0,incr(oddNs)) oddNs -> incr(pairNs) incr(cons(X,XS)) -> cons(s(X),incr(XS)) take(0,XS) -> nil take(s(N),cons(X,XS)) -> cons(X,take(N,XS)) zip(nil,XS) -> nil zip(X,nil) -> nil zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),zip(XS,YS)) tail(cons(X,XS)) -> XS repItems(nil) -> nil repItems(cons(X,XS)) -> cons(X,cons(X,repItems(XS))) ) Proving termination of context-sensitive rewriting for Ex5_DLMMU04: -> Dependency pairs: nF_oddNs -> nF_incr(pairNs) nF_oddNs -> nF_pairNs nF_tail(cons(X,XS)) -> XS -> Proof of termination for Ex5_DLMMU04_1: Termination proved: No cycles in dependency graph. SETTINGS: Base ordering: Polynomial ordering Proof mode: SCCs in CSDG + base ordering Upper bound for coeffs: 1 Rationals below 1 for all non-replacing args: No Polynomial interpretation: Linear Coeffs in polynomials: No rationals Delta: automatic Termination was proved succesfully.