MAYBE Problem: eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) eq(X,Y) -> false() inf(X) -> cons(X,n__inf(n__s(X))) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) length(nil()) -> 0() length(cons(X,L)) -> s(n__length(activate(L))) 0() -> n__0() s(X) -> n__s(X) inf(X) -> n__inf(X) take(X1,X2) -> n__take(X1,X2) length(X) -> n__length(X) activate(n__0()) -> 0() activate(n__s(X)) -> s(X) activate(n__inf(X)) -> inf(activate(X)) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__length(X)) -> length(activate(X)) activate(X) -> X Proof: DP Processor: DPs: eq#(n__s(X),n__s(Y)) -> activate#(Y) eq#(n__s(X),n__s(Y)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) take#(s(X),cons(Y,L)) -> activate#(L) take#(s(X),cons(Y,L)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(Y) length#(nil()) -> 0#() length#(cons(X,L)) -> activate#(L) length#(cons(X,L)) -> s#(n__length(activate(L))) activate#(n__0()) -> 0#() activate#(n__s(X)) -> s#(X) activate#(n__inf(X)) -> activate#(X) activate#(n__inf(X)) -> inf#(activate(X)) activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) activate#(n__length(X)) -> activate#(X) activate#(n__length(X)) -> length#(activate(X)) TRS: eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) eq(X,Y) -> false() inf(X) -> cons(X,n__inf(n__s(X))) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) length(nil()) -> 0() length(cons(X,L)) -> s(n__length(activate(L))) 0() -> n__0() s(X) -> n__s(X) inf(X) -> n__inf(X) take(X1,X2) -> n__take(X1,X2) length(X) -> n__length(X) activate(n__0()) -> 0() activate(n__s(X)) -> s(X) activate(n__inf(X)) -> inf(activate(X)) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__length(X)) -> length(activate(X)) activate(X) -> X EDG Processor: DPs: eq#(n__s(X),n__s(Y)) -> activate#(Y) eq#(n__s(X),n__s(Y)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) take#(s(X),cons(Y,L)) -> activate#(L) take#(s(X),cons(Y,L)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(Y) length#(nil()) -> 0#() length#(cons(X,L)) -> activate#(L) length#(cons(X,L)) -> s#(n__length(activate(L))) activate#(n__0()) -> 0#() activate#(n__s(X)) -> s#(X) activate#(n__inf(X)) -> activate#(X) activate#(n__inf(X)) -> inf#(activate(X)) activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) activate#(n__length(X)) -> activate#(X) activate#(n__length(X)) -> length#(activate(X)) TRS: eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) eq(X,Y) -> false() inf(X) -> cons(X,n__inf(n__s(X))) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) length(nil()) -> 0() length(cons(X,L)) -> s(n__length(activate(L))) 0() -> n__0() s(X) -> n__s(X) inf(X) -> n__inf(X) take(X1,X2) -> n__take(X1,X2) length(X) -> n__length(X) activate(n__0()) -> 0() activate(n__s(X)) -> s(X) activate(n__inf(X)) -> inf(activate(X)) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__length(X)) -> length(activate(X)) activate(X) -> X graph: length#(cons(X,L)) -> activate#(L) -> activate#(n__0()) -> 0#() length#(cons(X,L)) -> activate#(L) -> activate#(n__s(X)) -> s#(X) length#(cons(X,L)) -> activate#(L) -> activate#(n__inf(X)) -> activate#(X) length#(cons(X,L)) -> activate#(L) -> activate#(n__inf(X)) -> inf#(activate(X)) length#(cons(X,L)) -> activate#(L) -> activate#(n__take(X1,X2)) -> activate#(X2) length#(cons(X,L)) -> activate#(L) -> activate#(n__take(X1,X2)) -> activate#(X1) length#(cons(X,L)) -> activate#(L) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) length#(cons(X,L)) -> activate#(L) -> activate#(n__length(X)) -> activate#(X) length#(cons(X,L)) -> activate#(L) -> activate#(n__length(X)) -> length#(activate(X)) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__0()) -> 0#() take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__s(X)) -> s#(X) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__inf(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__inf(X)) -> inf#(activate(X)) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__take(X1,X2)) -> activate#(X2) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__take(X1,X2)) -> activate#(X1) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__length(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(L) -> activate#(n__length(X)) -> length#(activate(X)) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__0()) -> 0#() take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__s(X)) -> s#(X) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__inf(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__inf(X)) -> inf#(activate(X)) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__take(X1,X2)) -> activate#(X2) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__take(X1,X2)) -> activate#(X1) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__length(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(Y) -> activate#(n__length(X)) -> length#(activate(X)) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__0()) -> 0#() take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__s(X)) -> s#(X) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__inf(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__inf(X)) -> inf#(activate(X)) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X2) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X1) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__length(X)) -> length#(activate(X)) -> length#(nil()) -> 0#() activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(X,L)) -> activate#(L) activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(X,L)) -> s#(n__length(activate(L))) activate#(n__length(X)) -> activate#(X) -> activate#(n__0()) -> 0#() activate#(n__length(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__inf(X)) -> activate#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__inf(X)) -> inf#(activate(X)) activate#(n__length(X)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__length(X)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__length(X)) -> activate#(X) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) activate#(n__length(X)) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) -> take#(s(X),cons(Y,L)) -> activate#(L) activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) -> take#(s(X),cons(Y,L)) -> activate#(X) activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) -> take#(s(X),cons(Y,L)) -> activate#(Y) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__0()) -> 0#() activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__s(X)) -> s#(X) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__inf(X)) -> activate#(X) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__inf(X)) -> inf#(activate(X)) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__length(X)) -> activate#(X) activate#(n__take(X1,X2)) -> activate#(X2) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__0()) -> 0#() activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> s#(X) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__inf(X)) -> activate#(X) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__inf(X)) -> inf#(activate(X)) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__length(X)) -> activate#(X) activate#(n__take(X1,X2)) -> activate#(X1) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__inf(X)) -> activate#(X) -> activate#(n__0()) -> 0#() activate#(n__inf(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(X) activate#(n__inf(X)) -> activate#(X) -> activate#(n__inf(X)) -> activate#(X) activate#(n__inf(X)) -> activate#(X) -> activate#(n__inf(X)) -> inf#(activate(X)) activate#(n__inf(X)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__inf(X)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__inf(X)) -> activate#(X) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) activate#(n__inf(X)) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) activate#(n__inf(X)) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__0()) -> 0#() eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__s(X)) -> s#(X) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__inf(X)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__inf(X)) -> inf#(activate(X)) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__take(X1,X2)) -> activate#(X2) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__take(X1,X2)) -> activate#(X1) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__length(X)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> activate#(Y) -> activate#(n__length(X)) -> length#(activate(X)) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__0()) -> 0#() eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__s(X)) -> s#(X) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__inf(X)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__inf(X)) -> inf#(activate(X)) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X2) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__take(X1,X2)) -> activate#(X1) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) -> eq#(n__s(X),n__s(Y)) -> activate#(Y) eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) -> eq#(n__s(X),n__s(Y)) -> activate#(X) eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) -> eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) SCC Processor: #sccs: 2 #rules: 11 #arcs: 99/324 DPs: eq#(n__s(X),n__s(Y)) -> eq#(activate(X),activate(Y)) TRS: eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) eq(X,Y) -> false() inf(X) -> cons(X,n__inf(n__s(X))) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) length(nil()) -> 0() length(cons(X,L)) -> s(n__length(activate(L))) 0() -> n__0() s(X) -> n__s(X) inf(X) -> n__inf(X) take(X1,X2) -> n__take(X1,X2) length(X) -> n__length(X) activate(n__0()) -> 0() activate(n__s(X)) -> s(X) activate(n__inf(X)) -> inf(activate(X)) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__length(X)) -> length(activate(X)) activate(X) -> X Open DPs: length#(cons(X,L)) -> activate#(L) activate#(n__length(X)) -> length#(activate(X)) activate#(n__length(X)) -> activate#(X) activate#(n__take(X1,X2)) -> take#(activate(X1),activate(X2)) take#(s(X),cons(Y,L)) -> activate#(Y) activate#(n__take(X1,X2)) -> activate#(X1) activate#(n__take(X1,X2)) -> activate#(X2) activate#(n__inf(X)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(X) take#(s(X),cons(Y,L)) -> activate#(L) TRS: eq(n__0(),n__0()) -> true() eq(n__s(X),n__s(Y)) -> eq(activate(X),activate(Y)) eq(X,Y) -> false() inf(X) -> cons(X,n__inf(n__s(X))) take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(activate(Y),n__take(activate(X),activate(L))) length(nil()) -> 0() length(cons(X,L)) -> s(n__length(activate(L))) 0() -> n__0() s(X) -> n__s(X) inf(X) -> n__inf(X) take(X1,X2) -> n__take(X1,X2) length(X) -> n__length(X) activate(n__0()) -> 0() activate(n__s(X)) -> s(X) activate(n__inf(X)) -> inf(activate(X)) activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__length(X)) -> length(activate(X)) activate(X) -> X Open