MAYBE Problem: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Proof: DP Processor: DPs: a__from#(X) -> mark#(X) a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) EDG Processor: DPs: a__from#(X) -> mark#(X) a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(from(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) graph: a__after#(0(),XS) -> mark#(XS) -> mark#(from(X)) -> mark#(X) a__after#(0(),XS) -> mark#(XS) -> mark#(from(X)) -> a__from#(mark(X)) a__after#(0(),XS) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X2) a__after#(0(),XS) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X1) a__after#(0(),XS) -> mark#(XS) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(0(),XS) -> mark#(XS) -> mark#(cons(X1,X2)) -> mark#(X1) a__after#(0(),XS) -> mark#(XS) -> mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(0(),XS) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(s(N),cons(X,XS)) -> mark#(XS) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(s(N),cons(X,XS)) -> mark#(N) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) -> a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(from(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(from(X)) -> a__from#(mark(X)) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(after(X1,X2)) -> mark#(X2) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(after(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(cons(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(from(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(from(X)) -> a__from#(mark(X)) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X2) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(cons(X1,X2)) -> mark#(X1) a__after#(s(N),cons(X,XS)) -> mark#(XS) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(0(),XS) -> mark#(XS) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(s(N),cons(X,XS)) -> mark#(XS) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(s(N),cons(X,XS)) -> mark#(N) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) -> a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X2) -> mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(after(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(after(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> a__from#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X) a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X)) a__from#(X) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X2) a__from#(X) -> mark#(X) -> mark#(after(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X) SCC Processor: #sccs: 1 #rules: 12 #arcs: 72/144 DPs: a__after#(0(),XS) -> mark#(XS) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> a__after#(mark(X1),mark(X2)) a__after#(s(N),cons(X,XS)) -> a__after#(mark(N),mark(XS)) a__after#(s(N),cons(X,XS)) -> mark#(N) mark#(after(X1,X2)) -> mark#(X1) mark#(after(X1,X2)) -> mark#(X2) mark#(from(X)) -> a__from#(mark(X)) a__from#(X) -> mark#(X) mark#(from(X)) -> mark#(X) a__after#(s(N),cons(X,XS)) -> mark#(XS) TRS: a__from(X) -> cons(mark(X),from(s(X))) a__after(0(),XS) -> mark(XS) a__after(s(N),cons(X,XS)) -> a__after(mark(N),mark(XS)) mark(from(X)) -> a__from(mark(X)) mark(after(X1,X2)) -> a__after(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__from(X) -> from(X) a__after(X1,X2) -> after(X1,X2) Open