MAYBE Problem: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(from(X)) -> active#(X) active#(from(X)) -> from#(active(X)) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) active#(s(X)) -> s#(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#(minus(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) from#(mark(X)) -> from#(X) cons#(mark(X1),X2) -> cons#(X1,X2) s#(mark(X)) -> s#(X) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) minus#(mark(X1),X2) -> minus#(X1,X2) minus#(X1,mark(X2)) -> minus#(X1,X2) quot#(mark(X1),X2) -> quot#(X1,X2) quot#(X1,mark(X2)) -> quot#(X1,X2) zWquot#(mark(X1),X2) -> zWquot#(X1,X2) zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) proper#(from(X)) -> proper#(X) proper#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) from#(ok(X)) -> from#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) s#(ok(X)) -> s#(X) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) minus#(ok(X1),ok(X2)) -> minus#(X1,X2) quot#(ok(X1),ok(X2)) -> quot#(X1,X2) zWquot#(ok(X1),ok(X2)) -> zWquot#(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(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) TDG Processor: DPs: active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(from(X)) -> active#(X) active#(from(X)) -> from#(active(X)) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) active#(s(X)) -> s#(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#(minus(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) from#(mark(X)) -> from#(X) cons#(mark(X1),X2) -> cons#(X1,X2) s#(mark(X)) -> s#(X) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) minus#(mark(X1),X2) -> minus#(X1,X2) minus#(X1,mark(X2)) -> minus#(X1,X2) quot#(mark(X1),X2) -> quot#(X1,X2) quot#(X1,mark(X2)) -> quot#(X1,X2) zWquot#(mark(X1),X2) -> zWquot#(X1,X2) zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) proper#(from(X)) -> proper#(X) proper#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) from#(ok(X)) -> from#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) s#(ok(X)) -> s#(X) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) minus#(ok(X1),ok(X2)) -> minus#(X1,X2) quot#(ok(X1),ok(X2)) -> quot#(X1,X2) zWquot#(ok(X1),ok(X2)) -> zWquot#(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(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(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#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(quot(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(quot(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(minus(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(minus(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#(s(X)) -> s#(active(X)) top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X) 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#(from(X)) -> from#(active(X)) top#(ok(X)) -> active#(X) -> active#(from(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) top#(ok(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) top#(ok(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) top#(ok(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) top#(ok(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) top#(ok(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) top#(ok(X)) -> active#(X) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) top#(ok(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) top#(ok(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) top#(ok(X)) -> active#(X) -> active#(from(X)) -> s#(X) 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#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(minus(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#(s(X)) -> s#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) 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#(from(X)) -> from#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> from#(proper(X)) proper#(zWquot(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> from#(proper(X)) proper#(zWquot(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> proper#(X) proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> from#(proper(X)) proper#(quot(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> from#(proper(X)) proper#(quot(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> proper#(X) proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) -> quot#(X1,mark(X2)) -> quot#(X1,X2) proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) -> quot#(mark(X1),X2) -> quot#(X1,X2) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> from#(proper(X)) proper#(minus(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> from#(proper(X)) proper#(minus(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> proper#(X) proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) -> minus#(X1,mark(X2)) -> minus#(X1,X2) proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) -> minus#(mark(X1),X2) -> minus#(X1,X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(minus(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#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) 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#(from(X)) -> from#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(minus(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#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) 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#(from(X)) -> from#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(from(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#(cons(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(minus(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#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) 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#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(minus(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#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) 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#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(from(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#(s(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(minus(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#(s(X)) -> s#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) 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#(from(X)) -> from#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(from(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#(from(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> zWquot#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(zWquot(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> quot#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(quot(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(minus(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(from(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X)) proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) proper#(from(X)) -> from#(proper(X)) -> from#(ok(X)) -> from#(X) proper#(from(X)) -> from#(proper(X)) -> from#(mark(X)) -> from#(X) zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) zWquot#(mark(X1),X2) -> zWquot#(X1,X2) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) zWquot#(mark(X1),X2) -> zWquot#(X1,X2) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) zWquot#(mark(X1),X2) -> zWquot#(X1,X2) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) quot#(ok(X1),ok(X2)) -> quot#(X1,X2) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) quot#(ok(X1),ok(X2)) -> quot#(X1,X2) -> quot#(X1,mark(X2)) -> quot#(X1,X2) quot#(ok(X1),ok(X2)) -> quot#(X1,X2) -> quot#(mark(X1),X2) -> quot#(X1,X2) quot#(mark(X1),X2) -> quot#(X1,X2) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) quot#(mark(X1),X2) -> quot#(X1,X2) -> quot#(X1,mark(X2)) -> quot#(X1,X2) quot#(mark(X1),X2) -> quot#(X1,X2) -> quot#(mark(X1),X2) -> quot#(X1,X2) quot#(X1,mark(X2)) -> quot#(X1,X2) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) quot#(X1,mark(X2)) -> quot#(X1,X2) -> quot#(X1,mark(X2)) -> quot#(X1,X2) quot#(X1,mark(X2)) -> quot#(X1,X2) -> quot#(mark(X1),X2) -> quot#(X1,X2) minus#(ok(X1),ok(X2)) -> minus#(X1,X2) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) minus#(ok(X1),ok(X2)) -> minus#(X1,X2) -> minus#(X1,mark(X2)) -> minus#(X1,X2) minus#(ok(X1),ok(X2)) -> minus#(X1,X2) -> minus#(mark(X1),X2) -> minus#(X1,X2) minus#(mark(X1),X2) -> minus#(X1,X2) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) minus#(mark(X1),X2) -> minus#(X1,X2) -> minus#(X1,mark(X2)) -> minus#(X1,X2) minus#(mark(X1),X2) -> minus#(X1,X2) -> minus#(mark(X1),X2) -> minus#(X1,X2) minus#(X1,mark(X2)) -> minus#(X1,X2) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) minus#(X1,mark(X2)) -> minus#(X1,X2) -> minus#(X1,mark(X2)) -> minus#(X1,X2) minus#(X1,mark(X2)) -> minus#(X1,X2) -> minus#(mark(X1),X2) -> minus#(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) 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) from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X) from#(ok(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(ok(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X) 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#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) -> quot#(X1,mark(X2)) -> quot#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) -> quot#(mark(X1),X2) -> quot#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) -> zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) -> zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) -> zWquot#(mark(X1),X2) -> zWquot#(X1,X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(zWquot(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(active(X)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(from(X)) -> active#(X) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(zWquot(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(zWquot(X1,X2)) -> active#(X2) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(zWquot(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(zWquot(X1,X2)) -> active#(X2) -> active#(from(X)) -> cons#(X,from(s(X))) active#(zWquot(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(s(X)) active#(zWquot(X1,X2)) -> active#(X2) -> active#(from(X)) -> s#(X) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(zWquot(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(zWquot(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(zWquot(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(zWquot(X1,X2)) -> active#(X1) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(zWquot(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(zWquot(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(zWquot(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(zWquot(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) -> quot#(X1,mark(X2)) -> quot#(X1,X2) active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) -> quot#(mark(X1),X2) -> quot#(X1,X2) active#(quot(s(X),s(Y))) -> minus#(X,Y) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) active#(quot(s(X),s(Y))) -> minus#(X,Y) -> minus#(X1,mark(X2)) -> minus#(X1,X2) active#(quot(s(X),s(Y))) -> minus#(X,Y) -> minus#(mark(X1),X2) -> minus#(X1,X2) active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) -> s#(ok(X)) -> s#(X) active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) -> s#(mark(X)) -> s#(X) active#(quot(X1,X2)) -> quot#(active(X1),X2) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) active#(quot(X1,X2)) -> quot#(active(X1),X2) -> quot#(X1,mark(X2)) -> quot#(X1,X2) active#(quot(X1,X2)) -> quot#(active(X1),X2) -> quot#(mark(X1),X2) -> quot#(X1,X2) active#(quot(X1,X2)) -> quot#(X1,active(X2)) -> quot#(ok(X1),ok(X2)) -> quot#(X1,X2) active#(quot(X1,X2)) -> quot#(X1,active(X2)) -> quot#(X1,mark(X2)) -> quot#(X1,X2) active#(quot(X1,X2)) -> quot#(X1,active(X2)) -> quot#(mark(X1),X2) -> quot#(X1,X2) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(quot(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(quot(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(quot(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(active(X)) active#(quot(X1,X2)) -> active#(X2) -> active#(from(X)) -> active#(X) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(quot(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(quot(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(quot(X1,X2)) -> active#(X2) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(quot(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(quot(X1,X2)) -> active#(X2) -> active#(from(X)) -> cons#(X,from(s(X))) active#(quot(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(s(X)) active#(quot(X1,X2)) -> active#(X2) -> active#(from(X)) -> s#(X) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(quot(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(quot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(quot(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(quot(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(quot(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(quot(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X)) active#(quot(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(quot(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(quot(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(quot(X1,X2)) -> active#(X1) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(quot(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(quot(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(quot(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(quot(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) active#(minus(s(X),s(Y))) -> minus#(X,Y) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) active#(minus(s(X),s(Y))) -> minus#(X,Y) -> minus#(X1,mark(X2)) -> minus#(X1,X2) active#(minus(s(X),s(Y))) -> minus#(X,Y) -> minus#(mark(X1),X2) -> minus#(X1,X2) active#(minus(X1,X2)) -> minus#(active(X1),X2) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) active#(minus(X1,X2)) -> minus#(active(X1),X2) -> minus#(X1,mark(X2)) -> minus#(X1,X2) active#(minus(X1,X2)) -> minus#(active(X1),X2) -> minus#(mark(X1),X2) -> minus#(X1,X2) active#(minus(X1,X2)) -> minus#(X1,active(X2)) -> minus#(ok(X1),ok(X2)) -> minus#(X1,X2) active#(minus(X1,X2)) -> minus#(X1,active(X2)) -> minus#(X1,mark(X2)) -> minus#(X1,X2) active#(minus(X1,X2)) -> minus#(X1,active(X2)) -> minus#(mark(X1),X2) -> minus#(X1,X2) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(minus(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(minus(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(minus(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(active(X)) active#(minus(X1,X2)) -> active#(X2) -> active#(from(X)) -> active#(X) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(minus(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(minus(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(minus(X1,X2)) -> active#(X2) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(minus(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(minus(X1,X2)) -> active#(X2) -> active#(from(X)) -> cons#(X,from(s(X))) active#(minus(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(s(X)) active#(minus(X1,X2)) -> active#(X2) -> active#(from(X)) -> s#(X) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(minus(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(minus(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(minus(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(minus(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(minus(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(minus(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X)) active#(minus(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(minus(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(minus(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(minus(X1,X2)) -> active#(X1) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(minus(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(minus(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(minus(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(minus(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) 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#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(zWquot(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(minus(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#(s(X)) -> s#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) 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#(from(X)) -> from#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(sel(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(sel(X1,X2)) -> active#(X2) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(sel(X1,X2)) -> active#(X2) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(sel(X1,X2)) -> active#(X2) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> cons#(X,from(s(X))) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(s(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> s#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(minus(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#(s(X)) -> s#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) 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#(from(X)) -> from#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(sel(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(sel(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(sel(X1,X2)) -> active#(X1) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(from(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#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(zWquot(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(minus(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#(s(X)) -> s#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) 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#(from(X)) -> from#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(cons(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(cons(X1,X2)) -> active#(X1) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(cons(X1,X2)) -> active#(X1) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(cons(X1,X2)) -> active#(X1) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) 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#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(quot(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(quot(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(minus(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(minus(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#(s(X)) -> s#(active(X)) active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X) 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#(from(X)) -> from#(active(X)) active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(s(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(s(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(s(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(s(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(s(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(s(X)) -> active#(X) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(s(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(s(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) active#(s(X)) -> active#(X) -> active#(from(X)) -> s#(X) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(from(X)) -> cons#(X,from(s(X))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(from(X)) -> from#(s(X)) -> from#(ok(X)) -> from#(X) active#(from(X)) -> from#(s(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> from#(active(X)) -> from#(ok(X)) -> from#(X) active#(from(X)) -> from#(active(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> s#(X) -> s#(ok(X)) -> s#(X) active#(from(X)) -> s#(X) -> s#(mark(X)) -> s#(X) active#(from(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> zWquot#(X1,active(X2)) active#(from(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> active#(X2) active#(from(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> zWquot#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(zWquot(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(quot(X1,X2)) -> quot#(X1,active(X2)) active#(from(X)) -> active#(X) -> active#(quot(X1,X2)) -> active#(X2) active#(from(X)) -> active#(X) -> active#(quot(X1,X2)) -> quot#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(quot(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(minus(X1,X2)) -> minus#(X1,active(X2)) active#(from(X)) -> active#(X) -> active#(minus(X1,X2)) -> active#(X2) active#(from(X)) -> active#(X) -> active#(minus(X1,X2)) -> minus#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(minus(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(from(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(from(X)) -> from#(active(X)) active#(from(X)) -> active#(X) -> active#(from(X)) -> active#(X) active#(from(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> cons#(quot(X,Y),zWquot(XS,YS)) active#(from(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> quot#(X,Y) active#(from(X)) -> active#(X) -> active#(zWquot(cons(X,XS),cons(Y,YS))) -> zWquot#(XS,YS) active#(from(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> s#(quot(minus(X,Y),s(Y))) active#(from(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> quot#(minus(X,Y),s(Y)) active#(from(X)) -> active#(X) -> active#(quot(s(X),s(Y))) -> minus#(X,Y) active#(from(X)) -> active#(X) -> active#(minus(s(X),s(Y))) -> minus#(X,Y) active#(from(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(from(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) active#(from(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) active#(from(X)) -> active#(X) -> active#(from(X)) -> s#(X) SCC Processor: #sccs: 10 #rules: 43 #arcs: 775/5476 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: active#(from(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) active#(minus(X1,X2)) -> active#(X1) active#(minus(X1,X2)) -> active#(X2) active#(quot(X1,X2)) -> active#(X1) active#(quot(X1,X2)) -> active#(X2) active#(zWquot(X1,X2)) -> active#(X1) active#(zWquot(X1,X2)) -> active#(X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(active#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: proper#(from(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(minus(X1,X2)) -> proper#(X2) proper#(minus(X1,X2)) -> proper#(X1) proper#(quot(X1,X2)) -> proper#(X2) proper#(quot(X1,X2)) -> proper#(X1) proper#(zWquot(X1,X2)) -> proper#(X2) proper#(zWquot(X1,X2)) -> proper#(X1) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(proper#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: zWquot#(mark(X1),X2) -> zWquot#(X1,X2) zWquot#(X1,mark(X2)) -> zWquot#(X1,X2) zWquot#(ok(X1),ok(X2)) -> zWquot#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(zWquot#) = 1 problem: DPs: zWquot#(mark(X1),X2) -> zWquot#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(zWquot#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: quot#(mark(X1),X2) -> quot#(X1,X2) quot#(X1,mark(X2)) -> quot#(X1,X2) quot#(ok(X1),ok(X2)) -> quot#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(quot#) = 1 problem: DPs: quot#(mark(X1),X2) -> quot#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(quot#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: minus#(mark(X1),X2) -> minus#(X1,X2) minus#(X1,mark(X2)) -> minus#(X1,X2) minus#(ok(X1),ok(X2)) -> minus#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(minus#) = 1 problem: DPs: minus#(mark(X1),X2) -> minus#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(minus#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed 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(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(sel#) = 1 problem: DPs: sel#(mark(X1),X2) -> sel#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(sel#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: s#(mark(X)) -> s#(X) s#(ok(X)) -> s#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: from#(mark(X)) -> from#(X) from#(ok(X)) -> from#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Subterm Criterion Processor: simple projection: pi(from#) = 0 problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(minus(X,0())) -> mark(0()) active(minus(s(X),s(Y))) -> mark(minus(X,Y)) active(quot(0(),s(Y))) -> mark(0()) active(quot(s(X),s(Y))) -> mark(s(quot(minus(X,Y),s(Y)))) active(zWquot(XS,nil())) -> mark(nil()) active(zWquot(nil(),XS)) -> mark(nil()) active(zWquot(cons(X,XS),cons(Y,YS))) -> mark(cons(quot(X,Y),zWquot(XS,YS))) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) active(minus(X1,X2)) -> minus(active(X1),X2) active(minus(X1,X2)) -> minus(X1,active(X2)) active(quot(X1,X2)) -> quot(active(X1),X2) active(quot(X1,X2)) -> quot(X1,active(X2)) active(zWquot(X1,X2)) -> zWquot(active(X1),X2) active(zWquot(X1,X2)) -> zWquot(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) minus(mark(X1),X2) -> mark(minus(X1,X2)) minus(X1,mark(X2)) -> mark(minus(X1,X2)) quot(mark(X1),X2) -> mark(quot(X1,X2)) quot(X1,mark(X2)) -> mark(quot(X1,X2)) zWquot(mark(X1),X2) -> mark(zWquot(X1,X2)) zWquot(X1,mark(X2)) -> mark(zWquot(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) proper(quot(X1,X2)) -> quot(proper(X1),proper(X2)) proper(zWquot(X1,X2)) -> zWquot(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) quot(ok(X1),ok(X2)) -> ok(quot(X1,X2)) zWquot(ok(X1),ok(X2)) -> ok(zWquot(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed