/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO Problem: zeros() -> cons(0(),n__zeros()) U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) length(nil()) -> 0() length(cons(N,L)) -> U11(tt(),activate(L)) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> n__zeros() take(X1,X2) -> n__take(X1,X2) activate(n__zeros()) -> zeros() activate(n__take(X1,X2)) -> take(X1,X2) activate(X) -> X Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [1 0 0] [take](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1] [nil] = [1] [1], [1 0 1] [1 0 0] [n__take](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [1 0 0] [1 1 1] [1 0 0] [U23](x0, x1, x2, x3) = [0 0 0]x0 + [0 0 0]x1 + [0 0 1]x2 + [0 0 0]x3 [0 0 0] [0 0 0] [0 1 0] [0 0 0] , [1 0 0] [1 0 0] [1 1 1] [1 0 0] [U22](x0, x1, x2, x3) = [0 0 0]x0 + [0 0 0]x1 + [0 0 1]x2 + [0 0 0]x3 [0 0 0] [0 0 0] [0 1 0] [0 0 0] , [1 0 0] [1 1 0] [1 1 1] [1 0 0] [U21](x0, x1, x2, x3) = [0 0 0]x0 + [0 0 0]x1 + [0 0 1]x2 + [0 0 0]x3 [0 0 0] [0 0 0] [0 1 0] [0 0 0] , [1 0 1] [s](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [length](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [1 1 0] [U12](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 1] , [activate](x0) = x0 , [1 0 0] [1 1 0] [U11](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 1] , [0] [tt] = [0] [0], [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [0 1 0] , [0] [n__zeros] = [0] [0], [0] [0] = [1] [1], [0] [zeros] = [0] [0] orientation: [0] [0] zeros() = [0] >= [0] = cons(0(),n__zeros()) [0] [0] [1 1 0] [1 1 0] U11(tt(),L) = [0 1 0]L >= [0 1 0]L = U12(tt(),activate(L)) [0 0 1] [0 0 1] [1 1 0] [1 1 0] U12(tt(),L) = [0 1 0]L >= [0 1 0]L = s(length(activate(L))) [0 0 1] [0 0 1] [1 1 0] [1 1 1] [1 0 0] [1 0 0] [1 1 1] [1 0 0] U21(tt(),IL,M,N) = [0 0 0]IL + [0 0 1]M + [0 0 0]N >= [0 0 0]IL + [0 0 1]M + [0 0 0]N = U22(tt(),activate(IL),activate(M),activate(N)) [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 0] [1 1 1] [1 0 0] U22(tt(),IL,M,N) = [0 0 0]IL + [0 0 1]M + [0 0 0]N >= [0 0 0]IL + [0 0 1]M + [0 0 0]N = U23(tt(),activate(IL),activate(M),activate(N)) [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 0] [1 1 1] [1 0 0] U23(tt(),IL,M,N) = [0 0 0]IL + [0 0 1]M + [0 0 0]N >= [0 0 0]IL + [0 0 1]M + [0 0 0]N = cons(activate(N),n__take(activate(M),activate(IL))) [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [0 0 0] [1] [0] length(nil()) = [1] >= [1] = 0() [1] [1] [1 1 0] [1 0 0] [1 1 0] length(cons(N,L)) = [0 1 0]L + [0 0 0]N >= [0 1 0]L = U11(tt(),activate(L)) [0 0 1] [0 0 0] [0 0 1] [1 0 0] [1] [1] take(0(),IL) = [0 0 0]IL + [1] >= [1] = nil() [0 0 0] [1] [1] [1 1 0] [1 1 1] [1 0 0] [1 1 0] [1 1 1] [1 0 0] take(s(M),cons(N,IL)) = [0 0 0]IL + [0 0 1]M + [0 0 0]N >= [0 0 0]IL + [0 0 1]M + [0 0 0]N = U21(tt(),activate(IL),M,N) [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [0 0 0] [0] [0] zeros() = [0] >= [0] = n__zeros() [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] take(X1,X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = n__take(X1,X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [0] [0] activate(n__zeros()) = [0] >= [0] = zeros() [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] activate(n__take(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) length(cons(N,L)) -> U11(tt(),activate(L)) take(0(),IL) -> nil() take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> n__zeros() take(X1,X2) -> n__take(X1,X2) activate(n__zeros()) -> zeros() activate(n__take(X1,X2)) -> take(X1,X2) activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [take](x0, x1) = x0 + x1 + 1, [nil] = 0, [n__take](x0, x1) = x0 + x1 + 1, [U23](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U22](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [U21](x0, x1, x2, x3) = x0 + x1 + x2 + x3, [s](x0) = x0, [length](x0) = x0 + 1, [U12](x0, x1) = x0 + x1, [activate](x0) = x0, [U11](x0, x1) = x0 + x1, [tt] = 1, [cons](x0, x1) = x0 + x1, [n__zeros] = 0, [0] = 0, [zeros] = 0 orientation: zeros() = 0 >= 0 = cons(0(),n__zeros()) U11(tt(),L) = L + 1 >= L + 1 = U12(tt(),activate(L)) U12(tt(),L) = L + 1 >= L + 1 = s(length(activate(L))) U21(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) = IL + M + N + 1 >= IL + M + N + 1 = cons(activate(N),n__take(activate(M),activate(IL))) length(cons(N,L)) = L + N + 1 >= L + 1 = U11(tt(),activate(L)) take(0(),IL) = IL + 1 >= 0 = nil() take(s(M),cons(N,IL)) = IL + M + N + 1 >= IL + M + N + 1 = U21(tt(),activate(IL),M,N) zeros() = 0 >= 0 = n__zeros() take(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 1 = n__take(X1,X2) activate(n__zeros()) = 0 >= 0 = zeros() activate(n__take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,X2) activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U11(tt(),L) -> U12(tt(),activate(L)) U12(tt(),L) -> s(length(activate(L))) U21(tt(),IL,M,N) -> U22(tt(),activate(IL),activate(M),activate(N)) U22(tt(),IL,M,N) -> U23(tt(),activate(IL),activate(M),activate(N)) U23(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) length(cons(N,L)) -> U11(tt(),activate(L)) take(s(M),cons(N,IL)) -> U21(tt(),activate(IL),M,N) zeros() -> n__zeros() take(X1,X2) -> n__take(X1,X2) activate(n__zeros()) -> zeros() activate(n__take(X1,X2)) -> take(X1,X2) activate(X) -> X Unfolding Processor: loop length: 7 terms: U11(tt(),n__zeros()) U12(tt(),activate(n__zeros())) s(length(activate(activate(n__zeros())))) s(length(activate(n__zeros()))) s(length(zeros())) s(length(cons(0(),n__zeros()))) s(U11(tt(),activate(n__zeros()))) context: s([]) substitution: Qed