MAYBE Problem: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(fib(N)) -> s#(0()) active#(fib(N)) -> fib1#(s(0()),s(0())) active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(fib1(X,Y)) -> add#(X,Y) active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(add(s(X),Y)) -> add#(X,Y) active#(add(s(X),Y)) -> s#(add(X,Y)) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(fib(X)) -> active#(X) active#(fib(X)) -> fib#(active(X)) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> add#(active(X1),X2) active#(add(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> add#(X1,active(X2)) fib#(mark(X)) -> fib#(X) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) fib1#(mark(X1),X2) -> fib1#(X1,X2) fib1#(X1,mark(X2)) -> fib1#(X1,X2) s#(mark(X)) -> s#(X) cons#(mark(X1),X2) -> cons#(X1,X2) add#(mark(X1),X2) -> add#(X1,X2) add#(X1,mark(X2)) -> add#(X1,X2) proper#(fib(X)) -> proper#(X) proper#(fib(X)) -> fib#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) fib#(ok(X)) -> fib#(X) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) s#(ok(X)) -> s#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) add#(ok(X1),ok(X2)) -> add#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(fib(N)) -> s#(0()) active#(fib(N)) -> fib1#(s(0()),s(0())) active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(fib1(X,Y)) -> add#(X,Y) active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(add(s(X),Y)) -> add#(X,Y) active#(add(s(X),Y)) -> s#(add(X,Y)) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(fib(X)) -> active#(X) active#(fib(X)) -> fib#(active(X)) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> add#(active(X1),X2) active#(add(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> add#(X1,active(X2)) fib#(mark(X)) -> fib#(X) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) fib1#(mark(X1),X2) -> fib1#(X1,X2) fib1#(X1,mark(X2)) -> fib1#(X1,X2) s#(mark(X)) -> s#(X) cons#(mark(X1),X2) -> cons#(X1,X2) add#(mark(X1),X2) -> add#(X1,X2) add#(X1,mark(X2)) -> add#(X1,X2) proper#(fib(X)) -> proper#(X) proper#(fib(X)) -> fib#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) fib#(ok(X)) -> fib#(X) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) s#(ok(X)) -> s#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) add#(ok(X1),ok(X2)) -> add#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> active#(X) -> active#(add(X1,X2)) -> add#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(add(X1,X2)) -> add#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(fib1(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(fib1(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(fib(X)) -> fib#(active(X)) top#(ok(X)) -> active#(X) -> active#(fib(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) top#(ok(X)) -> active#(X) -> active#(add(s(X),Y)) -> s#(add(X,Y)) top#(ok(X)) -> active#(X) -> active#(add(s(X),Y)) -> add#(X,Y) top#(ok(X)) -> active#(X) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) top#(ok(X)) -> active#(X) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) top#(ok(X)) -> active#(X) -> active#(fib1(X,Y)) -> add#(X,Y) top#(ok(X)) -> active#(X) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) top#(ok(X)) -> active#(X) -> active#(fib(N)) -> fib1#(s(0()),s(0())) top#(ok(X)) -> active#(X) -> active#(fib(N)) -> s#(0()) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(fib(X)) -> fib#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(fib(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> fib#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> fib#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> proper#(X) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) -> cons#(mark(X1),X2) -> cons#(X1,X2) proper#(add(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(add(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(add(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> fib#(proper(X)) proper#(add(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> proper#(X) proper#(add(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(add(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(add(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(add(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> fib#(proper(X)) proper#(add(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> proper#(X) proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) -> add#(X1,mark(X2)) -> add#(X1,X2) proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) -> add#(mark(X1),X2) -> add#(X1,X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> fib#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> fib#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> proper#(X) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) -> sel#(X1,mark(X2)) -> sel#(X1,X2) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) -> sel#(mark(X1),X2) -> sel#(X1,X2) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(add(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> fib#(proper(X)) proper#(fib1(X1,X2)) -> proper#(X2) -> proper#(fib(X)) -> proper#(X) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(add(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> fib#(proper(X)) proper#(fib1(X1,X2)) -> proper#(X1) -> proper#(fib(X)) -> proper#(X) proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) proper#(s(X)) -> proper#(X) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(fib(X)) -> fib#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(fib(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X) proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X) proper#(fib(X)) -> proper#(X) -> proper#(add(X1,X2)) -> add#(proper(X1),proper(X2)) proper#(fib(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X1) proper#(fib(X)) -> proper#(X) -> proper#(add(X1,X2)) -> proper#(X2) proper#(fib(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(fib(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(fib(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(fib(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(fib(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(fib(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> fib1#(proper(X1),proper(X2)) proper#(fib(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> proper#(X1) proper#(fib(X)) -> proper#(X) -> proper#(fib1(X1,X2)) -> proper#(X2) proper#(fib(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(fib(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(fib(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(fib(X)) -> proper#(X) -> proper#(fib(X)) -> fib#(proper(X)) proper#(fib(X)) -> proper#(X) -> proper#(fib(X)) -> proper#(X) proper#(fib(X)) -> fib#(proper(X)) -> fib#(ok(X)) -> fib#(X) proper#(fib(X)) -> fib#(proper(X)) -> fib#(mark(X)) -> fib#(X) fib#(ok(X)) -> fib#(X) -> fib#(ok(X)) -> fib#(X) fib#(ok(X)) -> fib#(X) -> fib#(mark(X)) -> fib#(X) fib#(mark(X)) -> fib#(X) -> fib#(ok(X)) -> fib#(X) fib#(mark(X)) -> fib#(X) -> fib#(mark(X)) -> fib#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) add#(ok(X1),ok(X2)) -> add#(X1,X2) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) add#(ok(X1),ok(X2)) -> add#(X1,X2) -> add#(X1,mark(X2)) -> add#(X1,X2) add#(ok(X1),ok(X2)) -> add#(X1,X2) -> add#(mark(X1),X2) -> add#(X1,X2) add#(mark(X1),X2) -> add#(X1,X2) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) add#(mark(X1),X2) -> add#(X1,X2) -> add#(X1,mark(X2)) -> add#(X1,X2) add#(mark(X1),X2) -> add#(X1,X2) -> add#(mark(X1),X2) -> add#(X1,X2) add#(X1,mark(X2)) -> add#(X1,X2) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) add#(X1,mark(X2)) -> add#(X1,X2) -> add#(X1,mark(X2)) -> add#(X1,X2) add#(X1,mark(X2)) -> add#(X1,X2) -> add#(mark(X1),X2) -> add#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) fib1#(mark(X1),X2) -> fib1#(X1,X2) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) fib1#(mark(X1),X2) -> fib1#(X1,X2) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) fib1#(mark(X1),X2) -> fib1#(X1,X2) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) fib1#(X1,mark(X2)) -> fib1#(X1,X2) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) fib1#(X1,mark(X2)) -> fib1#(X1,X2) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) fib1#(X1,mark(X2)) -> fib1#(X1,X2) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) active#(cons(X1,X2)) -> cons#(active(X1),X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(cons(X1,X2)) -> cons#(active(X1),X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(cons(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(fib(X)) -> fib#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(fib(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(cons(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(cons(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> add#(X,Y) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(cons(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> add#(X,Y) active#(cons(X1,X2)) -> active#(X1) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(cons(X1,X2)) -> active#(X1) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(cons(X1,X2)) -> active#(X1) -> active#(fib(N)) -> s#(0()) active#(add(s(X),Y)) -> add#(X,Y) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) active#(add(s(X),Y)) -> add#(X,Y) -> add#(X1,mark(X2)) -> add#(X1,X2) active#(add(s(X),Y)) -> add#(X,Y) -> add#(mark(X1),X2) -> add#(X1,X2) active#(add(s(X),Y)) -> s#(add(X,Y)) -> s#(ok(X)) -> s#(X) active#(add(s(X),Y)) -> s#(add(X,Y)) -> s#(mark(X)) -> s#(X) active#(add(X1,X2)) -> add#(active(X1),X2) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) active#(add(X1,X2)) -> add#(active(X1),X2) -> add#(X1,mark(X2)) -> add#(X1,X2) active#(add(X1,X2)) -> add#(active(X1),X2) -> add#(mark(X1),X2) -> add#(X1,X2) active#(add(X1,X2)) -> add#(X1,active(X2)) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) active#(add(X1,X2)) -> add#(X1,active(X2)) -> add#(X1,mark(X2)) -> add#(X1,X2) active#(add(X1,X2)) -> add#(X1,active(X2)) -> add#(mark(X1),X2) -> add#(X1,X2) active#(add(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(add(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(add(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(add(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(add(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(add(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(add(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) -> active#(fib(X)) -> fib#(active(X)) active#(add(X1,X2)) -> active#(X2) -> active#(fib(X)) -> active#(X) active#(add(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(add(X1,X2)) -> active#(X2) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(add(X1,X2)) -> active#(X2) -> active#(add(s(X),Y)) -> add#(X,Y) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(add(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> add#(X,Y) active#(add(X1,X2)) -> active#(X2) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(add(X1,X2)) -> active#(X2) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(add(X1,X2)) -> active#(X2) -> active#(fib(N)) -> s#(0()) active#(add(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(add(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(add(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(add(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(add(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(add(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(add(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X1) -> active#(fib(X)) -> fib#(active(X)) active#(add(X1,X2)) -> active#(X1) -> active#(fib(X)) -> active#(X) active#(add(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(add(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(add(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> add#(X,Y) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(add(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> add#(X,Y) active#(add(X1,X2)) -> active#(X1) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(add(X1,X2)) -> active#(X1) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(add(X1,X2)) -> active#(X1) -> active#(fib(N)) -> s#(0()) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) -> sel#(mark(X1),X2) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(active(X1),X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(active(X1),X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(active(X1),X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) -> sel#(mark(X1),X2) -> sel#(X1,X2) active#(sel(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(fib(X)) -> fib#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(fib(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(sel(X1,X2)) -> active#(X2) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(sel(X1,X2)) -> active#(X2) -> active#(add(s(X),Y)) -> add#(X,Y) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(sel(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> add#(X,Y) active#(sel(X1,X2)) -> active#(X2) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(sel(X1,X2)) -> active#(X2) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(sel(X1,X2)) -> active#(X2) -> active#(fib(N)) -> s#(0()) active#(sel(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(fib(X)) -> fib#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(fib(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(sel(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(sel(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> add#(X,Y) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(sel(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> add#(X,Y) active#(sel(X1,X2)) -> active#(X1) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(sel(X1,X2)) -> active#(X1) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(sel(X1,X2)) -> active#(X1) -> active#(fib(N)) -> s#(0()) active#(fib1(X1,X2)) -> fib1#(active(X1),X2) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) active#(fib1(X1,X2)) -> fib1#(active(X1),X2) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) active#(fib1(X1,X2)) -> fib1#(active(X1),X2) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(add(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(fib1(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib(X)) -> fib#(active(X)) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib(X)) -> active#(X) active#(fib1(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(fib1(X1,X2)) -> active#(X2) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(fib1(X1,X2)) -> active#(X2) -> active#(add(s(X),Y)) -> add#(X,Y) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib1(X,Y)) -> add#(X,Y) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(fib1(X1,X2)) -> active#(X2) -> active#(fib(N)) -> s#(0()) active#(fib1(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(add(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(fib1(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(fib1(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(fib1(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib(X)) -> fib#(active(X)) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib(X)) -> active#(X) active#(fib1(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(fib1(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(fib1(X1,X2)) -> active#(X1) -> active#(add(s(X),Y)) -> add#(X,Y) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib1(X,Y)) -> add#(X,Y) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(fib1(X1,X2)) -> active#(X1) -> active#(fib(N)) -> s#(0()) active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(fib1(X,Y)) -> add#(X,Y) -> add#(ok(X1),ok(X2)) -> add#(X1,X2) active#(fib1(X,Y)) -> add#(X,Y) -> add#(X1,mark(X2)) -> add#(X1,X2) active#(fib1(X,Y)) -> add#(X,Y) -> add#(mark(X1),X2) -> add#(X1,X2) active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X) active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X) active#(s(X)) -> active#(X) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(fib1(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(fib1(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(fib(X)) -> fib#(active(X)) active#(s(X)) -> active#(X) -> active#(fib(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(s(X)) -> active#(X) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(s(X)) -> active#(X) -> active#(add(s(X),Y)) -> add#(X,Y) active#(s(X)) -> active#(X) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(s(X)) -> active#(X) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(s(X)) -> active#(X) -> active#(fib1(X,Y)) -> add#(X,Y) active#(s(X)) -> active#(X) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(s(X)) -> active#(X) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(s(X)) -> active#(X) -> active#(fib(N)) -> s#(0()) active#(fib(X)) -> fib#(active(X)) -> fib#(ok(X)) -> fib#(X) active#(fib(X)) -> fib#(active(X)) -> fib#(mark(X)) -> fib#(X) active#(fib(X)) -> active#(X) -> active#(add(X1,X2)) -> add#(X1,active(X2)) active#(fib(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X2) active#(fib(X)) -> active#(X) -> active#(add(X1,X2)) -> add#(active(X1),X2) active#(fib(X)) -> active#(X) -> active#(add(X1,X2)) -> active#(X1) active#(fib(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(fib(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(fib(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(fib(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(fib(X)) -> active#(X) -> active#(fib1(X1,X2)) -> fib1#(X1,active(X2)) active#(fib(X)) -> active#(X) -> active#(fib1(X1,X2)) -> active#(X2) active#(fib(X)) -> active#(X) -> active#(fib1(X1,X2)) -> fib1#(active(X1),X2) active#(fib(X)) -> active#(X) -> active#(fib1(X1,X2)) -> active#(X1) active#(fib(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(fib(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(fib(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(fib(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(fib(X)) -> active#(X) -> active#(fib(X)) -> fib#(active(X)) active#(fib(X)) -> active#(X) -> active#(fib(X)) -> active#(X) active#(fib(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(fib(X)) -> active#(X) -> active#(add(s(X),Y)) -> s#(add(X,Y)) active#(fib(X)) -> active#(X) -> active#(add(s(X),Y)) -> add#(X,Y) active#(fib(X)) -> active#(X) -> active#(fib1(X,Y)) -> cons#(X,fib1(Y,add(X,Y))) active#(fib(X)) -> active#(X) -> active#(fib1(X,Y)) -> fib1#(Y,add(X,Y)) active#(fib(X)) -> active#(X) -> active#(fib1(X,Y)) -> add#(X,Y) active#(fib(X)) -> active#(X) -> active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) active#(fib(X)) -> active#(X) -> active#(fib(N)) -> fib1#(s(0()),s(0())) active#(fib(X)) -> active#(X) -> active#(fib(N)) -> s#(0()) active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(fib(N)) -> sel#(N,fib1(s(0()),s(0()))) -> sel#(mark(X1),X2) -> sel#(X1,X2) active#(fib(N)) -> fib1#(s(0()),s(0())) -> fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) active#(fib(N)) -> fib1#(s(0()),s(0())) -> fib1#(X1,mark(X2)) -> fib1#(X1,X2) active#(fib(N)) -> fib1#(s(0()),s(0())) -> fib1#(mark(X1),X2) -> fib1#(X1,X2) active#(fib(N)) -> s#(0()) -> s#(ok(X)) -> s#(X) active#(fib(N)) -> s#(0()) -> s#(mark(X)) -> s#(X) SCC Processor: #sccs: 9 #rules: 36 #arcs: 556/3844 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(fib(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [cons](x0, x1) = x0, [add](x0, x1) = x0 + x1, [mark](x0) = 0, [sel](x0, x1) = x0 + x1, [fib1](x0, x1) = x0 + x1, [s](x0) = x0, [0] = 0, [active](x0) = x0, [fib](x0) = x0 + 1 orientation: active#(fib(X)) = X + 2 >= X + 1 = active#(X) active#(sel(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active#(sel(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active#(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active#(fib1(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active#(s(X)) = X + 1 >= X + 1 = active#(X) active#(cons(X1,X2)) = X1 + 1 >= X1 + 1 = active#(X1) active#(add(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active#(add(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active(fib(N)) = N + 1 >= 0 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = X + Y >= 0 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = X >= 0 = mark(X) active(add(s(X),Y)) = X + Y >= 0 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = X >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = N + X >= 0 = mark(sel(N,XS)) active(fib(X)) = X + 1 >= X + 1 = fib(active(X)) active(sel(X1,X2)) = X1 + X2 >= X1 + X2 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + X2 >= X1 + X2 = sel(X1,active(X2)) active(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(active(X1),X2) active(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(X1,active(X2)) active(s(X)) = X >= X = s(active(X)) active(cons(X1,X2)) = X1 >= X1 = cons(active(X1),X2) active(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(active(X1),X2) active(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(X1,active(X2)) fib(mark(X)) = 1 >= 0 = mark(fib(X)) sel(mark(X1),X2) = X2 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 >= 0 = mark(sel(X1,X2)) fib1(mark(X1),X2) = X2 >= 0 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = X1 >= 0 = mark(fib1(X1,X2)) s(mark(X)) = 0 >= 0 = mark(s(X)) cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2)) add(mark(X1),X2) = X2 >= 0 = mark(add(X1,X2)) add(X1,mark(X2)) = X1 >= 0 = mark(add(X1,X2)) proper(fib(X)) = X + 1 >= X + 1 = fib(proper(X)) proper(sel(X1,X2)) = X1 + X2 >= X1 + X2 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(proper(X1),proper(X2)) proper(s(X)) = X >= X = s(proper(X)) proper(0()) = 0 >= 0 = ok(0()) proper(cons(X1,X2)) = X1 >= X1 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(proper(X1),proper(X2)) fib(ok(X)) = X + 1 >= X + 1 = ok(fib(X)) sel(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(fib1(X1,X2)) s(ok(X)) = X >= X = ok(s(X)) cons(ok(X1),ok(X2)) = X1 >= X1 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [cons](x0, x1) = x0 + 1, [add](x0, x1) = x0 + x1, [mark](x0) = 0, [sel](x0, x1) = x0 + x1 + 1, [fib1](x0, x1) = x0 + x1, [s](x0) = x0 + 1, [0] = 0, [active](x0) = x0, [fib](x0) = 0 orientation: active#(sel(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(sel(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active#(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active#(fib1(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active#(s(X)) = X + 2 >= X + 1 = active#(X) active#(cons(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(add(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active#(add(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active(fib(N)) = 0 >= 0 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = X + Y >= 0 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = X >= 0 = mark(X) active(add(s(X),Y)) = X + Y + 1 >= 0 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = X + 2 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = N + X + 3 >= 0 = mark(sel(N,XS)) active(fib(X)) = 0 >= 0 = fib(active(X)) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(X1,active(X2)) active(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(active(X1),X2) active(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(X1,active(X2)) active(s(X)) = X + 1 >= X + 1 = s(active(X)) active(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(active(X1),X2) active(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(active(X1),X2) active(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(X1,active(X2)) fib(mark(X)) = 0 >= 0 = mark(fib(X)) sel(mark(X1),X2) = X2 + 1 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 1 >= 0 = mark(sel(X1,X2)) fib1(mark(X1),X2) = X2 >= 0 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = X1 >= 0 = mark(fib1(X1,X2)) s(mark(X)) = 1 >= 0 = mark(s(X)) cons(mark(X1),X2) = 1 >= 0 = mark(cons(X1,X2)) add(mark(X1),X2) = X2 >= 0 = mark(add(X1,X2)) add(X1,mark(X2)) = X1 >= 0 = mark(add(X1,X2)) proper(fib(X)) = 0 >= 0 = fib(proper(X)) proper(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(proper(X1),proper(X2)) proper(s(X)) = X + 1 >= X + 1 = s(proper(X)) proper(0()) = 0 >= 0 = ok(0()) proper(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(proper(X1),proper(X2)) fib(ok(X)) = 0 >= 0 = ok(fib(X)) sel(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(fib1(X1,X2)) s(ok(X)) = X + 1 >= X + 1 = ok(s(X)) cons(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) active#(add(X1,X2)) -> active#(X1) active#(add(X1,X2)) -> active#(X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0, [cons](x0, x1) = 0, [add](x0, x1) = x0 + x1 + 1, [mark](x0) = 0, [sel](x0, x1) = 0, [fib1](x0, x1) = x0 + x1, [s](x0) = 0, [0] = 0, [active](x0) = x0, [fib](x0) = 0 orientation: active#(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = active#(X1) active#(fib1(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = active#(X2) active#(add(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(add(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active(fib(N)) = 0 >= 0 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = X + Y >= 0 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = X + 1 >= 0 = mark(X) active(add(s(X),Y)) = Y + 1 >= 0 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = 0 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = 0 >= 0 = mark(sel(N,XS)) active(fib(X)) = 0 >= 0 = fib(active(X)) active(sel(X1,X2)) = 0 >= 0 = sel(active(X1),X2) active(sel(X1,X2)) = 0 >= 0 = sel(X1,active(X2)) active(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(active(X1),X2) active(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(X1,active(X2)) active(s(X)) = 0 >= 0 = s(active(X)) active(cons(X1,X2)) = 0 >= 0 = cons(active(X1),X2) active(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(active(X1),X2) active(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(X1,active(X2)) fib(mark(X)) = 0 >= 0 = mark(fib(X)) sel(mark(X1),X2) = 0 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = 0 >= 0 = mark(sel(X1,X2)) fib1(mark(X1),X2) = X2 >= 0 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = X1 >= 0 = mark(fib1(X1,X2)) s(mark(X)) = 0 >= 0 = mark(s(X)) cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2)) add(mark(X1),X2) = X2 + 1 >= 0 = mark(add(X1,X2)) add(X1,mark(X2)) = X1 + 1 >= 0 = mark(add(X1,X2)) proper(fib(X)) = 0 >= 0 = fib(proper(X)) proper(sel(X1,X2)) = 0 >= 0 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = X1 + X2 >= X1 + X2 = fib1(proper(X1),proper(X2)) proper(s(X)) = 0 >= 0 = s(proper(X)) proper(0()) = 0 >= 0 = ok(0()) proper(cons(X1,X2)) = 0 >= 0 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(proper(X1),proper(X2)) fib(ok(X)) = 0 >= 0 = ok(fib(X)) sel(ok(X1),ok(X2)) = 0 >= 0 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = 0 >= 0 = ok(fib1(X1,X2)) s(ok(X)) = 0 >= 0 = ok(s(X)) cons(ok(X1),ok(X2)) = 0 >= 0 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = 1 >= 0 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(fib1(X1,X2)) -> active#(X1) active#(fib1(X1,X2)) -> active#(X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [cons](x0, x1) = 0, [add](x0, x1) = x1, [mark](x0) = 0, [sel](x0, x1) = 0, [fib1](x0, x1) = x0 + x1 + 1, [s](x0) = 1, [0] = 0, [active](x0) = x0, [fib](x0) = 0 orientation: active#(fib1(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(fib1(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active(fib(N)) = 0 >= 0 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = X + Y + 1 >= 0 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = X >= 0 = mark(X) active(add(s(X),Y)) = Y >= 0 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = 0 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = 0 >= 0 = mark(sel(N,XS)) active(fib(X)) = 0 >= 0 = fib(active(X)) active(sel(X1,X2)) = 0 >= 0 = sel(active(X1),X2) active(sel(X1,X2)) = 0 >= 0 = sel(X1,active(X2)) active(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = fib1(active(X1),X2) active(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = fib1(X1,active(X2)) active(s(X)) = 1 >= 1 = s(active(X)) active(cons(X1,X2)) = 0 >= 0 = cons(active(X1),X2) active(add(X1,X2)) = X2 >= X2 = add(active(X1),X2) active(add(X1,X2)) = X2 >= X2 = add(X1,active(X2)) fib(mark(X)) = 0 >= 0 = mark(fib(X)) sel(mark(X1),X2) = 0 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = 0 >= 0 = mark(sel(X1,X2)) fib1(mark(X1),X2) = X2 + 1 >= 0 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = X1 + 1 >= 0 = mark(fib1(X1,X2)) s(mark(X)) = 1 >= 0 = mark(s(X)) cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2)) add(mark(X1),X2) = X2 >= 0 = mark(add(X1,X2)) add(X1,mark(X2)) = 0 >= 0 = mark(add(X1,X2)) proper(fib(X)) = 0 >= 0 = fib(proper(X)) proper(sel(X1,X2)) = 0 >= 0 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = fib1(proper(X1),proper(X2)) proper(s(X)) = 1 >= 1 = s(proper(X)) proper(0()) = 0 >= 0 = ok(0()) proper(cons(X1,X2)) = 0 >= 0 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X2 >= X2 = add(proper(X1),proper(X2)) fib(ok(X)) = 0 >= 0 = ok(fib(X)) sel(ok(X1),ok(X2)) = 0 >= 0 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(fib1(X1,X2)) s(ok(X)) = 1 >= 1 = ok(s(X)) cons(ok(X1),ok(X2)) = 0 >= 0 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = X2 >= X2 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(fib(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(fib1(X1,X2)) -> proper#(X2) proper#(fib1(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [cons](x0, x1) = x0 + x1, [add](x0, x1) = x0 + x1, [mark](x0) = 1, [sel](x0, x1) = x0 + x1, [fib1](x0, x1) = x0 + x1 + 1, [s](x0) = x0, [0] = 0, [active](x0) = x0 + 1, [fib](x0) = x0 + 1 orientation: proper#(fib(X)) = X + 2 >= X + 1 = proper#(X) proper#(sel(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2) proper#(sel(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1) proper#(fib1(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(fib1(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(s(X)) = X + 1 >= X + 1 = proper#(X) proper#(cons(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2) proper#(cons(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1) proper#(add(X1,X2)) = X1 + X2 + 1 >= X2 + 1 = proper#(X2) proper#(add(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = proper#(X1) active(fib(N)) = N + 2 >= 1 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = X + Y + 2 >= 1 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = X + 1 >= 1 = mark(X) active(add(s(X),Y)) = X + Y + 1 >= 1 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = X + XS + 1 >= 1 = mark(X) active(sel(s(N),cons(X,XS))) = N + X + XS + 1 >= 1 = mark(sel(N,XS)) active(fib(X)) = X + 2 >= X + 2 = fib(active(X)) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(X1,active(X2)) active(fib1(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = fib1(active(X1),X2) active(fib1(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = fib1(X1,active(X2)) active(s(X)) = X + 1 >= X + 1 = s(active(X)) active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2) active(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(active(X1),X2) active(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(X1,active(X2)) fib(mark(X)) = 2 >= 1 = mark(fib(X)) sel(mark(X1),X2) = X2 + 1 >= 1 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 1 >= 1 = mark(sel(X1,X2)) fib1(mark(X1),X2) = X2 + 2 >= 1 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = X1 + 2 >= 1 = mark(fib1(X1,X2)) s(mark(X)) = 1 >= 1 = mark(s(X)) cons(mark(X1),X2) = X2 + 1 >= 1 = mark(cons(X1,X2)) add(mark(X1),X2) = X2 + 1 >= 1 = mark(add(X1,X2)) add(X1,mark(X2)) = X1 + 1 >= 1 = mark(add(X1,X2)) proper(fib(X)) = X + 1 >= X + 1 = fib(proper(X)) proper(sel(X1,X2)) = X1 + X2 >= X1 + X2 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = fib1(proper(X1),proper(X2)) proper(s(X)) = X >= X = s(proper(X)) proper(0()) = 0 >= 0 = ok(0()) proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X1 + X2 >= X1 + X2 = add(proper(X1),proper(X2)) fib(ok(X)) = X + 1 >= X + 1 = ok(fib(X)) sel(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(fib1(X1,X2)) s(ok(X)) = X >= X = ok(s(X)) cons(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(add(X1,X2)) -> proper#(X2) proper#(add(X1,X2)) -> proper#(X1) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [cons](x0, x1) = x0 + x1 + 1, [add](x0, x1) = x0 + x1 + 1, [mark](x0) = 0, [sel](x0, x1) = x0 + x1 + 1, [fib1](x0, x1) = 0, [s](x0) = x0 + 1, [0] = 0, [active](x0) = x0, [fib](x0) = 0 orientation: proper#(sel(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(sel(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(s(X)) = X + 2 >= X + 1 = proper#(X) proper#(cons(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(cons(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(add(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(add(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) active(fib(N)) = 0 >= 0 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = 0 >= 0 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = X + 1 >= 0 = mark(X) active(add(s(X),Y)) = X + Y + 2 >= 0 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = X + XS + 2 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = N + X + XS + 3 >= 0 = mark(sel(N,XS)) active(fib(X)) = 0 >= 0 = fib(active(X)) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(X1,active(X2)) active(fib1(X1,X2)) = 0 >= 0 = fib1(active(X1),X2) active(fib1(X1,X2)) = 0 >= 0 = fib1(X1,active(X2)) active(s(X)) = X + 1 >= X + 1 = s(active(X)) active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2) active(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(active(X1),X2) active(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(X1,active(X2)) fib(mark(X)) = 0 >= 0 = mark(fib(X)) sel(mark(X1),X2) = X2 + 1 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 1 >= 0 = mark(sel(X1,X2)) fib1(mark(X1),X2) = 0 >= 0 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = 0 >= 0 = mark(fib1(X1,X2)) s(mark(X)) = 1 >= 0 = mark(s(X)) cons(mark(X1),X2) = X2 + 1 >= 0 = mark(cons(X1,X2)) add(mark(X1),X2) = X2 + 1 >= 0 = mark(add(X1,X2)) add(X1,mark(X2)) = X1 + 1 >= 0 = mark(add(X1,X2)) proper(fib(X)) = 0 >= 0 = fib(proper(X)) proper(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = 0 >= 0 = fib1(proper(X1),proper(X2)) proper(s(X)) = X + 1 >= X + 1 = s(proper(X)) proper(0()) = 0 >= 0 = ok(0()) proper(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = add(proper(X1),proper(X2)) fib(ok(X)) = 0 >= 0 = ok(fib(X)) sel(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = 0 >= 0 = ok(fib1(X1,X2)) s(ok(X)) = X + 1 >= X + 1 = ok(s(X)) cons(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: add#(mark(X1),X2) -> add#(X1,X2) add#(X1,mark(X2)) -> add#(X1,X2) add#(ok(X1),ok(X2)) -> add#(X1,X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [cons#](x0, x1) = x1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = x0 + 1, [cons](x0, x1) = x1 + 1, [add](x0, x1) = x0, [mark](x0) = 0, [sel](x0, x1) = x1 + 1, [fib1](x0, x1) = x1 + 1, [s](x0) = x0, [0] = 0, [active](x0) = x0, [fib](x0) = x0 + 1 orientation: cons#(mark(X1),X2) = X2 >= X2 = cons#(X1,X2) cons#(ok(X1),ok(X2)) = X2 + 1 >= X2 = cons#(X1,X2) active(fib(N)) = N + 1 >= 0 = mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) = Y + 1 >= 0 = mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) = 0 >= 0 = mark(X) active(add(s(X),Y)) = X >= 0 = mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) = XS + 2 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = XS + 2 >= 0 = mark(sel(N,XS)) active(fib(X)) = X + 1 >= X + 1 = fib(active(X)) active(sel(X1,X2)) = X2 + 1 >= X2 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X2 + 1 >= X2 + 1 = sel(X1,active(X2)) active(fib1(X1,X2)) = X2 + 1 >= X2 + 1 = fib1(active(X1),X2) active(fib1(X1,X2)) = X2 + 1 >= X2 + 1 = fib1(X1,active(X2)) active(s(X)) = X >= X = s(active(X)) active(cons(X1,X2)) = X2 + 1 >= X2 + 1 = cons(active(X1),X2) active(add(X1,X2)) = X1 >= X1 = add(active(X1),X2) active(add(X1,X2)) = X1 >= X1 = add(X1,active(X2)) fib(mark(X)) = 1 >= 0 = mark(fib(X)) sel(mark(X1),X2) = X2 + 1 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = 1 >= 0 = mark(sel(X1,X2)) fib1(mark(X1),X2) = X2 + 1 >= 0 = mark(fib1(X1,X2)) fib1(X1,mark(X2)) = 1 >= 0 = mark(fib1(X1,X2)) s(mark(X)) = 0 >= 0 = mark(s(X)) cons(mark(X1),X2) = X2 + 1 >= 0 = mark(cons(X1,X2)) add(mark(X1),X2) = 0 >= 0 = mark(add(X1,X2)) add(X1,mark(X2)) = X1 >= 0 = mark(add(X1,X2)) proper(fib(X)) = X + 2 >= X + 2 = fib(proper(X)) proper(sel(X1,X2)) = X2 + 2 >= X2 + 2 = sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) = X2 + 2 >= X2 + 2 = fib1(proper(X1),proper(X2)) proper(s(X)) = X + 1 >= X + 1 = s(proper(X)) proper(0()) = 1 >= 1 = ok(0()) proper(cons(X1,X2)) = X2 + 2 >= X2 + 2 = cons(proper(X1),proper(X2)) proper(add(X1,X2)) = X1 + 1 >= X1 + 1 = add(proper(X1),proper(X2)) fib(ok(X)) = X + 2 >= X + 2 = ok(fib(X)) sel(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(fib1(X1,X2)) s(ok(X)) = X + 1 >= X + 1 = ok(s(X)) cons(ok(X1),ok(X2)) = X2 + 2 >= X2 + 2 = ok(cons(X1,X2)) add(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(add(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: s#(mark(X)) -> s#(X) s#(ok(X)) -> s#(X) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: fib1#(mark(X1),X2) -> fib1#(X1,X2) fib1#(X1,mark(X2)) -> fib1#(X1,X2) fib1#(ok(X1),ok(X2)) -> fib1#(X1,X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: fib#(mark(X)) -> fib#(X) fib#(ok(X)) -> fib#(X) TRS: active(fib(N)) -> mark(sel(N,fib1(s(0()),s(0())))) active(fib1(X,Y)) -> mark(cons(X,fib1(Y,add(X,Y)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(fib(X)) -> fib(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(fib1(X1,X2)) -> fib1(active(X1),X2) active(fib1(X1,X2)) -> fib1(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(add(X1,X2)) -> add(active(X1),X2) active(add(X1,X2)) -> add(X1,active(X2)) fib(mark(X)) -> mark(fib(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) fib1(mark(X1),X2) -> mark(fib1(X1,X2)) fib1(X1,mark(X2)) -> mark(fib1(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) add(mark(X1),X2) -> mark(add(X1,X2)) add(X1,mark(X2)) -> mark(add(X1,X2)) proper(fib(X)) -> fib(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(fib1(X1,X2)) -> fib1(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(0()) -> ok(0()) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(add(X1,X2)) -> add(proper(X1),proper(X2)) fib(ok(X)) -> ok(fib(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) fib1(ok(X1),ok(X2)) -> ok(fib1(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) add(ok(X1),ok(X2)) -> ok(add(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open