YES Problem: a__app(nil(),YS) -> mark(YS) a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) a__from(X) -> cons(mark(X),from(s(X))) a__zWadr(nil(),YS) -> nil() a__zWadr(XS,nil()) -> nil() a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) a__prefix(L) -> cons(nil(),zWadr(L,prefix(L))) mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) mark(prefix(X)) -> a__prefix(mark(X)) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__app(X1,X2) -> app(X1,X2) a__from(X) -> from(X) a__zWadr(X1,X2) -> zWadr(X1,X2) a__prefix(X) -> prefix(X) Proof: DP Processor: DPs: a__app#(nil(),YS) -> mark#(YS) a__app#(cons(X,XS),YS) -> mark#(X) a__from#(X) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) a__zWadr#(cons(X,XS),cons(Y,YS)) -> a__app#(mark(Y),cons(mark(X),nil())) mark#(app(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(zWadr(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(prefix(X)) -> mark#(X) mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__app(nil(),YS) -> mark(YS) a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) a__from(X) -> cons(mark(X),from(s(X))) a__zWadr(nil(),YS) -> nil() a__zWadr(XS,nil()) -> nil() a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) a__prefix(L) -> cons(nil(),zWadr(L,prefix(L))) mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) mark(prefix(X)) -> a__prefix(mark(X)) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__app(X1,X2) -> app(X1,X2) a__from(X) -> from(X) a__zWadr(X1,X2) -> zWadr(X1,X2) a__prefix(X) -> prefix(X) TDG Processor: DPs: a__app#(nil(),YS) -> mark#(YS) a__app#(cons(X,XS),YS) -> mark#(X) a__from#(X) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) a__zWadr#(cons(X,XS),cons(Y,YS)) -> a__app#(mark(Y),cons(mark(X),nil())) mark#(app(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(zWadr(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(prefix(X)) -> mark#(X) mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__app(nil(),YS) -> mark(YS) a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) a__from(X) -> cons(mark(X),from(s(X))) a__zWadr(nil(),YS) -> nil() a__zWadr(XS,nil()) -> nil() a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) a__prefix(L) -> cons(nil(),zWadr(L,prefix(L))) mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) mark(prefix(X)) -> a__prefix(mark(X)) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__app(X1,X2) -> app(X1,X2) a__from(X) -> from(X) a__zWadr(X1,X2) -> zWadr(X1,X2) a__prefix(X) -> prefix(X) graph: a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(s(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(cons(X1,X2)) -> mark#(X1) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(prefix(X)) -> a__prefix#(mark(X)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(prefix(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(zWadr(X1,X2)) -> mark#(X1) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(zWadr(X1,X2)) -> mark#(X2) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(from(X)) -> a__from#(mark(X)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(from(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(app(X1,X2)) -> mark#(X1) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) -> mark#(app(X1,X2)) -> mark#(X2) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(prefix(X)) -> a__prefix#(mark(X)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(prefix(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X1) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X2) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X1) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X2) a__zWadr#(cons(X,XS),cons(Y,YS)) -> a__app#(mark(Y),cons(mark(X),nil())) -> a__app#(cons(X,XS),YS) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> a__app#(mark(Y),cons(mark(X),nil())) -> a__app#(nil(),YS) -> mark#(YS) a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(prefix(X)) -> a__prefix#(mark(X)) a__from#(X) -> mark#(X) -> mark#(prefix(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) a__from#(X) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X2) a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) a__from#(X) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X2) mark#(prefix(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(prefix(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(prefix(X)) -> mark#(X) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(prefix(X)) -> mark#(X) -> mark#(prefix(X)) -> mark#(X) mark#(prefix(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(prefix(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(prefix(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(prefix(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(prefix(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(prefix(X)) -> mark#(X) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(prefix(X)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X1) mark#(prefix(X)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) -> a__zWadr#(cons(X,XS),cons(Y,YS)) -> a__app#(mark(Y),cons(mark(X),nil())) mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) -> a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) -> a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(prefix(X)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> a__from#(mark(X)) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(app(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> mark#(X2) -> mark#(app(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(prefix(X)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> mark#(X2) mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(prefix(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(prefix(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(app(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> mark#(X2) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(app(X1,X2)) -> mark#(X2) -> mark#(prefix(X)) -> mark#(X) mark#(app(X1,X2)) -> mark#(X2) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(app(X1,X2)) -> mark#(X2) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> mark#(X2) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> a__from#(mark(X)) mark#(app(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(app(X1,X2)) -> mark#(X2) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(app(X1,X2)) -> mark#(X2) -> mark#(app(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> mark#(X2) -> mark#(app(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(app(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> mark#(X1) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(app(X1,X2)) -> mark#(X1) -> mark#(prefix(X)) -> mark#(X) mark#(app(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(app(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(app(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(app(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(app(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) -> a__app#(cons(X,XS),YS) -> mark#(X) mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) -> a__app#(nil(),YS) -> mark#(YS) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(prefix(X)) -> a__prefix#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(prefix(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zWadr(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(app(X1,X2)) -> mark#(X2) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(prefix(X)) -> a__prefix#(mark(X)) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(prefix(X)) -> mark#(X) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X1) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(zWadr(X1,X2)) -> mark#(X2) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X1) a__app#(cons(X,XS),YS) -> mark#(X) -> mark#(app(X1,X2)) -> mark#(X2) a__app#(nil(),YS) -> mark#(YS) -> mark#(s(X)) -> mark#(X) a__app#(nil(),YS) -> mark#(YS) -> mark#(cons(X1,X2)) -> mark#(X1) a__app#(nil(),YS) -> mark#(YS) -> mark#(prefix(X)) -> a__prefix#(mark(X)) a__app#(nil(),YS) -> mark#(YS) -> mark#(prefix(X)) -> mark#(X) a__app#(nil(),YS) -> mark#(YS) -> mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) a__app#(nil(),YS) -> mark#(YS) -> mark#(zWadr(X1,X2)) -> mark#(X1) a__app#(nil(),YS) -> mark#(YS) -> mark#(zWadr(X1,X2)) -> mark#(X2) a__app#(nil(),YS) -> mark#(YS) -> mark#(from(X)) -> a__from#(mark(X)) a__app#(nil(),YS) -> mark#(YS) -> mark#(from(X)) -> mark#(X) a__app#(nil(),YS) -> mark#(YS) -> mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) a__app#(nil(),YS) -> mark#(YS) -> mark#(app(X1,X2)) -> mark#(X1) a__app#(nil(),YS) -> mark#(YS) -> mark#(app(X1,X2)) -> mark#(X2) SCC Processor: #sccs: 1 #rules: 17 #arcs: 164/324 DPs: a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(Y) mark#(app(X1,X2)) -> mark#(X2) mark#(app(X1,X2)) -> mark#(X1) mark#(app(X1,X2)) -> a__app#(mark(X1),mark(X2)) a__app#(nil(),YS) -> mark#(YS) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) a__from#(X) -> mark#(X) mark#(zWadr(X1,X2)) -> mark#(X2) mark#(zWadr(X1,X2)) -> mark#(X1) mark#(zWadr(X1,X2)) -> a__zWadr#(mark(X1),mark(X2)) a__zWadr#(cons(X,XS),cons(Y,YS)) -> mark#(X) mark#(prefix(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) -> a__app#(mark(Y),cons(mark(X),nil())) a__app#(cons(X,XS),YS) -> mark#(X) TRS: a__app(nil(),YS) -> mark(YS) a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) a__from(X) -> cons(mark(X),from(s(X))) a__zWadr(nil(),YS) -> nil() a__zWadr(XS,nil()) -> nil() a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) a__prefix(L) -> cons(nil(),zWadr(L,prefix(L))) mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) mark(prefix(X)) -> a__prefix(mark(X)) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__app(X1,X2) -> app(X1,X2) a__from(X) -> from(X) a__zWadr(X1,X2) -> zWadr(X1,X2) a__prefix(X) -> prefix(X) Matrix Interpretation Processor: dim=1 interpretation: [a__zWadr#](x0, x1) = 2x0 + 3x1 + 4, [a__from#](x0) = 6x0 + 3, [mark#](x0) = 2x0 + 2, [a__app#](x0, x1) = 2x0 + 2x1, [prefix](x0) = x0 + 6, [a__prefix](x0) = x0 + 6, [zWadr](x0, x1) = x0 + 2x1 + 4, [a__zWadr](x0, x1) = x0 + 2x1 + 4, [from](x0) = 4x0 + 2, [s](x0) = x0 + 5, [a__from](x0) = 4x0 + 2, [app](x0, x1) = 2x0 + x1 + 4, [cons](x0, x1) = x0 + 2, [mark](x0) = x0, [a__app](x0, x1) = 2x0 + x1 + 4, [nil] = 4 orientation: a__zWadr#(cons(X,XS),cons(Y,YS)) = 2X + 3Y + 14 >= 2Y + 2 = mark#(Y) mark#(app(X1,X2)) = 4X1 + 2X2 + 10 >= 2X2 + 2 = mark#(X2) mark#(app(X1,X2)) = 4X1 + 2X2 + 10 >= 2X1 + 2 = mark#(X1) mark#(app(X1,X2)) = 4X1 + 2X2 + 10 >= 2X1 + 2X2 = a__app#(mark(X1),mark(X2)) a__app#(nil(),YS) = 2YS + 8 >= 2YS + 2 = mark#(YS) mark#(from(X)) = 8X + 6 >= 2X + 2 = mark#(X) mark#(from(X)) = 8X + 6 >= 6X + 3 = a__from#(mark(X)) a__from#(X) = 6X + 3 >= 2X + 2 = mark#(X) mark#(zWadr(X1,X2)) = 2X1 + 4X2 + 10 >= 2X2 + 2 = mark#(X2) mark#(zWadr(X1,X2)) = 2X1 + 4X2 + 10 >= 2X1 + 2 = mark#(X1) mark#(zWadr(X1,X2)) = 2X1 + 4X2 + 10 >= 2X1 + 3X2 + 4 = a__zWadr#(mark(X1),mark(X2)) a__zWadr#(cons(X,XS),cons(Y,YS)) = 2X + 3Y + 14 >= 2X + 2 = mark#(X) mark#(prefix(X)) = 2X + 14 >= 2X + 2 = mark#(X) mark#(cons(X1,X2)) = 2X1 + 6 >= 2X1 + 2 = mark#(X1) mark#(s(X)) = 2X + 12 >= 2X + 2 = mark#(X) a__zWadr#(cons(X,XS),cons(Y,YS)) = 2X + 3Y + 14 >= 2X + 2Y + 4 = a__app#(mark(Y),cons(mark(X),nil())) a__app#(cons(X,XS),YS) = 2X + 2YS + 4 >= 2X + 2 = mark#(X) a__app(nil(),YS) = YS + 12 >= YS = mark(YS) a__app(cons(X,XS),YS) = 2X + YS + 8 >= X + 2 = cons(mark(X),app(XS,YS)) a__from(X) = 4X + 2 >= X + 2 = cons(mark(X),from(s(X))) a__zWadr(nil(),YS) = 2YS + 8 >= 4 = nil() a__zWadr(XS,nil()) = XS + 12 >= 4 = nil() a__zWadr(cons(X,XS),cons(Y,YS)) = X + 2Y + 10 >= X + 2Y + 8 = cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) a__prefix(L) = L + 6 >= 6 = cons(nil(),zWadr(L,prefix(L))) mark(app(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = a__app(mark(X1),mark(X2)) mark(from(X)) = 4X + 2 >= 4X + 2 = a__from(mark(X)) mark(zWadr(X1,X2)) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = a__zWadr(mark(X1),mark(X2)) mark(prefix(X)) = X + 6 >= X + 6 = a__prefix(mark(X)) mark(nil()) = 4 >= 4 = nil() mark(cons(X1,X2)) = X1 + 2 >= X1 + 2 = cons(mark(X1),X2) mark(s(X)) = X + 5 >= X + 5 = s(mark(X)) a__app(X1,X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = app(X1,X2) a__from(X) = 4X + 2 >= 4X + 2 = from(X) a__zWadr(X1,X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = zWadr(X1,X2) a__prefix(X) = X + 6 >= X + 6 = prefix(X) problem: DPs: TRS: a__app(nil(),YS) -> mark(YS) a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) a__from(X) -> cons(mark(X),from(s(X))) a__zWadr(nil(),YS) -> nil() a__zWadr(XS,nil()) -> nil() a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) a__prefix(L) -> cons(nil(),zWadr(L,prefix(L))) mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) mark(prefix(X)) -> a__prefix(mark(X)) mark(nil()) -> nil() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__app(X1,X2) -> app(X1,X2) a__from(X) -> from(X) a__zWadr(X1,X2) -> zWadr(X1,X2) a__prefix(X) -> prefix(X) Qed