YES Problem: flatten(nil()) -> nil() flatten(unit(x)) -> flatten(x) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil()) -> nil() rev(unit(x)) -> unit(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x ++(x,nil()) -> x ++(nil(),y) -> y ++(++(x,y),z) -> ++(x,++(y,z)) Proof: DP Processor: DPs: flatten#(unit(x)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(x) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) rev#(++(x,y)) -> rev#(x) rev#(++(x,y)) -> rev#(y) rev#(++(x,y)) -> ++#(rev(y),rev(x)) ++#(++(x,y),z) -> ++#(y,z) ++#(++(x,y),z) -> ++#(x,++(y,z)) TRS: flatten(nil()) -> nil() flatten(unit(x)) -> flatten(x) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil()) -> nil() rev(unit(x)) -> unit(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x ++(x,nil()) -> x ++(nil(),y) -> y ++(++(x,y),z) -> ++(x,++(y,z)) TDG Processor: DPs: flatten#(unit(x)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(x) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) rev#(++(x,y)) -> rev#(x) rev#(++(x,y)) -> rev#(y) rev#(++(x,y)) -> ++#(rev(y),rev(x)) ++#(++(x,y),z) -> ++#(y,z) ++#(++(x,y),z) -> ++#(x,++(y,z)) TRS: flatten(nil()) -> nil() flatten(unit(x)) -> flatten(x) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil()) -> nil() rev(unit(x)) -> unit(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x ++(x,nil()) -> x ++(nil(),y) -> y ++(++(x,y),z) -> ++(x,++(y,z)) graph: rev#(++(x,y)) -> rev#(y) -> rev#(++(x,y)) -> ++#(rev(y),rev(x)) rev#(++(x,y)) -> rev#(y) -> rev#(++(x,y)) -> rev#(y) rev#(++(x,y)) -> rev#(y) -> rev#(++(x,y)) -> rev#(x) rev#(++(x,y)) -> rev#(x) -> rev#(++(x,y)) -> ++#(rev(y),rev(x)) rev#(++(x,y)) -> rev#(x) -> rev#(++(x,y)) -> rev#(y) rev#(++(x,y)) -> rev#(x) -> rev#(++(x,y)) -> rev#(x) rev#(++(x,y)) -> ++#(rev(y),rev(x)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) rev#(++(x,y)) -> ++#(rev(y),rev(x)) -> ++#(++(x,y),z) -> ++#(y,z) ++#(++(x,y),z) -> ++#(y,z) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) ++#(++(x,y),z) -> ++#(y,z) -> ++#(++(x,y),z) -> ++#(y,z) ++#(++(x,y),z) -> ++#(x,++(y,z)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) ++#(++(x,y),z) -> ++#(x,++(y,z)) -> ++#(++(x,y),z) -> ++#(y,z) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(y,z) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(++(x,y)) -> flatten#(x) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(++(x,y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(y) -> flatten#(unit(x)) -> flatten#(x) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(++(x,y)) -> flatten#(x) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(++(x,y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(x) -> flatten#(unit(x)) -> flatten#(x) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(y,z) flatten#(++(x,y)) -> flatten#(y) -> flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) flatten#(++(x,y)) -> flatten#(y) -> flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(y) -> flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(y) -> flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(x,y)) -> flatten#(y) -> flatten#(++(x,y)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(y) -> flatten#(++(x,y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(y) -> flatten#(unit(x)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) flatten#(++(x,y)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(x) -> flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(x,y)) -> flatten#(x) -> flatten#(++(x,y)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(x) -> flatten#(++(x,y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(x) -> flatten#(unit(x)) -> flatten#(x) flatten#(unit(x)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) flatten#(unit(x)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> flatten#(x) flatten#(unit(x)) -> flatten#(x) -> flatten#(++(unit(x),y)) -> flatten#(y) flatten#(unit(x)) -> flatten#(x) -> flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(unit(x)) -> flatten#(x) -> flatten#(++(x,y)) -> flatten#(x) flatten#(unit(x)) -> flatten#(x) -> flatten#(++(x,y)) -> flatten#(y) flatten#(unit(x)) -> flatten#(x) -> flatten#(unit(x)) -> flatten#(x) CDG Processor: DPs: flatten#(unit(x)) -> flatten#(x) flatten#(++(x,y)) -> flatten#(y) flatten#(++(x,y)) -> flatten#(x) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) flatten#(++(unit(x),y)) -> flatten#(y) flatten#(++(unit(x),y)) -> flatten#(x) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) rev#(++(x,y)) -> rev#(x) rev#(++(x,y)) -> rev#(y) rev#(++(x,y)) -> ++#(rev(y),rev(x)) ++#(++(x,y),z) -> ++#(y,z) ++#(++(x,y),z) -> ++#(x,++(y,z)) TRS: flatten(nil()) -> nil() flatten(unit(x)) -> flatten(x) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil()) -> nil() rev(unit(x)) -> unit(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x ++(x,nil()) -> x ++(nil(),y) -> y ++(++(x,y),z) -> ++(x,++(y,z)) graph: rev#(++(x,y)) -> ++#(rev(y),rev(x)) -> ++#(++(x,y),z) -> ++#(y,z) rev#(++(x,y)) -> ++#(rev(y),rev(x)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(y,z) flatten#(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(y,z) flatten#(++(x,y)) -> ++#(flatten(x),flatten(y)) -> ++#(++(x,y),z) -> ++#(x,++(y,z)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 6/144