YES Problem: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Proof: DP Processor: DPs: active#(eq(0(),0())) -> mark#(true()) active#(eq(s(X),s(Y))) -> eq#(X,Y) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) active#(eq(X,Y)) -> mark#(false()) active#(inf(X)) -> s#(X) active#(inf(X)) -> inf#(s(X)) active#(inf(X)) -> cons#(X,inf(s(X))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) active#(take(0(),X)) -> mark#(nil()) active#(take(s(X),cons(Y,L))) -> take#(X,L) active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) active#(length(nil())) -> mark#(0()) active#(length(cons(X,L))) -> length#(L) active#(length(cons(X,L))) -> s#(length(L)) active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(0()) -> active#(0()) mark#(true()) -> active#(true()) mark#(s(X)) -> active#(s(X)) mark#(false()) -> active#(false()) mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> inf#(mark(X)) mark#(inf(X)) -> active#(inf(mark(X))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) eq#(mark(X1),X2) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) inf#(mark(X)) -> inf#(X) inf#(active(X)) -> inf#(X) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) TDG Processor: DPs: active#(eq(0(),0())) -> mark#(true()) active#(eq(s(X),s(Y))) -> eq#(X,Y) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) active#(eq(X,Y)) -> mark#(false()) active#(inf(X)) -> s#(X) active#(inf(X)) -> inf#(s(X)) active#(inf(X)) -> cons#(X,inf(s(X))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) active#(take(0(),X)) -> mark#(nil()) active#(take(s(X),cons(Y,L))) -> take#(X,L) active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) active#(length(nil())) -> mark#(0()) active#(length(cons(X,L))) -> length#(L) active#(length(cons(X,L))) -> s#(length(L)) active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(0()) -> active#(0()) mark#(true()) -> active#(true()) mark#(s(X)) -> active#(s(X)) mark#(false()) -> active#(false()) mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> inf#(mark(X)) mark#(inf(X)) -> active#(inf(mark(X))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) eq#(mark(X1),X2) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) inf#(mark(X)) -> inf#(X) inf#(active(X)) -> inf#(X) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) graph: length#(mark(X)) -> length#(X) -> length#(active(X)) -> length#(X) length#(mark(X)) -> length#(X) -> length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) -> length#(active(X)) -> length#(X) length#(active(X)) -> length#(X) -> length#(mark(X)) -> length#(X) take#(mark(X1),X2) -> take#(X1,X2) -> take#(X1,active(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(active(X1),X2) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) -> take#(X1,active(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) -> take#(active(X1),X2) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(X1,active(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(active(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) -> take#(X1,active(X2)) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) -> take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,active(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) inf#(mark(X)) -> inf#(X) -> inf#(active(X)) -> inf#(X) inf#(mark(X)) -> inf#(X) -> inf#(mark(X)) -> inf#(X) inf#(active(X)) -> inf#(X) -> inf#(active(X)) -> inf#(X) inf#(active(X)) -> inf#(X) -> inf#(mark(X)) -> inf#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) eq#(mark(X1),X2) -> eq#(X1,X2) -> eq#(X1,active(X2)) -> eq#(X1,X2) eq#(mark(X1),X2) -> eq#(X1,X2) -> eq#(active(X1),X2) -> eq#(X1,X2) eq#(mark(X1),X2) -> eq#(X1,X2) -> eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(mark(X1),X2) -> eq#(X1,X2) -> eq#(mark(X1),X2) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) -> eq#(X1,active(X2)) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) -> eq#(active(X1),X2) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) -> eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) -> eq#(mark(X1),X2) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) -> eq#(X1,active(X2)) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) -> eq#(active(X1),X2) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) -> eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) -> eq#(mark(X1),X2) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) -> eq#(X1,active(X2)) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) -> eq#(active(X1),X2) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) -> eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) -> eq#(mark(X1),X2) -> eq#(X1,X2) mark#(length(X)) -> length#(mark(X)) -> length#(active(X)) -> length#(X) mark#(length(X)) -> length#(mark(X)) -> length#(mark(X)) -> length#(X) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(mark(X))) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> inf#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(false()) -> active#(false()) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(length(X)) -> mark#(X) -> mark#(true()) -> active#(true()) mark#(length(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(length(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(cons(X,L))) -> length#(L) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(length(X)) -> active#(length(mark(X))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(length(X)) -> active#(length(mark(X))) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(length(X)) -> active#(length(mark(X))) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(length(X)) -> active#(length(mark(X))) -> active#(take(0(),X)) -> mark#(nil()) mark#(length(X)) -> active#(length(mark(X))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(length(X)) -> active#(length(mark(X))) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(length(X)) -> active#(length(mark(X))) -> active#(inf(X)) -> inf#(s(X)) mark#(length(X)) -> active#(length(mark(X))) -> active#(inf(X)) -> s#(X) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(X,Y)) -> mark#(false()) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(0(),0())) -> mark#(true()) mark#(nil()) -> active#(nil()) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(nil()) -> active#(nil()) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(nil()) -> active#(nil()) -> active#(length(cons(X,L))) -> length#(L) mark#(nil()) -> active#(nil()) -> active#(length(nil())) -> mark#(0()) mark#(nil()) -> active#(nil()) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(nil()) -> active#(nil()) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(nil()) -> active#(nil()) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(nil()) -> active#(nil()) -> active#(take(0(),X)) -> mark#(nil()) mark#(nil()) -> active#(nil()) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(nil()) -> active#(nil()) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(nil()) -> active#(nil()) -> active#(inf(X)) -> inf#(s(X)) mark#(nil()) -> active#(nil()) -> active#(inf(X)) -> s#(X) mark#(nil()) -> active#(nil()) -> active#(eq(X,Y)) -> mark#(false()) mark#(nil()) -> active#(nil()) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(nil()) -> active#(nil()) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(nil()) -> active#(nil()) -> active#(eq(0(),0())) -> mark#(true()) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) -> take#(X1,active(X2)) -> take#(X1,X2) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) -> take#(active(X1),X2) -> take#(X1,X2) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) -> take#(X1,mark(X2)) -> take#(X1,X2) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) -> take#(mark(X1),X2) -> take#(X1,X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> active#(length(mark(X))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> length#(mark(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> inf#(mark(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(false()) -> active#(false()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(true()) -> active#(true()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> active#(length(mark(X))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> length#(mark(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> inf#(mark(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(false()) -> active#(false()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(true()) -> active#(true()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(length(cons(X,L))) -> length#(L) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(length(nil())) -> mark#(0()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(0(),X)) -> mark#(nil()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(inf(X)) -> inf#(s(X)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(inf(X)) -> s#(X) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(X,Y)) -> mark#(false()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(0(),0())) -> mark#(true()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(length(cons(X,L))) -> length#(L) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(take(0(),X)) -> mark#(nil()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(inf(X)) -> inf#(s(X)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(inf(X)) -> s#(X) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(X,Y)) -> mark#(false()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(0(),0())) -> mark#(true()) mark#(inf(X)) -> inf#(mark(X)) -> inf#(active(X)) -> inf#(X) mark#(inf(X)) -> inf#(mark(X)) -> inf#(mark(X)) -> inf#(X) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(mark(X))) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> length#(mark(X)) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(inf(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> inf#(mark(X)) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) -> mark#(false()) -> active#(false()) mark#(inf(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(inf(X)) -> mark#(X) -> mark#(true()) -> active#(true()) mark#(inf(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(inf(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(length(cons(X,L))) -> length#(L) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(take(0(),X)) -> mark#(nil()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(inf(X)) -> inf#(s(X)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(inf(X)) -> s#(X) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(X,Y)) -> mark#(false()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(0(),0())) -> mark#(true()) mark#(false()) -> active#(false()) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(false()) -> active#(false()) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(false()) -> active#(false()) -> active#(length(cons(X,L))) -> length#(L) mark#(false()) -> active#(false()) -> active#(length(nil())) -> mark#(0()) mark#(false()) -> active#(false()) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(false()) -> active#(false()) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(false()) -> active#(false()) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(false()) -> active#(false()) -> active#(take(0(),X)) -> mark#(nil()) mark#(false()) -> active#(false()) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(false()) -> active#(false()) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(false()) -> active#(false()) -> active#(inf(X)) -> inf#(s(X)) mark#(false()) -> active#(false()) -> active#(inf(X)) -> s#(X) mark#(false()) -> active#(false()) -> active#(eq(X,Y)) -> mark#(false()) mark#(false()) -> active#(false()) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(false()) -> active#(false()) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(false()) -> active#(false()) -> active#(eq(0(),0())) -> mark#(true()) mark#(s(X)) -> active#(s(X)) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(s(X)) -> active#(s(X)) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(s(X)) -> active#(s(X)) -> active#(length(cons(X,L))) -> length#(L) mark#(s(X)) -> active#(s(X)) -> active#(length(nil())) -> mark#(0()) mark#(s(X)) -> active#(s(X)) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(s(X)) -> active#(s(X)) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(s(X)) -> active#(s(X)) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(s(X)) -> active#(s(X)) -> active#(take(0(),X)) -> mark#(nil()) mark#(s(X)) -> active#(s(X)) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(s(X)) -> active#(s(X)) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(s(X)) -> active#(s(X)) -> active#(inf(X)) -> inf#(s(X)) mark#(s(X)) -> active#(s(X)) -> active#(inf(X)) -> s#(X) mark#(s(X)) -> active#(s(X)) -> active#(eq(X,Y)) -> mark#(false()) mark#(s(X)) -> active#(s(X)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(s(X)) -> active#(s(X)) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(s(X)) -> active#(s(X)) -> active#(eq(0(),0())) -> mark#(true()) mark#(true()) -> active#(true()) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(true()) -> active#(true()) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(true()) -> active#(true()) -> active#(length(cons(X,L))) -> length#(L) mark#(true()) -> active#(true()) -> active#(length(nil())) -> mark#(0()) mark#(true()) -> active#(true()) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(true()) -> active#(true()) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(true()) -> active#(true()) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(true()) -> active#(true()) -> active#(take(0(),X)) -> mark#(nil()) mark#(true()) -> active#(true()) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(true()) -> active#(true()) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(true()) -> active#(true()) -> active#(inf(X)) -> inf#(s(X)) mark#(true()) -> active#(true()) -> active#(inf(X)) -> s#(X) mark#(true()) -> active#(true()) -> active#(eq(X,Y)) -> mark#(false()) mark#(true()) -> active#(true()) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(true()) -> active#(true()) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(true()) -> active#(true()) -> active#(eq(0(),0())) -> mark#(true()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(length(cons(X,L))) -> length#(L) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(length(nil())) -> mark#(0()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(take(0(),X)) -> mark#(nil()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(inf(X)) -> inf#(s(X)) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(inf(X)) -> s#(X) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(X,Y)) -> mark#(false()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(0(),0())) -> mark#(true()) mark#(0()) -> active#(0()) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(0()) -> active#(0()) -> active#(length(cons(X,L))) -> s#(length(L)) mark#(0()) -> active#(0()) -> active#(length(cons(X,L))) -> length#(L) mark#(0()) -> active#(0()) -> active#(length(nil())) -> mark#(0()) mark#(0()) -> active#(0()) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(0()) -> active#(0()) -> active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) mark#(0()) -> active#(0()) -> active#(take(s(X),cons(Y,L))) -> take#(X,L) mark#(0()) -> active#(0()) -> active#(take(0(),X)) -> mark#(nil()) mark#(0()) -> active#(0()) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(0()) -> active#(0()) -> active#(inf(X)) -> cons#(X,inf(s(X))) mark#(0()) -> active#(0()) -> active#(inf(X)) -> inf#(s(X)) mark#(0()) -> active#(0()) -> active#(inf(X)) -> s#(X) mark#(0()) -> active#(0()) -> active#(eq(X,Y)) -> mark#(false()) mark#(0()) -> active#(0()) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(0()) -> active#(0()) -> active#(eq(s(X),s(Y))) -> eq#(X,Y) mark#(0()) -> active#(0()) -> active#(eq(0(),0())) -> mark#(true()) active#(length(nil())) -> mark#(0()) -> mark#(length(X)) -> active#(length(mark(X))) active#(length(nil())) -> mark#(0()) -> mark#(length(X)) -> length#(mark(X)) active#(length(nil())) -> mark#(0()) -> mark#(length(X)) -> mark#(X) active#(length(nil())) -> mark#(0()) -> mark#(nil()) -> active#(nil()) active#(length(nil())) -> mark#(0()) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(length(nil())) -> mark#(0()) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(length(nil())) -> mark#(0()) -> mark#(take(X1,X2)) -> mark#(X1) active#(length(nil())) -> mark#(0()) -> mark#(take(X1,X2)) -> mark#(X2) active#(length(nil())) -> mark#(0()) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(length(nil())) -> mark#(0()) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(length(nil())) -> mark#(0()) -> mark#(inf(X)) -> inf#(mark(X)) active#(length(nil())) -> mark#(0()) -> mark#(inf(X)) -> mark#(X) active#(length(nil())) -> mark#(0()) -> mark#(false()) -> active#(false()) active#(length(nil())) -> mark#(0()) -> mark#(s(X)) -> active#(s(X)) active#(length(nil())) -> mark#(0()) -> mark#(true()) -> active#(true()) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(length(nil())) -> mark#(0()) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(length(cons(X,L))) -> length#(L) -> length#(active(X)) -> length#(X) active#(length(cons(X,L))) -> length#(L) -> length#(mark(X)) -> length#(X) active#(length(cons(X,L))) -> s#(length(L)) -> s#(active(X)) -> s#(X) active#(length(cons(X,L))) -> s#(length(L)) -> s#(mark(X)) -> s#(X) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(length(X)) -> active#(length(mark(X))) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(length(X)) -> length#(mark(X)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(length(X)) -> mark#(X) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(nil()) -> active#(nil()) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> mark#(X1) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> mark#(X2) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(inf(X)) -> inf#(mark(X)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(inf(X)) -> mark#(X) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(false()) -> active#(false()) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(s(X)) -> active#(s(X)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(true()) -> active#(true()) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(0()) -> active#(0()) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(take(s(X),cons(Y,L))) -> take#(X,L) -> take#(X1,active(X2)) -> take#(X1,X2) active#(take(s(X),cons(Y,L))) -> take#(X,L) -> take#(active(X1),X2) -> take#(X1,X2) active#(take(s(X),cons(Y,L))) -> take#(X,L) -> take#(X1,mark(X2)) -> take#(X1,X2) active#(take(s(X),cons(Y,L))) -> take#(X,L) -> take#(mark(X1),X2) -> take#(X1,X2) active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(take(s(X),cons(Y,L))) -> cons#(Y,take(X,L)) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(length(X)) -> active#(length(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(length(X)) -> length#(mark(X)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(length(X)) -> mark#(X) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(nil()) -> active#(nil()) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> mark#(X1) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> mark#(X2) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(inf(X)) -> inf#(mark(X)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(inf(X)) -> mark#(X) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(false()) -> active#(false()) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(s(X)) -> active#(s(X)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(true()) -> active#(true()) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(0()) -> active#(0()) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(take(0(),X)) -> mark#(nil()) -> mark#(length(X)) -> active#(length(mark(X))) active#(take(0(),X)) -> mark#(nil()) -> mark#(length(X)) -> length#(mark(X)) active#(take(0(),X)) -> mark#(nil()) -> mark#(length(X)) -> mark#(X) active#(take(0(),X)) -> mark#(nil()) -> mark#(nil()) -> active#(nil()) active#(take(0(),X)) -> mark#(nil()) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(take(0(),X)) -> mark#(nil()) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(take(0(),X)) -> mark#(nil()) -> mark#(take(X1,X2)) -> mark#(X1) active#(take(0(),X)) -> mark#(nil()) -> mark#(take(X1,X2)) -> mark#(X2) active#(take(0(),X)) -> mark#(nil()) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(take(0(),X)) -> mark#(nil()) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(take(0(),X)) -> mark#(nil()) -> mark#(inf(X)) -> inf#(mark(X)) active#(take(0(),X)) -> mark#(nil()) -> mark#(inf(X)) -> mark#(X) active#(take(0(),X)) -> mark#(nil()) -> mark#(false()) -> active#(false()) active#(take(0(),X)) -> mark#(nil()) -> mark#(s(X)) -> active#(s(X)) active#(take(0(),X)) -> mark#(nil()) -> mark#(true()) -> active#(true()) active#(take(0(),X)) -> mark#(nil()) -> mark#(0()) -> active#(0()) active#(take(0(),X)) -> mark#(nil()) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(inf(X)) -> cons#(X,inf(s(X))) -> cons#(X1,active(X2)) -> cons#(X1,X2) active#(inf(X)) -> cons#(X,inf(s(X))) -> cons#(active(X1),X2) -> cons#(X1,X2) active#(inf(X)) -> cons#(X,inf(s(X))) -> cons#(X1,mark(X2)) -> cons#(X1,X2) active#(inf(X)) -> cons#(X,inf(s(X))) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(inf(X)) -> inf#(s(X)) -> inf#(active(X)) -> inf#(X) active#(inf(X)) -> inf#(s(X)) -> inf#(mark(X)) -> inf#(X) active#(inf(X)) -> s#(X) -> s#(active(X)) -> s#(X) active#(inf(X)) -> s#(X) -> s#(mark(X)) -> s#(X) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(length(X)) -> active#(length(mark(X))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(length(X)) -> length#(mark(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(length(X)) -> mark#(X) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(nil()) -> active#(nil()) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> mark#(X1) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> mark#(X2) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(inf(X)) -> inf#(mark(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(inf(X)) -> mark#(X) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(false()) -> active#(false()) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(s(X)) -> active#(s(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(true()) -> active#(true()) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(0()) -> active#(0()) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(s(X),s(Y))) -> eq#(X,Y) -> eq#(X1,active(X2)) -> eq#(X1,X2) active#(eq(s(X),s(Y))) -> eq#(X,Y) -> eq#(active(X1),X2) -> eq#(X1,X2) active#(eq(s(X),s(Y))) -> eq#(X,Y) -> eq#(X1,mark(X2)) -> eq#(X1,X2) active#(eq(s(X),s(Y))) -> eq#(X,Y) -> eq#(mark(X1),X2) -> eq#(X1,X2) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(length(X)) -> active#(length(mark(X))) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(length(X)) -> length#(mark(X)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(length(X)) -> mark#(X) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(nil()) -> active#(nil()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> mark#(X1) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> mark#(X2) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(inf(X)) -> inf#(mark(X)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(inf(X)) -> mark#(X) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(false()) -> active#(false()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(s(X)) -> active#(s(X)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(true()) -> active#(true()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(0()) -> active#(0()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(0(),0())) -> mark#(true()) -> mark#(length(X)) -> active#(length(mark(X))) active#(eq(0(),0())) -> mark#(true()) -> mark#(length(X)) -> length#(mark(X)) active#(eq(0(),0())) -> mark#(true()) -> mark#(length(X)) -> mark#(X) active#(eq(0(),0())) -> mark#(true()) -> mark#(nil()) -> active#(nil()) active#(eq(0(),0())) -> mark#(true()) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(eq(0(),0())) -> mark#(true()) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(eq(0(),0())) -> mark#(true()) -> mark#(take(X1,X2)) -> mark#(X1) active#(eq(0(),0())) -> mark#(true()) -> mark#(take(X1,X2)) -> mark#(X2) active#(eq(0(),0())) -> mark#(true()) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(eq(0(),0())) -> mark#(true()) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(eq(0(),0())) -> mark#(true()) -> mark#(inf(X)) -> inf#(mark(X)) active#(eq(0(),0())) -> mark#(true()) -> mark#(inf(X)) -> mark#(X) active#(eq(0(),0())) -> mark#(true()) -> mark#(false()) -> active#(false()) active#(eq(0(),0())) -> mark#(true()) -> mark#(s(X)) -> active#(s(X)) active#(eq(0(),0())) -> mark#(true()) -> mark#(true()) -> active#(true()) active#(eq(0(),0())) -> mark#(true()) -> mark#(0()) -> active#(0()) active#(eq(0(),0())) -> mark#(true()) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(X,Y)) -> mark#(false()) -> mark#(length(X)) -> active#(length(mark(X))) active#(eq(X,Y)) -> mark#(false()) -> mark#(length(X)) -> length#(mark(X)) active#(eq(X,Y)) -> mark#(false()) -> mark#(length(X)) -> mark#(X) active#(eq(X,Y)) -> mark#(false()) -> mark#(nil()) -> active#(nil()) active#(eq(X,Y)) -> mark#(false()) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(eq(X,Y)) -> mark#(false()) -> mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) active#(eq(X,Y)) -> mark#(false()) -> mark#(take(X1,X2)) -> mark#(X1) active#(eq(X,Y)) -> mark#(false()) -> mark#(take(X1,X2)) -> mark#(X2) active#(eq(X,Y)) -> mark#(false()) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(eq(X,Y)) -> mark#(false()) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(eq(X,Y)) -> mark#(false()) -> mark#(inf(X)) -> inf#(mark(X)) active#(eq(X,Y)) -> mark#(false()) -> mark#(inf(X)) -> mark#(X) active#(eq(X,Y)) -> mark#(false()) -> mark#(false()) -> active#(false()) active#(eq(X,Y)) -> mark#(false()) -> mark#(s(X)) -> active#(s(X)) active#(eq(X,Y)) -> mark#(false()) -> mark#(true()) -> active#(true()) active#(eq(X,Y)) -> mark#(false()) -> mark#(0()) -> active#(0()) active#(eq(X,Y)) -> mark#(false()) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) SCC Processor: #sccs: 7 #rules: 40 #arcs: 456/2601 DPs: mark#(length(X)) -> mark#(X) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(0(),0())) -> mark#(true()) mark#(0()) -> active#(0()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(true()) -> active#(true()) active#(eq(X,Y)) -> mark#(false()) mark#(s(X)) -> active#(s(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(false()) -> active#(false()) active#(take(0(),X)) -> mark#(nil()) mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> active#(inf(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(length(nil())) -> mark#(0()) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(nil()) -> active#(nil()) mark#(length(X)) -> active#(length(mark(X))) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) EDG Processor: DPs: mark#(length(X)) -> mark#(X) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(0(),0())) -> mark#(true()) mark#(0()) -> active#(0()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(true()) -> active#(true()) active#(eq(X,Y)) -> mark#(false()) mark#(s(X)) -> active#(s(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(false()) -> active#(false()) active#(take(0(),X)) -> mark#(nil()) mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> active#(inf(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(length(nil())) -> mark#(0()) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(nil()) -> active#(nil()) mark#(length(X)) -> active#(length(mark(X))) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) graph: mark#(length(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(length(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(length(X)) -> mark#(X) -> mark#(true()) -> active#(true()) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(length(X)) -> mark#(X) -> mark#(false()) -> active#(false()) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(length(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(mark(X))) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(0(),0())) -> mark#(true()) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(length(X)) -> active#(length(mark(X))) -> active#(eq(X,Y)) -> mark#(false()) mark#(length(X)) -> active#(length(mark(X))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(length(X)) -> active#(length(mark(X))) -> active#(take(0(),X)) -> mark#(nil()) mark#(length(X)) -> active#(length(mark(X))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(true()) -> active#(true()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(false()) -> active#(false()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> active#(length(mark(X))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(true()) -> active#(true()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(false()) -> active#(false()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> active#(length(mark(X))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(0(),0())) -> mark#(true()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(eq(X,Y)) -> mark#(false()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(0(),X)) -> mark#(nil()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(length(nil())) -> mark#(0()) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(0(),0())) -> mark#(true()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(eq(X,Y)) -> mark#(false()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(take(0(),X)) -> mark#(nil()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(length(nil())) -> mark#(0()) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(inf(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(inf(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(inf(X)) -> mark#(X) -> mark#(true()) -> active#(true()) mark#(inf(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(inf(X)) -> mark#(X) -> mark#(false()) -> active#(false()) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(inf(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(inf(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(mark(X))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(0(),0())) -> mark#(true()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(eq(X,Y)) -> mark#(false()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(take(0(),X)) -> mark#(nil()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(s(X)) -> active#(s(X)) -> active#(eq(0(),0())) -> mark#(true()) mark#(s(X)) -> active#(s(X)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(s(X)) -> active#(s(X)) -> active#(eq(X,Y)) -> mark#(false()) mark#(s(X)) -> active#(s(X)) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(s(X)) -> active#(s(X)) -> active#(take(0(),X)) -> mark#(nil()) mark#(s(X)) -> active#(s(X)) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(s(X)) -> active#(s(X)) -> active#(length(nil())) -> mark#(0()) mark#(s(X)) -> active#(s(X)) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(0(),0())) -> mark#(true()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(X,Y)) -> mark#(false()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(take(0(),X)) -> mark#(nil()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(length(nil())) -> mark#(0()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(length(cons(X,L))) -> mark#(s(length(L))) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(s(X)) -> active#(s(X)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(inf(X)) -> mark#(X) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> mark#(X2) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> mark#(X1) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(length(X)) -> mark#(X) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(length(X)) -> active#(length(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(s(X)) -> active#(s(X)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(inf(X)) -> mark#(X) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> mark#(X2) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> mark#(X1) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(length(X)) -> mark#(X) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(length(X)) -> active#(length(mark(X))) active#(take(0(),X)) -> mark#(nil()) -> mark#(nil()) -> active#(nil()) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(s(X)) -> active#(s(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(inf(X)) -> mark#(X) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> mark#(X2) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> mark#(X1) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(length(X)) -> mark#(X) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(length(X)) -> active#(length(mark(X))) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(s(X)) -> active#(s(X)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(inf(X)) -> mark#(X) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(inf(X)) -> active#(inf(mark(X))) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> mark#(X2) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> mark#(X1) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(length(X)) -> mark#(X) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(length(X)) -> active#(length(mark(X))) active#(eq(0(),0())) -> mark#(true()) -> mark#(true()) -> active#(true()) active#(eq(X,Y)) -> mark#(false()) -> mark#(false()) -> active#(false()) CDG Processor: DPs: mark#(length(X)) -> mark#(X) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(0(),0())) -> mark#(true()) mark#(0()) -> active#(0()) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(true()) -> active#(true()) active#(eq(X,Y)) -> mark#(false()) mark#(s(X)) -> active#(s(X)) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(false()) -> active#(false()) active#(take(0(),X)) -> mark#(nil()) mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> active#(inf(mark(X))) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(length(nil())) -> mark#(0()) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(nil()) -> active#(nil()) mark#(length(X)) -> active#(length(mark(X))) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) graph: mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(mark(X))) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(length(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(false()) -> active#(false()) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(length(X)) -> mark#(X) -> mark#(true()) -> active#(true()) mark#(length(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(length(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(cons(X,L))) -> mark#(s(length(L))) mark#(length(X)) -> active#(length(mark(X))) -> active#(length(nil())) -> mark#(0()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> active#(length(mark(X))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(nil()) -> active#(nil()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(take(X1,X2)) -> mark#(X2) -> mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(false()) -> active#(false()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(true()) -> active#(true()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(take(X1,X2)) -> mark#(X2) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> active#(length(mark(X))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(nil()) -> active#(nil()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(take(X1,X2)) -> mark#(X1) -> mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(false()) -> active#(false()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(true()) -> active#(true()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(take(X1,X2)) -> mark#(X1) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) -> active#(take(0(),X)) -> mark#(nil()) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> active#(length(mark(X))) mark#(inf(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) -> mark#(nil()) -> active#(nil()) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(inf(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(inf(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> active#(inf(mark(X))) mark#(inf(X)) -> mark#(X) -> mark#(inf(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) -> mark#(false()) -> active#(false()) mark#(inf(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(X)) mark#(inf(X)) -> mark#(X) -> mark#(true()) -> active#(true()) mark#(inf(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(inf(X)) -> mark#(X) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) mark#(inf(X)) -> active#(inf(mark(X))) -> active#(inf(X)) -> mark#(cons(X,inf(s(X)))) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(X,Y)) -> mark#(false()) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) mark#(eq(X1,X2)) -> active#(eq(X1,X2)) -> active#(eq(0(),0())) -> mark#(true()) active#(length(nil())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(length(cons(X,L))) -> mark#(s(length(L))) -> mark#(s(X)) -> active#(s(X)) active#(take(s(X),cons(Y,L))) -> mark#(cons(Y,take(X,L))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(take(0(),X)) -> mark#(nil()) -> mark#(nil()) -> active#(nil()) active#(inf(X)) -> mark#(cons(X,inf(s(X)))) -> mark#(cons(X1,X2)) -> active#(cons(X1,X2)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) -> mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(0(),0())) -> mark#(true()) -> mark#(true()) -> active#(true()) active#(eq(X,Y)) -> mark#(false()) -> mark#(false()) -> active#(false()) SCC Processor: #sccs: 2 #rules: 6 #arcs: 72/484 DPs: mark#(length(X)) -> mark#(X) mark#(inf(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: mark#(eq(X1,X2)) -> active#(eq(X1,X2)) active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = 2x0, [active#](x0) = 1x0, [length](x0) = 0, [nil] = 1, [take](x0, x1) = x1, [cons](x0, x1) = 2, [inf](x0) = 1x0 + 2, [false] = 1, [s](x0) = 1x0 + 1, [mark](x0) = x0 + 1, [true] = 2, [active](x0) = x0 + 1, [eq](x0, x1) = 4x1, [0] = 0 orientation: mark#(eq(X1,X2)) = 6X2 >= 5X2 = active#(eq(X1,X2)) active#(eq(s(X),s(Y))) = 6Y + 6 >= 6Y = mark#(eq(X,Y)) active(eq(0(),0())) = 4 >= 2 = mark(true()) active(eq(s(X),s(Y))) = 5Y + 5 >= 4Y + 1 = mark(eq(X,Y)) active(eq(X,Y)) = 4Y + 1 >= 1 = mark(false()) active(inf(X)) = 1X + 2 >= 2 = mark(cons(X,inf(s(X)))) active(take(0(),X)) = X + 1 >= 1 = mark(nil()) active(take(s(X),cons(Y,L))) = 2 >= 2 = mark(cons(Y,take(X,L))) active(length(nil())) = 1 >= 1 = mark(0()) active(length(cons(X,L))) = 1 >= 1 = mark(s(length(L))) mark(eq(X1,X2)) = 4X2 + 1 >= 4X2 + 1 = active(eq(X1,X2)) mark(0()) = 1 >= 1 = active(0()) mark(true()) = 2 >= 2 = active(true()) mark(s(X)) = 1X + 1 >= 1X + 1 = active(s(X)) mark(false()) = 1 >= 1 = active(false()) mark(inf(X)) = 1X + 2 >= 1X + 2 = active(inf(mark(X))) mark(cons(X1,X2)) = 2 >= 2 = active(cons(X1,X2)) mark(take(X1,X2)) = X2 + 1 >= X2 + 1 = active(take(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(length(X)) = 1 >= 1 = active(length(mark(X))) eq(mark(X1),X2) = 4X2 >= 4X2 = eq(X1,X2) eq(X1,mark(X2)) = 4X2 + 5 >= 4X2 = eq(X1,X2) eq(active(X1),X2) = 4X2 >= 4X2 = eq(X1,X2) eq(X1,active(X2)) = 4X2 + 5 >= 4X2 = eq(X1,X2) s(mark(X)) = 1X + 2 >= 1X + 1 = s(X) s(active(X)) = 1X + 2 >= 1X + 1 = s(X) inf(mark(X)) = 1X + 2 >= 1X + 2 = inf(X) inf(active(X)) = 1X + 2 >= 1X + 2 = inf(X) cons(mark(X1),X2) = 2 >= 2 = cons(X1,X2) cons(X1,mark(X2)) = 2 >= 2 = cons(X1,X2) cons(active(X1),X2) = 2 >= 2 = cons(X1,X2) cons(X1,active(X2)) = 2 >= 2 = cons(X1,X2) take(mark(X1),X2) = X2 >= X2 = take(X1,X2) take(X1,mark(X2)) = X2 + 1 >= X2 = take(X1,X2) take(active(X1),X2) = X2 >= X2 = take(X1,X2) take(X1,active(X2)) = X2 + 1 >= X2 = take(X1,X2) length(mark(X)) = 0 >= 0 = length(X) length(active(X)) = 0 >= 0 = length(X) problem: DPs: active#(eq(s(X),s(Y))) -> mark#(eq(X,Y)) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/1 DPs: eq#(mark(X1),X2) -> eq#(X1,X2) eq#(X1,mark(X2)) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) eq#(X1,active(X2)) -> eq#(X1,X2) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(eq#) = 1 problem: DPs: eq#(mark(X1),X2) -> eq#(X1,X2) eq#(active(X1),X2) -> eq#(X1,X2) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(eq#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: inf#(mark(X)) -> inf#(X) inf#(active(X)) -> inf#(X) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(inf#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(cons#) = 1 problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(take#) = 1 problem: DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(take#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed DPs: length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Subterm Criterion Processor: simple projection: pi(length#) = 0 problem: DPs: TRS: active(eq(0(),0())) -> mark(true()) active(eq(s(X),s(Y))) -> mark(eq(X,Y)) active(eq(X,Y)) -> mark(false()) active(inf(X)) -> mark(cons(X,inf(s(X)))) active(take(0(),X)) -> mark(nil()) active(take(s(X),cons(Y,L))) -> mark(cons(Y,take(X,L))) active(length(nil())) -> mark(0()) active(length(cons(X,L))) -> mark(s(length(L))) mark(eq(X1,X2)) -> active(eq(X1,X2)) mark(0()) -> active(0()) mark(true()) -> active(true()) mark(s(X)) -> active(s(X)) mark(false()) -> active(false()) mark(inf(X)) -> active(inf(mark(X))) mark(cons(X1,X2)) -> active(cons(X1,X2)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(length(X)) -> active(length(mark(X))) eq(mark(X1),X2) -> eq(X1,X2) eq(X1,mark(X2)) -> eq(X1,X2) eq(active(X1),X2) -> eq(X1,X2) eq(X1,active(X2)) -> eq(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) inf(mark(X)) -> inf(X) inf(active(X)) -> inf(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) Qed