/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO Problem: active(zeros()) -> mark(cons(0(),zeros())) active(and(tt(),X)) -> mark(X) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = 4x0, [length](x0) = x0, [active](x0) = x0, [cons](x0, x1) = 4x0 + 4x1, [tt] = 1, [zeros] = 0, [nil] = 0, [s](x0) = x0, [and](x0, x1) = 6x0 + 6x1 + 4, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(and(tt(),X)) = 6X + 10 >= 4X = mark(X) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 4L + 4N >= 4L = mark(s(length(L))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 16X1 + 16X2 >= 16X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(and(X1,X2)) = 24X1 + 24X2 + 16 >= 24X1 + 6X2 + 4 = active(and(mark(X1),X2)) mark(tt()) = 4 >= 1 = active(tt()) mark(length(X)) = 4X >= 4X = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) mark(s(X)) = 4X >= 4X = active(s(mark(X))) cons(mark(X1),X2) = 16X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + 16X2 >= 4X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) and(mark(X1),X2) = 24X1 + 6X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2) and(X1,mark(X2)) = 6X1 + 24X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2) and(active(X1),X2) = 6X1 + 6X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2) and(X1,active(X2)) = 6X1 + 6X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2) length(mark(X)) = 4X >= X = length(X) length(active(X)) = X >= X = length(X) s(mark(X)) = 4X >= X = s(X) s(active(X)) = X >= X = s(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0, [length](x0) = 4x0, [active](x0) = x0, [cons](x0, x1) = 2x0 + 4x1, [zeros] = 0, [nil] = 4, [s](x0) = x0, [and](x0, x1) = x0 + 2x1 + 1, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(length(nil())) = 16 >= 0 = mark(0()) active(length(cons(N,L))) = 16L + 8N >= 4L = mark(s(length(L))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(length(X)) = 4X >= 4X = active(length(mark(X))) mark(nil()) = 4 >= 4 = active(nil()) mark(s(X)) = X >= X = active(s(mark(X))) cons(mark(X1),X2) = 2X1 + 4X2 >= 2X1 + 4X2 = cons(X1,X2) cons(X1,mark(X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 2X1 + 4X2 >= 2X1 + 4X2 = cons(X1,X2) cons(X1,active(X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = cons(X1,X2) and(mark(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = and(X1,X2) and(X1,mark(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = and(X1,X2) and(active(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = and(X1,X2) and(X1,active(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = and(X1,X2) length(mark(X)) = 4X >= 4X = length(X) length(active(X)) = 4X >= 4X = length(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 1 1]x0 + [1] [0 0 0] [0], [1 0 0] [1] [length](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [0] [active](x0) = [0 0 0]x0 + [1] [0 1 1] [0], [1 0 0] [1 1 1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [zeros] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 1 1]x1 [1 0 0] [0 1 1] , [0] [0] = [0] [0] orientation: [1] [1] active(zeros()) = [1] >= [1] = mark(cons(0(),zeros())) [0] [0] [1 1 1] [1 0 0] [1] [1 0 0] [1] active(length(cons(N,L))) = [0 0 0]L + [0 0 0]N + [1] >= [0 0 0]L + [1] = mark(s(length(L))) [0 0 0] [0 0 0] [0] [0 0 0] [0] [1] [1] mark(zeros()) = [1] >= [1] = active(zeros()) [0] [0] [1 0 0] [1 1 1] [0] [1 0 0] [1 1 1] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(0()) = [1] >= [1] = active(0()) [0] [0] [1 0 0] [1] [1 0 0] [1] mark(length(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(length(mark(X))) [0 0 0] [0] [0 0 0] [0] [1] [1] mark(nil()) = [1] >= [1] = active(nil()) [0] [0] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(s(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 1 1] [1 0 0] [1 1 1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 1 1] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = and(X1,X2) [1 0 0] [0 1 1] [1 0 0] [0 1 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] and(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 1]X2 = and(X1,X2) [1 0 0] [0 1 1] [1] [1 0 0] [0 1 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(active(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = and(X1,X2) [1 0 0] [0 1 1] [1 0 0] [0 1 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] and(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 1]X2 = and(X1,X2) [1 0 0] [0 1 1] [1] [1 0 0] [0 1 1] [1 0 0] [1] [1 0 0] [1] length(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = length(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] length(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = length(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] problem: active(zeros()) -> mark(cons(0(),zeros())) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1 0 0] [length](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [active](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1 0 0] [1 1 1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [zeros] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 1 1] [and](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 1 0] [1 1 0] , [0] [0] = [0] [0] orientation: [0] [0] active(zeros()) = [0] >= [0] = mark(cons(0(),zeros())) [1] [1] [1 1 1] [1 0 0] [0] [1 0 0] [0] active(length(cons(N,L))) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0] = mark(s(length(L))) [0 0 0] [0 0 0] [1] [0 0 0] [1] [0] [0] mark(zeros()) = [0] >= [0] = active(zeros()) [1] [1] [1 0 0] [1 1 1] [0] [1 0 0] [1 1 1] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 0 0] [0] [1 0 0] [0] mark(length(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(length(mark(X))) [0 0 0] [1] [0 0 0] [1] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 1 1] [1 0 0] [1 1 1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 1 1] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 1 1] and(mark(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = and(X1,X2) [0 1 1] [1 1 0] [0 1 0] [1 1 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] and(X1,mark(X2)) = [0 0 0]X1 + [1 0 0]X2 + [0] >= [0 0 0]X1 + [1 0 0]X2 = and(X1,X2) [0 1 0] [1 1 1] [0] [0 1 0] [1 1 0] [1 0 0] [1 1 1] [1 0 0] [1 1 1] and(active(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = and(X1,X2) [0 1 1] [1 1 0] [0 1 0] [1 1 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] and(X1,active(X2)) = [0 0 0]X1 + [1 0 0]X2 + [0] >= [0 0 0]X1 + [1 0 0]X2 = and(X1,X2) [0 1 0] [1 1 1] [0] [0 1 0] [1 1 0] [1 0 0] [1 0 0] length(mark(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] length(active(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] problem: active(zeros()) -> mark(cons(0(),zeros())) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = 2x0, [length](x0) = x0, [active](x0) = x0, [cons](x0, x1) = 2x0 + 4x1, [zeros] = 0, [nil] = 2, [s](x0) = 2x0, [and](x0, x1) = x0 + x1, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(length(cons(N,L))) = 4L + 2N >= 4L = mark(s(length(L))) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(length(X)) = 2X >= 2X = active(length(mark(X))) mark(nil()) = 4 >= 2 = active(nil()) mark(s(X)) = 4X >= 4X = active(s(mark(X))) cons(mark(X1),X2) = 4X1 + 4X2 >= 2X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 2X1 + 4X2 >= 2X1 + 4X2 = cons(X1,X2) and(mark(X1),X2) = 2X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) length(mark(X)) = 2X >= X = length(X) length(active(X)) = X >= X = length(X) s(mark(X)) = 4X >= 2X = s(X) s(active(X)) = 2X >= 2X = s(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(length(X)) -> active(length(mark(X))) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 1 1] [1], [1 0 0] [length](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [active](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [zeros] = [0] [0], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1 0 0] [and](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [0] orientation: [0] [0] active(zeros()) = [0] >= [0] = mark(cons(0(),zeros())) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [0] active(length(cons(N,L))) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0] = mark(s(length(L))) [0 0 0] [0 0 0] [1] [0 0 0] [1] [0] [0] mark(zeros()) = [0] >= [0] = active(zeros()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 0 0] [0] [1 0 0] [0] mark(length(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(length(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] and(mark(X1),X2) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] and(active(X1),X2) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] length(mark(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] length(active(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] problem: active(zeros()) -> mark(cons(0(),zeros())) active(length(cons(N,L))) -> mark(s(length(L))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(length(X)) -> active(length(mark(X))) mark(s(X)) -> active(s(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) length(mark(X)) -> length(X) length(active(X)) -> length(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Unfolding Processor: loop length: 6 terms: active(length(cons(N,zeros()))) mark(s(length(zeros()))) active(s(mark(length(zeros())))) active(s(active(length(mark(zeros()))))) active(s(active(length(active(zeros()))))) active(s(active(length(mark(cons(0(),zeros())))))) context: active(s([])) substitution: N -> 0() Qed