YES Input TRS: 1: a__app(nil(),YS) -> mark(YS) 2: a__app(cons(X,XS),YS) -> cons(mark(X),app(XS,YS)) 3: a__from(X) -> cons(mark(X),from(s(X))) 4: a__zWadr(nil(),YS) -> nil() 5: a__zWadr(XS,nil()) -> nil() 6: a__zWadr(cons(X,XS),cons(Y,YS)) -> cons(a__app(mark(Y),cons(mark(X),nil())),zWadr(XS,YS)) 7: a__prefix(L) -> cons(nil(),zWadr(L,prefix(L))) 8: mark(app(X1,X2)) -> a__app(mark(X1),mark(X2)) 9: mark(from(X)) -> a__from(mark(X)) 10: mark(zWadr(X1,X2)) -> a__zWadr(mark(X1),mark(X2)) 11: mark(prefix(X)) -> a__prefix(mark(X)) 12: mark(nil()) -> nil() 13: mark(cons(X1,X2)) -> cons(mark(X1),X2) 14: mark(s(X)) -> s(mark(X)) 15: a__app(X1,X2) -> app(X1,X2) 16: a__from(X) -> from(X) 17: a__zWadr(X1,X2) -> zWadr(X1,X2) 18: a__prefix(X) -> prefix(X) Number of strict rules: 18 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__app(cons(X,XS),YS) -> #mark(X) #2: #a__zWadr(cons(X,XS),cons(Y,YS)) -> #a__app(mark(Y),cons(mark(X),nil())) #3: #a__zWadr(cons(X,XS),cons(Y,YS)) -> #mark(Y) #4: #a__zWadr(cons(X,XS),cons(Y,YS)) -> #mark(X) #5: #mark(cons(X1,X2)) -> #mark(X1) #6: #mark(from(X)) -> #a__from(mark(X)) #7: #mark(from(X)) -> #mark(X) #8: #mark(prefix(X)) -> #a__prefix(mark(X)) #9: #mark(prefix(X)) -> #mark(X) #10: #mark(s(X)) -> #mark(X) #11: #mark(zWadr(X1,X2)) -> #a__zWadr(mark(X1),mark(X2)) #12: #mark(zWadr(X1,X2)) -> #mark(X1) #13: #mark(zWadr(X1,X2)) -> #mark(X2) #14: #a__from(X) -> #mark(X) #15: #a__app(nil(),YS) -> #mark(YS) #16: #mark(app(X1,X2)) -> #a__app(mark(X1),mark(X2)) #17: #mark(app(X1,X2)) -> #mark(X1) #18: #mark(app(X1,X2)) -> #mark(X2) Number of SCCs: 1, DPs: 17 SCC { #1..7 #9..18 } POLO(Sum)... succeeded. #a__zWadr w: x1 + x2 + 4 s w: x1 + 1 #a__from w: x1 + 2 a__prefix w: x1 + 18460 a__from w: x1 + 2 prefix w: x1 + 18460 #a__app w: x1 + x2 a__app w: x1 + x2 + 2 zWadr w: x1 + x2 + 4 a__zWadr w: x1 + x2 + 4 #a__prefix w: 0 #mark w: x1 + 1 from w: x1 + 2 nil w: 18459 mark w: x1 cons w: x1 + 1 app w: x1 + x2 + 2 USABLE RULES: { 1..18 } Removed DPs: #2..7 #9..18 Number of SCCs: 0, DPs: 0