(VAR N X Y XS) (STRATEGY CONTEXTSENSITIVE (fib 1) (sel 1 2) (fib1 1 2) (s 1) (0) (cons 1) (add 1 2) ) (RULES fib(N) -> sel(N,fib1(s(0),s(0))) fib1(X,Y) -> cons(X,fib1(Y,add(X,Y))) add(0,X) -> X add(s(X),Y) -> s(add(X,Y)) sel(0,cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,XS) ) The TRS is orthogonal, thus termination of innermost context-sensitive rewriting is equivalent to termination of context-sensitive rewriting. Proving termination of context-sensitive rewriting for Ex8_BLR02: -> Dependency pairs: nF_fib(N) -> nF_sel(N,fib1(s(0),s(0))) nF_fib(N) -> nF_fib1(s(0),s(0)) nF_add(s(X),Y) -> nF_add(X,Y) nF_sel(s(N),cons(X,XS)) -> nF_sel(N,XS) nF_sel(s(N),cons(X,XS)) -> XS -> Proof of termination for Ex8_BLR02_1_1: -> -> Dependency pairs in cycle: nF_sel(s(N),cons(X,XS)) -> nF_sel(N,XS) Termination proved: Cycles verify subterm criterion. -> Proof of termination for Ex8_BLR02_1_2: -> -> Dependency pairs in cycle: nF_add(s(X),Y) -> nF_add(X,Y) Termination proved: Cycles verify subterm criterion. 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.