MAYBE Problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Proof: DP Processor: DPs: a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> mark#(L) a__U12#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U11#(tt(),L) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) TDG Processor: DPs: a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> mark#(L) a__U12#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U11#(tt(),L) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) graph: a__length#(cons(N,L)) -> a__U11#(tt(),L) -> a__U11#(tt(),L) -> a__U12#(tt(),L) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__U11#(tt(),L) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U12(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) -> a__U12#(tt(),L) -> a__length#(mark(L)) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) -> a__U12#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),L) -> a__U12#(tt(),L) 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#(length(X)) -> a__length#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() 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#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() a__U12#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__U11#(tt(),L) a__U12#(tt(),L) -> mark#(L) -> mark#(s(X)) -> mark#(X) a__U12#(tt(),L) -> mark#(L) -> mark#(cons(X1,X2)) -> mark#(X1) a__U12#(tt(),L) -> mark#(L) -> mark#(length(X)) -> a__length#(mark(X)) a__U12#(tt(),L) -> mark#(L) -> mark#(length(X)) -> mark#(X) a__U12#(tt(),L) -> mark#(L) -> mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) a__U12#(tt(),L) -> mark#(L) -> mark#(U12(X1,X2)) -> mark#(X1) a__U12#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U12#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> mark#(X1) a__U12#(tt(),L) -> mark#(L) -> mark#(zeros()) -> a__zeros#() a__U11#(tt(),L) -> a__U12#(tt(),L) -> a__U12#(tt(),L) -> a__length#(mark(L)) a__U11#(tt(),L) -> a__U12#(tt(),L) -> a__U12#(tt(),L) -> mark#(L) SCC Processor: #sccs: 1 #rules: 12 #arcs: 62/169 DPs: a__length#(cons(N,L)) -> a__U11#(tt(),L) a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) a__U12#(tt(),L) -> a__length#(mark(L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Arctic Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = x0, [mark#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [length](x0) = x0, [U12](x0, x1) = x0 + x1 + 0, [U11](x0, x1) = x0 + x1 + 0, [nil] = 5, [s](x0) = x0, [a__length](x0) = x0, [mark](x0) = x0, [a__U12](x0, x1) = x0 + x1 + 0, [a__U11](x0, x1) = x0 + x1 + 0, [tt] = 0, [cons](x0, x1) = 3x0 + x1 + 0, [zeros] = 3, [0] = 0, [a__zeros] = 3 orientation: a__length#(cons(N,L)) = L + 3N + 0 >= L = a__U11#(tt(),L) a__U11#(tt(),L) = L >= L = a__U12#(tt(),L) a__U12#(tt(),L) = L >= L = mark#(L) mark#(U11(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(U11(X1,X2)) = X1 + X2 + 0 >= X2 = a__U11#(mark(X1),X2) mark#(U12(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 + 0 >= X2 = a__U12#(mark(X1),X2) a__U12#(tt(),L) = L >= L = a__length#(mark(L)) mark#(length(X)) = X >= X = mark#(X) mark#(length(X)) = X >= X = a__length#(mark(X)) mark#(cons(X1,X2)) = 3X1 + X2 + 0 >= X1 = mark#(X1) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 3 >= 3 = cons(0(),zeros()) a__U11(tt(),L) = L + 0 >= L + 0 = a__U12(tt(),L) a__U12(tt(),L) = L + 0 >= L = s(a__length(mark(L))) a__length(nil()) = 5 >= 0 = 0() a__length(cons(N,L)) = L + 3N + 0 >= L + 0 = a__U11(tt(),L) mark(zeros()) = 3 >= 3 = a__zeros() mark(U11(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__U12(mark(X1),X2) mark(length(X)) = X >= X = a__length(mark(X)) mark(cons(X1,X2)) = 3X1 + X2 + 0 >= 3X1 + X2 + 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 5 >= 5 = nil() a__zeros() = 3 >= 3 = zeros() a__U11(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = U12(X1,X2) a__length(X) = X >= X = length(X) problem: DPs: a__length#(cons(N,L)) -> a__U11#(tt(),L) a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) a__U12#(tt(),L) -> a__length#(mark(L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Arctic Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = x0, [mark#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [length](x0) = x0 + 7, [U12](x0, x1) = x0 + x1 + 7, [U11](x0, x1) = 7x0 + x1, [nil] = 4, [s](x0) = x0, [a__length](x0) = x0 + 7, [mark](x0) = x0, [a__U12](x0, x1) = x0 + x1 + 7, [a__U11](x0, x1) = 7x0 + x1, [tt] = 0, [cons](x0, x1) = x1 + 0, [zeros] = 0, [0] = 2, [a__zeros] = 0 orientation: a__length#(cons(N,L)) = L + 0 >= L = a__U11#(tt(),L) a__U11#(tt(),L) = L >= L = a__U12#(tt(),L) a__U12#(tt(),L) = L >= L = mark#(L) mark#(U11(X1,X2)) = 7X1 + X2 >= X1 = mark#(X1) mark#(U11(X1,X2)) = 7X1 + X2 >= X2 = a__U11#(mark(X1),X2) mark#(U12(X1,X2)) = X1 + X2 + 7 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + X2 + 7 >= X2 = a__U12#(mark(X1),X2) a__U12#(tt(),L) = L >= L = a__length#(mark(L)) mark#(length(X)) = X + 7 >= X = mark#(X) mark#(length(X)) = X + 7 >= X = a__length#(mark(X)) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = L + 7 >= L + 7 = a__U12(tt(),L) a__U12(tt(),L) = L + 7 >= L + 7 = s(a__length(mark(L))) a__length(nil()) = 7 >= 2 = 0() a__length(cons(N,L)) = L + 7 >= L + 7 = a__U11(tt(),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 7X1 + X2 >= 7X1 + X2 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = a__U12(mark(X1),X2) mark(length(X)) = X + 7 >= X + 7 = a__length(mark(X)) mark(cons(X1,X2)) = X2 + 0 >= X2 + 0 = cons(mark(X1),X2) mark(0()) = 2 >= 2 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 4 >= 4 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 7X1 + X2 >= 7X1 + X2 = U11(X1,X2) a__U12(X1,X2) = X1 + X2 + 7 >= X1 + X2 + 7 = U12(X1,X2) a__length(X) = X + 7 >= X + 7 = length(X) problem: DPs: a__length#(cons(N,L)) -> a__U11#(tt(),L) a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> a__U12#(mark(X1),X2) a__U12#(tt(),L) -> a__length#(mark(L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Arctic Interpretation Processor: dimension: 1 interpretation: [a__length#](x0) = x0, [mark#](x0) = x0, [a__U12#](x0, x1) = x1, [a__U11#](x0, x1) = x1, [length](x0) = 1x0, [U12](x0, x1) = x0 + 1x1, [U11](x0, x1) = 1x1 + 0, [nil] = 2, [s](x0) = x0, [a__length](x0) = 1x0, [mark](x0) = x0, [a__U12](x0, x1) = x0 + 1x1, [a__U11](x0, x1) = 1x1 + 0, [tt] = 0, [cons](x0, x1) = x0 + x1 + 0, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__length#(cons(N,L)) = L + N + 0 >= L = a__U11#(tt(),L) a__U11#(tt(),L) = L >= L = a__U12#(tt(),L) a__U12#(tt(),L) = L >= L = mark#(L) mark#(U11(X1,X2)) = 1X2 + 0 >= X2 = a__U11#(mark(X1),X2) mark#(U12(X1,X2)) = X1 + 1X2 >= X1 = mark#(X1) mark#(U12(X1,X2)) = X1 + 1X2 >= X2 = a__U12#(mark(X1),X2) a__U12#(tt(),L) = L >= L = a__length#(mark(L)) mark#(length(X)) = 1X >= X = mark#(X) mark#(length(X)) = 1X >= X = a__length#(mark(X)) mark#(s(X)) = X >= X = mark#(X) a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 1L + 0 >= 1L + 0 = a__U12(tt(),L) a__U12(tt(),L) = 1L + 0 >= 1L = s(a__length(mark(L))) a__length(nil()) = 3 >= 0 = 0() a__length(cons(N,L)) = 1L + 1N + 1 >= 1L + 0 = a__U11(tt(),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 1X2 + 0 >= 1X2 + 0 = a__U11(mark(X1),X2) mark(U12(X1,X2)) = X1 + 1X2 >= X1 + 1X2 = a__U12(mark(X1),X2) mark(length(X)) = 1X >= 1X = a__length(mark(X)) mark(cons(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 2 >= 2 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 1X2 + 0 >= 1X2 + 0 = U11(X1,X2) a__U12(X1,X2) = X1 + 1X2 >= X1 + 1X2 = U12(X1,X2) a__length(X) = 1X >= 1X = length(X) problem: DPs: a__length#(cons(N,L)) -> a__U11#(tt(),L) a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> mark#(L) mark#(U12(X1,X2)) -> mark#(X1) a__U12#(tt(),L) -> a__length#(mark(L)) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) SCC Processor: #sccs: 2 #rules: 5 #arcs: 56/36 DPs: a__length#(cons(N,L)) -> a__U11#(tt(),L) a__U11#(tt(),L) -> a__U12#(tt(),L) a__U12#(tt(),L) -> a__length#(mark(L)) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Open DPs: mark#(U12(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> a__U12(tt(),L) a__U12(tt(),L) -> s(a__length(mark(L))) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(tt(),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X1,X2) -> U12(X1,X2) a__length(X) -> length(X) Qed